Measurement of the double-βdecay half-life ofNd150and search for neutrinoless decay modes with the NEMO-3 detector

The half-life for double-{beta} decay of {sup 150}Nd has been measured by the NEMO-3 experiment at the Modane Underground Laboratory. Using 924.7 days of data recorded with 36.55 g of {sup 150}Nd, we measured the half-life for 2{nu}{beta}{beta} decay to be T{sub 1/2}{sup 2{nu}}=(9.11{sub -0.22}{sup +0.25}(stat.){+-}0.63(syst.))x10{sup 18} yr. The observed limit on the half-life for neutrinoless double-{beta} decay is found to be T{sub 1/2}{sup 0{nu}}>1.8x10{sup 22} yr at 90% confidence level. This translates into a limit on the effective Majorana neutrino mass of <4.0-6.3 eV if the nuclear deformation is taken into account. We also set limits on models involving Majoron emission, right-hand…

Three beta-decaying states in 128In and 130In resolved for the first time using Penning-trap techniques

Isomeric states in 128In and 130In have been studied with the JYFLTRAP Penning trap at the IGISOL facility. By employing state-of-the-art ion manipulation techniques, three different beta-decaying states in 128In and 130In have been separated and their masses measured. JYFLTRAP was also used to select the ions of interest for identification at a post-trap decay spectroscopy station. A new beta-decaying high-spin isomer feeding the isomer in 128Sn has been discovered in 128In at 1797.6(20) keV. Shell-model calculations employing a CD-Bonn potential re-normalized with the perturbative G-matrix approach suggest this new isomer to be a 16⁺ spin-trap isomer. In 130In, the lowest-lying (10⁻) isom…

Ordinary muon capture studies for the matrix elements in ββ decay

Precise measurement of $\gamma$-rays following ordinary (non-radiative) capture of negative muons by natural Se, Kr, Cd and Sm, as well as isotopically enriched $^{48}$Ti, $^{76}$Se, $^{82}$Kr, $^{106}$Cd and $^{150}$Sm targets was performed by means of HPGe detectors. Energy and time distributions were investigated and total life time of negative muon in different isotopes was deduced. Detailed analysis of $\gamma$-lines intensity allows to extract relative yield of several daughter nuclei and partial rates of ($\mu$,$\nu$) capture to numerous excited levels of the $^{48}$Sc, $^{76}$As, $^{82}$Br, $^{106}$Ag and $^{150}$Tc isotopes which are considered to be virtual states of an intermedia…

Shell-model study of the 4th- and 6th-forbidden β -decay branches of 48-Ca

The highly forbidden β− decay of 48Ca is reexamined by performing shell-model calculations with the GXPF1A effective interaction. We examine the three available decay branches to the lowest 6+, 5+, and 4+ states of 48Sc, and extract a theoretical half-life of T β 1/2 = 5.2+1.7 −1.3 × 1020 g−2 A yr for the β− decay, where gA is the value of the axial-vector coupling constant. The current half-life estimate suggests stronger competition between the single-β-decay and double-β-decay branches of 48Ca than previously expected on theoretical grounds. peerReviewed

Questioning model-independent estimates of 2 νββ decay rates

Abstract In this work we discuss the validity of recently published results, by Rumyantsev and Urin, concerning nuclear matrix elements of the two-neutrino double-beta decay transitions. These authors claim that these matrix elements can be calculated in a model-independent way. We have re-analyzed their results and extended their formalism to account for proton-neutron correlations at the QRPA level of approximation. We have found that the formalism fails in describing the double beta decay observables.

A novel experimental system for the KDK measurement of the 40K decay scheme relevant for rare event searches

Potassium-40 ($^{40}$K) is a long-lived, naturally occurring radioactive isotope. The decay products are prominent backgrounds for many rare event searches, including those involving NaI-based scintillators. $^{40}$K also plays a role in geochronological dating techniques. The branching ratio of the electron capture directly to the ground state of argon-40 has never been measured, which can cause difficulty in interpreting certain results or can lead to lack of precision depending on the field and analysis technique. The KDK (Potassium (K) Decay (DK)) collaboration is measuring this decay. A composite method has a silicon drift detector with an enriched, thermally deposited $^{40}$K source …

Two-Quasiparticle Mixing in Odd-Odd Nuclei

In Chap. 16 the residual Hamiltonian was used to mix proton-proton and neutron—neutron two-quasiparticle configurations. The resulting wave functions described states in even-even open-shell nuclei. In this chapter we develop a corresponding formalism, the proton-neutron QTDA, for mixing proton-neutron two-quasiparticle configurations. This mixing produces wave functions that describe states in odd-odd open-shell nuclei. The quasiparticles are obtained from a BCS calculation for an even-even reference nucleus next to the odd-odd nucleus of interest.

Shell-model study on event rates of lightest supersymmetric particles scattering off 83Kr and 125Te

We investigate the elastic and inelastic scattering of lightest supersymmetric particle (LSP) dark matter off two possible target nuclei, 83Kr and 125Te. For the nuclear-structure calculations, we employ the nuclear shell model using recently generated realistic interactions. We have condensed the nuclear-physics contribution to a set of nuclear-structure factors that are independent of the adopted supersymmetric (SUSY) model. Total event rates are then easily calculated by combining the nuclear-structure factors with SUSY parameters of choice. In particular, 125Te shows promise as a detector material with both the elastic and inelastic channels yielding an appreciable nuclear response. pee…

Systematic approach toβand2νββdecays of massA=100–136nuclei

In this work we perform a systematic study of pairs of single-$\ensuremath{\beta}$-decaying nuclei in the mass region $A=100--136$ to extract information on the effective value of the axial-vector coupling constant ${g}_{\mathrm{A}}$. As the many-body framework we use the quasiparticle random-phase approximation (QRPA) and its proton-neutron variant (pnQRPA) in single-particle valence bases with Woods-Saxon-calculated single-particle energies. It is found that, to a reasonable approximation, ${g}_{\mathrm{A}}$ is a linear function of the mass number $A$, with a slightly different parametrization below and above the mass $A=121$. Using the values of ${g}_{\mathrm{A}}$ extracted from the line…

Electromagnetic properties of some positive parity dipole states described in terms of quadrupole and octupole interacting bosons

The first three positive parity dipole states predicted by a phenomenological quadrupole-octupole boson Hamiltonian are extensively studied. Their coupling to the neighboring positive and negative parity states, due to the {ital M}1 and {ital E}{lambda} ({lambda}=1,3) transitions, respectively, are considered. Special attention is paid to the lowest two states which are of collective {ital M}1 nature. The signature which distinguishes them from the {ital M}1 state describing the scissors mode is also discussed.

Comparative Analysis of Nuclear Matrix Elements of 0νβ+β+ Decay and Muon Capture in 106Cd

Comparative analyses of the nuclear matrix elements (NMEs) related to the 0νβ+β+ decay of 106Cd to the ground state of 106Pd and the ordinary muon capture (OMC) in 106Cd are performed. This is the first time the OMC NMEs are studied for a nucleus decaying via positron-emitting/electron-capture modes of double beta decay. All the present calculations are based on the proton-neutron quasiparticle random-phase approximation with large no-core single-particle bases and realistic two-nucleon interactions. The effect of the particle-particle interaction parameter gpp of pnQRPA on the NMEs is discussed. In the case of the OMC, the effect of different bound-muon wave functions is studied. peerRevie…

Two-Quasiparticle Mixing by the QRPA

In the previous two chapters we introduced two-quasiparticle configuration mixing. The method was based on the QTDA. In this chapter we extend the formalism to the QRPA. We derive the QRPA equations by the equations-ofmotion method. Due to approximations in the derivation the resulting equations do not satisfy a variational principle. The properties of QRPA solutions are similar to those of the particle-hole RPA of Chap. 11.

The gallium anomaly reassessed using a Bayesian approach

The solar-neutrino detectors GALLEX and SAGE were calibrated by electron-neutrino flux from the $^{37}$Ar and $^{51}$Cr calibration sources. A deficit in the measured neutrino flux was recorded by counting the number of neutrino-induced conversions of the $^{71}$Ga nuclei to $^{71}$Ge nuclei. This deficit was coined ``gallium anomaly'' and it has lead to speculations about beyond-the-standard-model physics in the form of eV-mass sterile neutrinos. Notably, this anomaly has already defied final solution for more than 20 years. Here we reassess the statistical significance of this anomaly and improve the related statistical approaches by treating the neutrino experiments as repeated Bernoulli…

Experimental study of 100Tc β decay with total absorption γ -ray spectroscopy

The β decay of 100Tc has been studied by using the total absorption γ -ray spectroscopy technique at the Ion Guide Isotope Separator On-Line facility in Jyväskylä. In this work the new Decay Total Absorption γ -ray Spectrometer in coincidence with a cylindrical plastic β detector has been employed. The β intensity to the ground state obtained from the analysis is in good agreement with previous high-resolution measurements. However, differences in the feeding to the first-excited state as well as weak feeding to a new level at high excitation energy have been deduced from this experiment. Theoretical calculations performed in the quasiparticle random-phase approximation framework are also r…

Opening of the Z=40 subshell gap and the double-beta decay of 100Mo

Abstract Experimental and theoretical study of the β − decay of 100 Nb to the two-quasiparticle states in 100 Mo suggests the opening of the Z =40 subshell gap in the proton pf-0g 9/2 shell for isobars near 100 Mo. Assuming the opening of the Z =40 subshell gap both for 100 Mo and 100 Ru enables the study of the effects of this subshell gap upon the two-neutrino and neutrinoless double-beta-decay rates of 100 Mo to the ground state and excited states in 100 Ru. It is found that the influence of the opening of the Z =40 gap has very minor effects on the beta-decay and double-beta-decay feeding of the 0 + and 2 + states of 100 Ru.

βdecay of the5+isomer of the odd-odd nucleus100Nb

The decay of the $3s$ isomer of ${}^{100}\mathrm{Nb}$ has been investigated by $\ensuremath{\gamma}$ spectroscopy of online mass separated ${}^{100}\mathrm{Nb}.$ Several new transitions in the daughter nucleus ${}^{100}\mathrm{Mo}$ have been observed. This results in a more consistent decay pattern leading to a firm ${5}^{+}$ assignment to the ${}^{100}\mathrm{Nb}$ isomer. A QRPA based calculation reproduces the decay features best if the $\ensuremath{\pi}{g}_{9/2}\ensuremath{-}\ensuremath{\pi}{p}_{1/2}$ gap is enlarged, confirming the importance of the subshell gap at $Z=40$ previously introduced to account for low-lying ${0}^{+}$ states in other $N=58$ isotones.

Neutrinolessββdecays to excited0+states and the Majorana-neutrino mass

Isovector and isoscalar spin-multipole giant resonances in the parent and daughter nuclei of double-β-decay triplets

The strength distributions, including giant resonances, of isovector and isoscalar spin-multipole transitions in the commonly studied double-β-decay triplets are computed in the framework of the quasiparticle random-phase approximation (QRPA) using the Bonn-A two-body interaction in no-core single-particle valence spaces. The studied nuclei include the double-β parent and daughter pairs (76Ge, 76Se), (82Se, 82Kr), (96Zr, 96Mo), (100Mo, 100Ru), (116Cd, 116Sn), (128Te, 128Xe), (130Te, 130Xe), and (136Xe, 136Ba). The studied transitions proceed from the ground states to the Jπ=0−,1−,2− (spin-dipole transitions) and Jπ=1+,2+,3+ (spin-quadrupole transitions) excited states in these nuclei. Compa…

Shell-Model Effective Operators for Muon Capture in ^{20}Ne

It has been proposed that the discrepancy between the partially-conserved axial-current prediction and the nuclear shell-model calculations of the ratio $C_P/C_A$ in the muon-capture reactions can be solved in the case of ^{28}Si by introducing effective transition operators. Recently there has been experimental interest in measuring the needed angular correlations also in ^{20}Ne. Inspired by this, we have performed a shell-model analysis employing effective transition operators in the shell-model formalism for the transition $^{20}Ne(0^+_{g.s.})+\mu^- \to ^{20}F(1^+; 1.057 MeV) + \nu_\mu$. Comparison of the calculated capture rates with existing data supports the use of effective transiti…

Is the single-state dominance realized in double-β-decay transitions?

In the single-state-dominance hypothesis (SSDH) the decay rate of the two-neutrino double-\ensuremath{\beta} decay to the final ground state is solely determined by virtual single-\ensuremath{\beta}-decay transitions via the ${1}^{+}$ ground state of the intermediate nucleus. A very important consequence the SSDH will be that some of nonaccelerator measurements of double-\ensuremath{\beta}-decay observables could be circumvented by single-\ensuremath{\beta}-decay measurements. To assess the validity of the SSDH, we have carried out a theoretical analysis of all double-\ensuremath{\beta}-decay transitions where the spin-parity of the ground-state of the intermediate nucleus is ${1}^{+}$. The…

Theoretical estimates of supernova-neutrino cross sections for the stable even-even lead isotopes: Charged-current reactions

A detailed study of the charged-current supernova electron neutrino and electron antineutrino scattering off the stable even-mass lead isotopes $A=204$, 206, and 208 is reported in this work. The proton-neutron quasiparticle random-phase approximation (pnQRPA) is adopted to construct the nuclear final and initial states. Three different Skyrme interactions are tested for their isospin and spin-isospin properties and then applied to produce (anti)neutrino-nucleus scattering cross sections for (anti)neutrino energies below 80 MeV. Realistic estimates of the nuclear responses to supernova (anti)neutrinos are computed by folding the computed cross sections with a two-parameter Fermi-Dirac distr…

Electron capture decay of116Inand nuclear structure of doubleβdecays

Quasiparticle-random-phase-approximation (QRPA) calculations of double $\ensuremath{\beta}$ decays have not been able to reproduce data in the $A=100$ system. We propose the $A=116$ system---because of its smaller deformation---as a simpler system to test QRPA calculations. We present results of two experiments we performed, which determine the electron-capture-decay branch of ${}^{116}\mathrm{In}$ to be $(2.27\ifmmode\pm\else\textpm\fi{}0.63)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}%$, from which we deduce $\mathrm{log}{ft=4.39}_{\ensuremath{-}0.15}^{+0.10}$. We present QRPA calculations and compare their predictions to experimental data. Finally we use these calculations to…

Single and Double Beta-DecayQValues among the TripletZr96,Nb96, andMo96

The atomic mass relations among the mass triplet ^{96}Zr, ^{96}Nb, and ^{96}Mo have been determined by means of high-precision mass measurements using the JYFLTRAP mass spectrometer at the IGISOL facility of the University of Jyvaskyla. We report Q values for the ^{96}Zr single and double β decays to ^{96}Nb and ^{96}Mo, as well as the Q value for the ^{96}Nb single β decay to ^{96}Mo, which are Q_{β}(^{96}Zr)=163.96(13), Q_{ββ}(^{96}Zr)=3356.097(86), and Q_{β}(^{96}Nb)=3192.05(16)  keV. Of special importance is the ^{96}Zr single β-decay Q value, which has never been determined directly. The single β decay, whose main branch is fourfold unique forbidden, is an alternative decay path to the…

Event rates for CDM detectors from large-scale shell-model calculations

Abstract We investigate the scattering of the CDM candidate LSP (Lightest Supersymmetric Particle) off nuclei. We have computed the associated event rates and annual modulation signals for the 23 Na, 71 Ga, 73 Ge and 127 I CDM detectors by using the nuclear shell model in realistic model spaces and exploiting microscopic effective two-body interactions. Large-scale computations had to be performed in order to achieve convergence of the results. We have tabulated the associated nuclear-structure coefficients for several LSP masses enabling easy interpolation of our results for any other mass. The relevance of the spin-dependent and coherent channels for the event rates is discussed, from bot…

Gamow–Teller beta decays of the odd-mass neighbors of the solar-neutrino detector 127I

Abstract Calculations of the energy spectra and the log ft values of Gamow–Teller beta transitions of neutron-odd and proton-odd nuclei close to the solar-neutrino detector 127I are performed using the microscopic quasiparticle–phonon model. The information obtained from the beta transition strengths is valuable in solar-neutrino detection and dark matter search both in present and future large-scale experiments. Realistic interactions within a realistic single-particle valence space were used in the calculations. The overall correspondence in terms of the excitation spectra and the log ft values between theory and experiments can be regarded as quite good when considering the completely mi…

Quenching of gA deduced from the β-spectrum shape of 113Cd measured with the COBRA experiment

A dedicated study of the quenching of the weak axial-vector coupling strength $g_{\rm A}$ in nuclear processes has been performed by the COBRA collaboration. This investigation is driven by nuclear model calculations which show that the $\beta$-spectrum shape of the fourfold forbidden non-unique decay of $^{113}$Cd strongly depends on the effective value of $g_{\rm A}$. Using an array of CdZnTe semiconductor detectors, 45 independent $^{113}$Cd spectra were obtained and interpreted in the context of three nuclear models. The resulting effective mean values are $\bar{g}_{\rm A}(\text{ISM}) = 0.915 \pm 0.007$, $\bar{g}_{\rm A}(\text{MQPM}) = 0.911 \pm 0.013$ and $\bar{g}_{\rm A}(\text{IBFM-2}…

MQPM description of the structure and beta decays of the odd Mo and Tc isotopes

The odd-mass isotopes A=95,97 of molybdenum are of interest for neutrino-physics applications. The microscopic quasiparticle-phonon model (MQPM) is used to calculate energy and decay characteristics of these nuclei and their beta-decay partners (Tc95 and Tc97). A realistic single-particle valence space and two-body interaction are used in the calculations. The computed results are compared with available data. The obtained energy spectra are also compared with earlier calculations. We present the first ever calculations for the rates of allowed and forbidden β+/EC decay transitions in these nuclei. In general our computed numbers agree rather well with the available data.

Effects of orbital occupancies on the neutrinoless beta-beta matrix element of 76Ge

In this work we use the recently measured neutron occupancies in the 76Ge and 76Se nuclei as a guideline to define the neutron quasiparticle states in the 1p0f0g shell. We define the proton quasiparticles by inspecting the odd-mass nuclei adjacent to 76Ge and 76Se. We insert the resulting quasiparticles in a proton-neutron quasiparticle random-phase approximation (pnQRPA) calculation of the nuclear matrix element of the neutrinoless double beta (0-nu-beta-beta) decay of 76Ge. A realistic model space and effective microscopic two-nucleon interactions are used. We include the nucleon-nucleon short-range correlations and other relevant corrections at the nucleon level. It is found that the res…

Results of the search for neutrinoless double-βdecay inMo100with the NEMO-3 experiment

The NEMO-3 detector, which had been operating in the Modane Underground Laboratory from 2003 to 2010, was designed to search for neutrinoless double $\beta$ ($0\nu\beta\beta$) decay. We report final results of a search for $0\nu\beta\beta$ decays with $6.914$ kg of $^{100}$Mo using the entire NEMO-3 data set with a detector live time of $4.96$ yr, which corresponds to an exposure of 34.3 kg$\cdot$yr. We perform a detailed study of the expected background in the $0\nu\beta\beta$ signal region and find no evidence of $0\nu\beta\beta$ decays in the data. The level of observed background in the $0\nu\beta\beta$ signal region $[2.8-3.2]$ MeV is $0.44 \pm 0.13$ counts/yr/kg, and no events are obs…

α-decay spectroscopy of deformed nuclei reexamined

We perform an extensive analysis of $\ensuremath{\alpha}$-decays to ${2}^{+}$ and ${4}^{+}$ states in deformed even-even nuclei by using the stationary coupled channels approach. Collective excitations are described within the rigid rotor model. The $\ensuremath{\alpha}$-nucleus interaction is given by a double folding procedure with M3Y plus Coulomb nucleon-nucleon forces. We use a repulsive potential with one independent parameter in order to localize the $\ensuremath{\alpha}$-particle on the nuclear surface and to fit the experimental $Q$-value. The decaying state is identified with the first resonance inside the resulting pocket-like potential, as suggested by microscopic calculations. …

Microscopic quasiparticle–phonon description of beta decays of 113Cd and 115In using proton–neutron phonons

Abstract The fourth-forbidden non-unique ground-state-to-ground-state beta decays of 113 Cd and 115 In are calculated using a realistic microscopic two-body interaction and a realistic single-particle model space. To describe the involved initial and final nuclear states we introduce a proton–neutron variant of the microscopic quasiparticle–phonon model (MQPM), the proton–neutron MQPM (pnMQPM). The states of the pnMQPM are created by coupling quasiparticles with phonons of the proton–neutron quasiparticle random-phase approximation (pnQRPA). The computed half-lives and log f t values are found to be in excellent agreement with experimental data. Computed beta spectra of the decays are also …

Estimating the flux of the 14.4 keV solar axions

In this paper we present a calculation of the expected flux of the mono-energetic 14.4 keV solar axions emitted by the M1 type nuclear transition of $^{57}$Fe in the Sun. These axions can be detected, e.g., by inverse coherent Bragg-Primakoff conversion in single-crystal TeO$_2$ bolometers. The ingredients of this calculation are i) the axion nucleon coupling, estimated in several popular axion models and ii)the nuclear spin matrix elements involving realistic shell model calculations with both proton and neutron excitations. For the benefit of the experiments we have also calculated the branching ratio involving axion and photon emission

Universal features of the nuclear matrix elements governing the mass sector of the 0νββ decay

In this work we report on manifest universal features found in the nuclear matrix elements which govern the mass sector of the neutrinoless double beta decay. The results are based on the analysis of the calculated matrix elements corresponding to the decays of 76Ge, 82Se, 100Mo, and 116Cd. The results suggest a dominance of few low-lying nuclear states of few multipoles in these matrix elements. Dedicated charge-exchange reactions could be used to probe these key states to determine experimentally the value of the nuclear matrix element.

NUCLEAR MATRIX ELEMENTS FOR DOUBLE BETA DECAY

The neutrinoless double beta (0νββ) decay of atomic nuclei plays a key role in the search for massive Majorana neutrinos and their mass scale. To extract the necessary information from the measured data the nuclear-structure effects have to be accounted for by computation of the associated nuclear matrix elements (NME's). In this article the NME's for the light-neutrino exchange mechanism are discussed. They are computed by using the proton-neutron quasiparticle random-phase approximation (pnQRPA). Recent developments in this field relate to the handling of the nucleon-nucleon short-range correlations and independent experimental probes of the wave functions relevant for the NME's.

Theoretical description of the fourth-forbidden non-unique β decays ofCd113andIn115

The half-lives and $\mathrm{log}\mathit{ft}$ values for the fourth-forbidden non-unique beta decays of the ground states of $^{113}\mathrm{Cd}$ and $^{115}\mathrm{In}$ were calculated using a transparent formulation for the ${\ensuremath{\beta}}^{\ensuremath{-}}$ transition amplitude. The microscopic quasiparticle-phonon model (MQPM) was used to calculate the initial and final states of the transitions. The corresponding wave functions were described as linear combinations of one- and three-quasiparticle configurations built in a realistic single-particle model space by using a realistic microscopic two-body interaction. The computed results for the $\mathrm{log}\mathit{ft}$ values and half…

Microscopic anharmonic vibrator approach for beta decays

Abstract We formulate a microscopic description of charge-changing excitations, including dynamical mixture of one- and two-phonon states. The present formalism generalizes our previous microscopic anharmonic vibrator approach (MAVA), designed to treat charge-conserving two- and four-quasiparticle degrees of freedom and their mixing. In the present formalism, the proton–neutron MAVA, pnMAVA, the main building blocks are the quasiparticle random-phase approximation (QRPA) phonons in the charge-conserving channels, and the proton–neutron QRPA (pnQRPA) phonons in the charge-changing channels. The QRPA and pnQRPA equations are directly used in deriving the equations of motion for two-phonon sta…

Folding description of the fine structure of α decay to2+vibrational and transitional states

We analyze \ensuremath{\alpha}-decays to ground and ${2}^{+}$ vibrational states in even-even nuclei by using a coupled channels formalism. The \ensuremath{\alpha}-nucleus interaction is simulated by a double folding procedure using M3Y plus Coulomb two-body forces. Collective excitations are described by vibrations of the nuclear surface. We use a repulsive potential, with one independent parameter, in order to simulate Pauli principle and to adjust the energy of the resonant state to the experimental $Q$-value. The decaying state is identified with the zero nodes resonance inside the resulting pocket-like potential. We have found that the fine structure is very sensitive to the strength o…

Smallest KnownQValue of Any Nuclear Decay: The Rareβ−Decay ofIn115(9/2+)→Sn115(3/2+)

The ground-state-to-ground-state Q_{beta;{-}} value of ;{115}In was determined to 497.68(17) keV using a high-precision Penning trap facility at the University of Jyvaskyla, Finland. From this, a Q_{beta;{-}} value of 0.35(17) keV was obtained for the rare beta;{-} decay to the first excited state of ;{115}Sn at 497.334(22) keV. The partial half-life was determined to 4.1(6) x 10;{20} yr using ultra low-background gamma-ray spectrometry in an underground laboratory. Theoretical modeling of this 2nd-forbidden unique beta;{-} transition was also undertaken and resulted in Q_{beta;{-}} = 57_{-12};{+19} eV using the measured half-life. The discrepancy between theory and experiment could be attr…

Microscopic quasiparticle-phonon description of odd-mass127−133Xeisotopes and their β decay

Quasiparticle-phonon equations of motion are solved starting from a microscopic realistic many-body Hamiltonian. In this microscopic quasiparticle-phonon model (MQPM) the relevant part of the three-quasiparticle Hilbert space may possibly be taken into account even in calculations using large single-particle bases. As an example, the MQPM is applied to the calculation of energy levels and Fermi and Gamow-Teller beta-decay transition amplitudes for transitions between odd-mass ${}^{127\ensuremath{-}133}\mathrm{Xe}$, ${}^{127\ensuremath{-}133}\mathrm{I}$, and ${}^{127\ensuremath{-}133}\mathrm{Cs}$ isotopes. Considering the fully microscopic nature of the MQPM, comparison of its results and da…

Massive neutrinos and right-handed weak currents in double beta decay.

The contributions of right-handed weak currents in neutrinoless double beta decay are studied taking explicitly into account the mass corrections to the intermediate neutrino propagator. Due to these corrections the right-handed currents become effective even if all neutrinos are light ([ital m][sub [nu]][gt]10 MeV). Explicit expressions for the neutrino-momentum integrals and the decay half-life are derived. As an example two neutrino-mass scenarios containing the hypothetical 17-keV neutrino are discussed. The experimental half-life of the [sup 76]Ge[r arrow][sup 76]Se decay is used to obtain an upper limit for a new kind of effective right-handed coupling within the two scenarios.

Discovery of an Exceptionally Strong β -Decay Transition of F20 and Implications for the Fate of Intermediate-Mass Stars

A significant fraction of stars between 7 and 11 solar masses are thought to become supernovae, but the explosion mechanism is unclear. The answer depends critically on the rate of electron capture on ^{20}Ne in the degenerate oxygen-neon stellar core. However, because of the unknown strength of the transition between the ground states of ^{20}Ne and ^{20}F, it has not previously been possible to fully constrain the rate. By measuring the transition, we establish that its strength is exceptionally large and that it enhances the capture rate by several orders of magnitude. This has a decisive impact on the evolution of the core, increasing the likelihood that the star is (partially) disrupte…

Radioactivity of neutron-rich oxygen fluorine and neon isotopes

The $\ensuremath{\gamma}$ radiation and neutrons emitted following the $\ensuremath{\beta}$ decays of ${}^{24}\mathrm{O},$ ${}^{25--27}\mathrm{F},$ and ${}^{28\ensuremath{-}30}\mathrm{Ne}$ have been measured. The nuclides were produced in the quasifragmentation of a 2.8 GeV ${}^{36}\mathrm{S}$ beam, separated in-flight and identified through time-of-flight and energy-loss measurements. The ions were stopped in a silicon detector telescope, which was used to detect the $\ensuremath{\beta}$ particles emitted in their subsequent radioactive decay. The coincident $\ensuremath{\gamma}$ rays were measured using four large volume germanium detectors mounted close to the implantation point and the …

Schematic and realistic model calculations of the isovector spin monopole excitations in 116In

The excitation of Gamow-Teller (GT) and isovector spin monopole (IVSM) J π = 1+ modes in 116In by (p,n) and (n, p) charge-exchange reactions on 116Cd and on 116Sn, respectively, is studied within the framework of the quasiparticle random-phase approximation. The calculations have been performed both for schematic and realistic model situations. It appears that the calculated admixture of the IVSM and Gamow-Teller (GT) J π = 1+ excitations is negligible and that the contribution to the strength above 20 MeV of excitation energy, in 116In, is due to the IVSM (σr2t±) mode. This result is compared with the recent experimental work that reported a large amount of both (p,n) and (n,p) strength be…

EPM calculations of E2/M1 mixing ratios for even samarium isotopes 146–152Sm

Abstract The M1 operator and the E2/M1 mixing ratios, Δ (E2/M1), are discussed in the framework of the extended phonon projection model (EPM). The model is applied to 146, 148, 150, 152 Sm to describe their M1 properties. Comparison is made between the EPM, the consistent- Q formalism (CQF) of the basic interacting-boson approximation (IBA-1) and the experimental Δ(E2/M1) data. Both theoretical approaches give reasonably good results and parameter systematics.

Calculation of allowed and first-forbidden beta-decay transitions of odd-odd nuclei

Abstract A method for calculating the β − and β + EC transitions from an odd-odd nucleus to the excited states of the adjacent even-even nucleus is presented. The beta transitions are treated combining the charge-conserving and the charge-changing mode of the quasi-particle random- phase approximation assuming a common vacuum. The beta-decay transitions are treated in their allowed and first-forbidden approximations, including also the ground-state transition. As a test case of the present formalism, detailed beta-decay properties of the following odd-odd-to-even-even transitions have been calculated and compared with experiment: the β − decay transitions 136 I (2 − )→ 136 Xe (J π ) and 136…

Tensor Operators and the Wigner-Eckart Theorem

In this chapter we pave the way to the use of the coupling methods of Chap. 1 for manipulating operators and their matrix elements. To enable smooth application of the angular momentum methods, we introduce so-called spherical tensor operators. Spherical tensors can be related to Cartesian tensors. A Cartesian tensor of a given Cartesian rank can be reduced to spherical tensors of several spherical ranks. There is a very convenient procedure, the so-called Wigner-Eckart theorem, to separate the part containing the projection quantum numbers from the rest of the matrix element of a spherical tensor operator. The remaining piece, called the reduced matrix element, is rotationally invariant an…

Shell-model study of partial muon-capture rates in light nuclei

Abstract The nuclear shell model is used to study ordinary muon capture of light nuclei in the p, sd and p-sd shell-model spaces. Several well-established two-body interactions are applied to calculate the involved nuclear matrix elements and the emerging results are compared with each other. The resulting theoretical partial muon-capture rates are compared with experimental data and their stability against different model spaces and interactions studied. The effects of the induced-pseudoscalar strength, C p , on the capture rates is discussed. The relation between the allowed partial muon capture rates and the Gamow-Teller strength function is stressed.

Isovector spin-multipole strength distributions in double- β -decay triplets

In this work the energetics and strength distributions of isovector spin-dipole and spin-quadrupole transitions from the ground states of the pairs ($^{76}\mathrm{Ge}, ^{76}\mathrm{Se}$), ($^{82}\mathrm{Se}, ^{82}\mathrm{Kr}$), ($^{96}\mathrm{Zr}, ^{96}\mathrm{Mo}$), ($^{100}\mathrm{Mo}, ^{100}\mathrm{Ru}$), ($^{116}\mathrm{Cd}, ^{116}\mathrm{Sn}$), ($^{128}\mathrm{Te}, ^{128}\mathrm{Xe}$), ($^{130}\mathrm{Te}, ^{130}\mathrm{Xe}$), and ($^{136}\mathrm{Xe}, ^{136}\mathrm{Ba}$), of double-$\ensuremath{\beta}$-decay initial and final nuclei, to the ${J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}},{1}^{\ensuremath{-}},{2}^{\ensuremath{-}},{1}^{+},{2}^{+}$, and ${3}^{+}$ excited states of the interm…

Charged-current neutrino and antineutrino scattering off 116Cd described by Skyrme forces

We perform calculations of the cross sections for charged-current neutrino and antineutrino scattering off 116Cd using ten different Skyrme interactions, at energies typical of supernova neutrinos. We use the quasiparticle random-phase approximation in its charged-changing mode (pnQRPA) to construct the required nuclear wave functions for the participant initial and final states. We compare the results of these calculations with the results of calculations based on the Bonn one-boson-exchange potential. The response of 116Cd to supernova neutrinos is calculated by folding the obtained cross sections with suitably parametrized Fermi-Dirac distributions of the electron-neutrino and electron-a…

Double beta decays of 124Xe investigated in the QRPA framework

The two-neutrino (2ν2β) and neutrinoless (0ν2β) double beta decays of 124Xe are investigated. Decays to the ground state, , and various 0+ and 2+ excited states in 124Te are considered. The corresponding nuclear matrix elements have been calculated by using the quasiparticle random-phase approximation combined with the multiple-commutator model. G-matrix-based effective nuclear interactions have been used in realistic single-particle model spaces. All possible channels, β+β+, β+EC, and ECEC, are discussed for both the 2ν2β and 0ν2β decays. The associated half-lives are computed, in particular the one corresponding to the resonant neutrinoless double electron capture transition to the 2790.4…

Search for doubleβdecay of106Cd by using isotopically enriched106CdWO4crystal scintillator

A search for double ? processes in 106Cd was carried out at the Gran Sasso National Laboratories of the INFN, Italy; by using a CdWC4 crystal scintillator (mass of 215 g) enriched in 106Cd up to 66%. After 6590 h of data taking, half-life limits on double beta processes in 106Cd were set at level of 1019 ? 1021 yr. A possible resonant enhancement of the 0?2? processes has also been estimated in the framework of the QRPA approach.

Magnetic hexadecapole gamma transitions and neutrino-nuclear responses in medium heavy nuclei

Neutrino-nuclear responses in the form of squares of nuclear matrix elements,NMEs, are crucial for studies of neutrino-induced processes in nuclei. In this work we investigate magnetic hexadecapole (M4) NMEs in medium-heavy nuclei. The experimentally derived NMEs, $M_{\rm EXP}$(M4), deduced from observed M4 $\gamma $ transition half-lives are compared with the single-quasiparticle (QP) NMEs, $M_{\rm QP}$(M4), and the microscopic quasiparticle-phonon model (MQPM) NMEs $M_{\rm MQPM}$(M4). The experimentally driven M4 NMEs are found to be reduced by a coefficient $k \approx 0.29 $ with respect to $M_{\rm QP}$(M4) and by $k \approx 0.33$ with respect to $M_{\rm MQPM}$(M4). The M4 NMEs are reduc…

Description of the two-neutrino ββ decay of100Mo by pnMAVA

The microscopic anharmonic vibrator approach (MAVA) is a scheme where the one- and two-phonon states of an even–even nucleus are treated consistently by using a realistic microscopic nuclear Hamiltonian. This model has recently been extended to describe odd–odd nuclei by adding proton–neutron phonons in a scheme called the proton–neutron MAVA (pnMAVA). In this paper, we apply pnMAVA to compute the nuclear matrix elements corresponding to the two-neutrino double beta (2νββ) decay of 100Mo to the ground state and the first excited 0+ state of 100Ru in a realistic single-particle space. We also compute the GT− and GT+ Gamow–Teller strength functions and compare them with the plain pnQRPA (prot…

Nuclear matrix elements for0νββdecays with light or heavy Majorana-neutrino exchange

We compute the nuclear matrix elements (NMEs) corresponding to the neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of nuclei which attract current experimental interest. We concentrate on ground-state-to-ground-state decay transitions mediated by light (l-NMEs) or heavy (h-NMEs) Majorana neutrinos. The computations are done in realistic single-particle model spaces using the proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. Both the l-NMEs and the h-NMEs include the appropriate short-range correlations, nucleon form factors, and higher-order nucleonic weak …

Transitions in the Quasiparticle Picture

In this chapter we deal with electromagnetic and beta-decay transitions in terms of independent quasiparticles. Transition amplitudes are derived for transitions between one-quasiparticle states and between two-quasiparticle states. Derivations and applications are made within the BCS framework, but the expressions for the amplitudes are valid also in the LNBCS description.

Neutrino-nucleus scattering off 136Xe

Background: Theoretical estimates of the cross sections for the neutrino-nucleus scattering off relevant nuclei for supernova neutrinos are essential for many applications in neutrino physics and astrophysics. The double- β-decaying nucleus 136Xe nucleus is used by the EXO Collaboration in the search for neutrinoless double-β decay. A ton-scale experiment based on 136Xe could also be used for studies of supernova neutrinos and/or solar neutrinos. Purpose: The purpose of the present work is, thus, to perform a study of the charged-current and neutral-current nuclear responses to supernova neutrinos for 136Xe. Method: The cross sections are computed by using the well-established framework for…

Erratum to “The response of 95,97Mo to supernova neutrinos” [Nucl. Phys. A 866 (2011) 67–78]

Strength of J(pi)=1(+) Gamow-Teller and isovector spin monopole transitions in double-beta-decay triplets

In this work we study systematically the energetics and intensity distributions of Gamow-Teller (GT ± )and isovector spin monopole (IVSM ± ) transitions from the ground states of the pairs ( 76 Ge, 76 Se), ( 82 Se, 82 Kr), ( 100 Mo, 100 Ru), ( 116 Cd, 116 Sn), ( 128 Te, 128 Xe), ( 130 Te, 130 Xe), and ( 136 Xe, 136 Ba), of double-beta-decay initial and final nuclei, to the J π = 1 + excited states of the intermediate odd-odd nuclei 76 As, 82 Br, 100 Tc, 116 In, 128 , 130 I, and 136 Cs. We use a proton-neutron quasiparticle random-phase approximation (QRPA) theory framework with the Bonn-A two-body interaction in large no-core single-particle valence bases. Our studies indicate that the GT −…

Second-forbidden nonunique β− decays of 24Na and 36Cl assessed by the nuclear shell model

We have performed a systematic study of the log f t values, shape factors, and electron spectra for the second-forbidden nonunique β− decays of 24Na(4+) →24Mg(2+) and 36Cl(2+) →36Ar(0+) transitions under the framework of the nuclear shell model. We have performed the shell model calculations in the sd model space, using more recent microscopic effective interactions such as Daejeon16, chiral N3LO, and JISP16. These interactions are derived from the no-core shell model wave functions using Okubo-Lee-Suzuki transformation. For comparison, we have also shown the results obtain from the phenomenological USDB interaction. To test the predictive power of these interactions first we have computed …

Theoretical analysis of the possible ultra-low-Q-value decay branch of 135Cs

Abstract We have investigated the feasibility of observing an ultra-low- Q -value beta-decay branch of 135 Cs by applying the microscopic quasiparticle–phonon model with a realistic two-body nuclear interaction. This work was motivated by an earlier combined experimental and theoretical work on decays of 115 In. The inaccuracy of the ground-state-to-ground-state Q value limits our ability to draw definite conclusions, and therefore modern precision measurements for it are called for. We present the computed partial half-lives of each channel for the most likely ranges of Q values.

On the resonant neutrinoless double-electron-capture decay of ^{136}Ce

Abstract The double-electron-capture Q value for the 136Ce decay to 136Ba has been determined at JYFLTRAP. The measured value 2378.53(27) keV excludes the energy degeneracy with the 0 + excited state of the decay daughter 136Ba at 2315.32(7) keV in a resonant 0 ν ECEC decay by 11.67 keV. The new Q value differs from the old adopted value 2419(13) keV (Atomic Mass Evaluation 2003) by 40 keV and is 50 times more precise. Our calculations show that the precise Q value renders the resonant 0 ν ECEC decay of 136Ce undetectable by the future underground detectors. We measured also the double-β decay Q value of 136Xe to be 2457.86(48) keV which agrees well with the value 2457.83(37) keV measured a…

Nuclear matrix elements for double beta decay in the QRPA approach: a critical review

The calculation of nuclear matrix elements (NME) for double beta decay transitions (DBD) relies upon several approximations. The purpose of this note is to review some of these approximations, and their impact upon the NME. We shall present our results, which have been obtained in the framework of the proton-neutron quasiparticle random phase approximation (pnQRPA), and we shall focus on short range correlations, pairing, and symmetry effects.

Spin-dipole nuclear matrix elements for double beta decays and astro-neutrinos

Spin-dipole (SD) nuclear matrix elements (NMEs) M±(SD2) for unique first forbidden β±2−→0+ ground-state-to-ground-state transitions are studied by using effective microscopic two-nucleon interactions in realistic single-particle model spaces. The observed values of the NMEs Mexp±(SD2) are compared with the values of the single-quasiparticle NMEs Mqp±(SD2) without nucleon spin–isospin (στ) correlation and the QRPA NMEs MQRPA±(SD2) with the στ correlation. The observed SD matrix elements are found to be reduced by the factor k≈0.2 with respect to Mqp±(SD2) and by the factor kNM≈0.5 with respect to MQRPA±(SD2). We then infer that the SD NME is reduced considerably partly by the nucleon στ corr…

Nuclear responses for double beta decay and muon capture

The existence of the neutrinoless double beta (0νββ) decay is one of the most intriguing open questions in the neutrino physics field. Despite many large-scale experiments have aimed to measure the reaction for decades, it has not yet been observed. Therefore, accurate theoretical calculations on 0νββ are crucial. To describe the double beta decay processes reliably one needs a possibility to test the involved virtual transitions against experimental data. In this work we manifest how to utilise the charge-exchange and ordinary muon capture (OMC) data in the study of 0νββ decay.The existence of the neutrinoless double beta (0νββ) decay is one of the most intriguing open questions in the neu…

Pinning down the strength function for ordinary muon capture on 100Mo

Ordinary muon capture (OMC) on 100Mo is studied both experimentally and theoretically in order to access the weak responses in wide energy and momentum regions. The OMC populates states in 100Nb up to some 50 MeV in excitation energy. For the first time the associated OMC strength function has been computed and compared with the obtained data. The present computations are performed using the Morita-Fujii formalism of OMC by extending the original formalism beyond the leading order. The participant nuclear wave functions are obtained in extended no-core single-particle model space using the spherical version of proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon…

Dark-matter detection by elastic and inelastic LSP scattering on 129Xe and 131Xe

Abstract We calculate the nuclear matrix elements involved in the elastic and inelastic scattering of the lightest supersymmetric particle (LSP) on the 129Xe and 131Xe dark-matter detector nuclei. This is the first time when both channels are addressed within the same unified microscopic nuclear framework, namely we perform large-scale shell-model calculations with a realistic two-body interaction to produce the participant nuclear wave functions. These wave functions successfully reproduce the spectroscopic data on the relevant magnetic moments and M1 decays. The tested wave functions are used to produce annual average detection rates for both the elastic and inelastic channels. It is foun…

Neutral-current supernova-neutrino cross sections for 204,206,208Pb calculated by Skyrme quasiparticle random-phase approximation

The present work constitutes a detailed study of neutral-current (NC) supernova-neutrino scattering off the stable even-even lead isotopes 204,206,208Pb. This is a continuation of our previous work [Almosly et al., Phys. Rev. C. 94, 044614 (2016)] where we investigated charged-current processes on the same nuclei. As in the previous work, we have adopted the quasiparticle random-phase approximation (QRPA) as the theory framework and use three different Skyrme interactions to build the involved nuclear wave functions. We test the Skyrme forces by computing the location of the lowest-order isovector spin-multipole giant resonances and comparing with earlier calculations. We have computed the …

Short-range correlations and neutrinoless double beta decay

In this work we report on the effects of short-range correlations upon the matrix elements of neutrinoless double beta decay. We focus on the calculation of the matrix elements of the neutrino-mass mode of neutrinoless double beta decays of 48Ca and 76Ge. The nuclear-structure components of the calculation, that is the participant nuclear wave functions, have been calculated in the shell-model scheme for 48Ca and in the proton-neutron quasiparticle random-phase approximation (pnQRPA) scheme for 76Ge. We compare the traditional approach of using the Jastrow correlation function with the more complete scheme of the unitary correlation operator method (UCOM). Our results indicate that the Jast…

Magnetic Hexadecapole γ Transitions and Neutrino-Nuclear Responses in Medium-Heavy Nuclei

Neutrino-nuclear responses in the form of squares of nuclear matrix elements, NMEs, are crucial for studies of neutrino-induced processes in nuclei. In this work we investigate magnetic hexadecapole (M4) NMEs in medium-heavy nuclei. The experimentally derived NMEs,MEXP(M4), deduced from observed M4γtransition half-lives are compared with the single-quasiparticle (QP) NMEs,MQP(M4), and the microscopic quasiparticle-phonon model (MQPM) NMEsMMQPM(M4). The experimentally derived M4 NMEs are found to be reduced by a coefficientk≈0.29with respect toMQP(M4) and byk≈0.33with respect toMMQPM(M4). The M4 NMEs are reduced a little by the quasiparticle-phonon correlations of the MQPM wave functions but…

gA -driven shapes of electron spectra of forbidden β decays in the nuclear shell model

The evolution of the shape of the electron spectra of 16 forbidden ${\ensuremath{\beta}}^{\ensuremath{-}}$ decays as a function of ${g}_{\mathrm{A}}$ was studied using the nuclear shell model in appropriate single-particle model spaces with established, well-tested nuclear Hamiltonians. The $\ensuremath{\beta}$ spectra of $^{94}\mathrm{Nb}({6}^{+})\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{94}\mathrm{Mo}({4}^{+})$ and $^{98}\mathrm{Tc}({6}^{+})\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{98}\mathrm{Ru}({4}^{+})$ were found to depend strongly on ${g}_{\mathrm{A}}$, which makes them excellent candidates for the determination of the effective value of ${g}_{\mathrm{A}}$ wit…

Collective 2$^{+1}$ excitations in$^{206}$Po and$^{208,210}$Rn

In the present study, $B(E2; 2^{+}_{1}\rightarrow 0^{+}_{1})$ values have been measured in the 208,210Rn and 206Po nuclei through Coulomb excitation of re-accelerated radioactive beams in inverse kinematics at CERN-ISOLDE. These nuclei have been proposed to lie in, or at the boundary of the region where the seniority scheme should persist. However, contributions from collective excitations are likely to be present when moving away from the N=126 closed shell. Such an effect is confirmed by the observed increased collectivity of the $2^{+}_{1}\rightarrow 0^{+}_{1}$ transitions. Experimental results have been interpreted with the aid of theoretical studies carried out within the BCS-based QRP…

Microscopic description of α-like resonances

A description of $\ensuremath{\alpha}$-like resonances is given in terms of single-particle states including narrow Gamow resonances in continuum. The equations of motion are derived within the multistep shell-model approach; the lowest collective two-particle eigenmodes are used as building blocks for the four-particle states. A good agreement with the low-lying states in ${}^{212}\mathrm{Po}$ is obtained. A new technique to estimate the $\ensuremath{\alpha}$-particle formation amplitude for any multipolarity is proposed. The spectroscopic factor of the $\ensuremath{\alpha}$-decay between ground states is reproduced, but the total width is by two orders of magnitude less than the experimen…

Electron spectra in forbidden β decays and the quenching of the weak axial-vector coupling constant gA

Evolution of the electron spectra with the effective value of the weak axial-vector coupling constant ${g}_{\mathrm{A}}$ was followed for 26 first-, second-, third-, fourth- and fifth-forbidden ${\ensuremath{\beta}}^{\ensuremath{-}}$ decays of odd-$A$ nuclei by calculating the involved nuclear matrix elements (NMEs) in the framework of the microscopic quasiparticle-phonon model (MQPM). The next-to-leading-order terms were included in the $\ensuremath{\beta}$-decay shape factor of the electron spectra. The spectrum shapes of third- and fourth-forbidden nonunique decays were found to depend strongly on the value of ${g}_{\mathrm{A}}$, while first- and second-forbidden decays were mostly unaff…

Measurement of the two neutrino double beta decay half-life of Zr-96 with the NEMO-3 detector

Using 9.4 g of Zr-96 and 1221 days of data from the NEMO-3 detector corresponding to 0.031 kg yr, the obtained 2vbb decay half-life measurement is [2.35 +/- 0.14(stat) +/- 0.16(syst)] x 10^19 yr. Different characteristics of the final state electrons have been studied, such as the energy sum, individual electron energy, and angular distribution. The 2v nuclear matrix element is extracted using the measured 2vbb half-life and is 0.049 +/- 0.002. Constraints on 0vbb decay have also been set.

Neutral-current supernova neutrino-nucleus scattering off 127I and 133Cs

A large number of the presently running neutrino and dark-matter experiments use thallium-doped cesium-iodide CsI[Tl] crystals, sodium-doped cesium-iodide CsI[Na] crystals, or thallium-doped sodium-iodide NaI[Tl] crystals. In the present paper we calculate elastic and inelastic cross sections for neutral-current supernova-neutrino scattering off 127I and 133Cs, relevant for experiments using CsI[Tl], CsI[Na], or NaI[Tl] crystals. We study also the cross sections folded with two-parameter Fermi-Dirac distributions of the supernova-neutrino spectrum. The adopted nuclear-theory framework is the microscopic quasiparticle-phonon model, able to operate in large single-particle valence bases and u…

Calculated solar-neutrino capture rate for a radiochemical Tl205 -based solar-neutrino detector

Radiochemical experiments for low-energy solar-neutrino detection have been making headlines by exploiting the isotopes $^{37}\mathrm{Cl}$ and $^{71}\mathrm{Ga}$. Such a very low-threshold measurement of this type can also be performed using $^{205}\mathrm{Tl}$, which has been considered for decades for this purpose. A unique feature of this detector nucleus is the integration in the solar-neutrino flux over ${10}^{6}$ of years owing to its long-living daughter $^{205}\mathrm{Pb}$. In this Rapid Communication, we have calculated for the first time the cross section for the charged-current solar-neutrino scattering off $^{205}\mathrm{Tl}$. Taking into account the solar-model-predicted neutri…

Probing the quenching of gA by single and double beta decays

Abstract Ground-state-to-ground-state two-neutrino double beta ( 2 ν β β ) decays and single beta (EC and β − ) decays are studied for the A = 100 (100Mo 100Tc 100Ru), A = 116 (116Cd 116In 116Sn) and A = 128 (128Te 128I 128Xe) nuclear systems by using the proton–neutron quasiparticle random-phase approximation exploiting realistic effective interactions in very large single-particle bases. The aim of this exercise is to see if both the single-beta and double-beta decay observables related to the ground states of the initial, intermediate and final nuclei participant in the decays can be described simultaneously by changing the value of the axial-vector coupling constant g A . In spite of th…

Nuclear matrix elements of ββ decay from β-decay data

Abstract The evaluation of the nuclear matrix elements (NME) of the two-neutrino double beta ( 2 ν β β ) decay and neutrinoless double beta ( 0 ν β β ) decay using the proton–neutron quasiparticle random-phase approximation (pnQRPA) is addressed. In particular, the extraction of a proper value of the proton–neutron particle–particle interaction parameter, g pp , of this theory is analyzed in detail. Evidence is shown, that it can be misleading to use the experimental half-life of the 2 ν β β decay to extract a value for g pp . Rather, arguments are given in favour of using the available data on single beta decay for this purpose.

Investigation of the ββ decay of 116Cd into excited states of 116Sn

Abstract The double-beta decay of 116Cd into excited states of 116Sn is experimentally and theoretically investigated. From an inclusive experiment, using an external source of isotopically enriched Cd, new most stringent limits for the allowed and non-standard-model decays into excited states are derived. It is further investigated whether the bremsstrahlung emitted by the ββ electrons can be used to derive information on the ground-state decay. For the two-neutrino-decay mode a calculation, using the quasiparticle random-phase approximation, shows that the disadvantage in phase space, in comparison to the ground-state decay, is partially compensated through the nuclear-matrix element. Exp…

Accurate Q value for the 74Se double-electron-capture decay

Abstract The Q value of the neutrinoless double-electron-capture ( 0 ν ECEC ) decay of 74Se was measured by using the JYFLTRAP Penning trap. The determined value is 1209.169(49) keV, which practically excludes the possibility of a complete energy degeneracy with the second 2 + state (1204.205(7) keV) of 74Ge in a resonant 0 ν ECEC decay. We have also computed the associated nuclear matrix element by using a microscopic nuclear model with realistic two-nucleon interactions. The computed matrix element is found to be quite small. The failure of the resonant condition, combined with the small nuclear matrix element and needed p-wave capture, suppresses the decay rate strongly and thus excludes…

Shell-model study of the highly forbidden beta decay 48 Ca → 48 Sc

Ordinary β− decay of the 0+ ground state of 48Ca is studied. Partial half-lives for the highly-forbidden transitions to the three lowest-lying states (6+,5+,4+) of 48Sc are calculated by using both the harmonic oscillator and the Woods-Saxon mean-field wave functions. We find the decay to be dominated, as expected, by the unique fourth-forbidden transition to the excited 5+ state of 48Sc. The theoretical beta-decay half-life of 48Ca is found to be 1.1−0.6+0.8·1021 years which is approximately 25 times longer than the measured double-beta-decay half-life of T1/22ν = (4.3−1.1+2.4[stat] ± 1.4[syst])·1019 years.

Spectral shapes of forbidden argon β decays as background component for rare-event searches

The spectral shape of the electrons from the two first-forbidden unique ${\beta }^{-}$ decays of 39Ar and 42Ar were calculated for the first time to the next-to-leading order. Especially the spectral shape of the 39Ar decay can be used to characterize this background component for dark matter searches based on argon. Alternatively, due to the low thresholds of these experiments, the spectral shape can be investigated over a wide energy range with high statistics and thus allow a sensitive comparison with the theoretical predictions, in particular at low electron energies where the shape of the computed β spectrum has a slight dependence on the value of the weak axial-vector coupling constan…

Microscopic calculation of the electric decay properties of low-energy vibrational states in even110−120Cdisotopes

Consistent large-scale shell-model analysis of the two-neutrino ββ and single β branchings in 48Ca and 96Zr

Abstract Two-neutrino double-beta-decay matrix elements M 2 ν and single beta-decay branching ratios were calculated for 48Ca and 96Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For 48Ca the matrix element M 2 ν = 0.0511 is obtained, which is 5.5% smaller than the previously reported value of 0.0539. For 96Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value M 2 ν = 0.0747 with extreme single-state dominance. These matrix elements, combined with the available ββ-decay half-life data, yield effective values of the weak axial coupling which in turn are u…

Low-lying collective states inRu98–106isotopes studied using a microscopic anharmonic vibrator approach

Anharmonic features of the low-lying collective states in the $^{98--106}\mathrm{Ru}$ isotopes have been investigated systematically by using the microscopic anharmonic vibrator approach (MAVA). MAVA is based on a realistic microscopic $G$-matrix Hamiltonian, only slightly renormalized in the adopted large realistic single-particle spaces. This Hamiltonian is used to derive equations of motion for the mixing of one- and two-phonon degrees of freedom starting from collective phonons of the quasiparticle random-phase approximation. Analysis of the level energies and the electric quadrupole decays of the two-phonon type of states indicates that $^{100}\mathrm{Ru}$ can be interpreted as being a…

First-forbidden transitions in reactor antineutrino spectra

© 2019 American Physical Society. We study the dominant forbidden transitions in the antineutrino spectra of the fission actinides from 4 MeV onward using the nuclear shell model. Through explicit calculation of the shape factor, we show the expected changes in cumulative electron and antineutrino spectra. Relative to the allowed approximation this results in a minor decrease of electron spectra above 4 MeV, whereas an increase of several percent is observed in antineutrino spectra. We show that forbidden transitions dominate the spectral flux for most of the experimentally accessible range. Based on the shell model calculations we attempt a parametrization of forbidden transitions and prop…

Neutral- and charged-current supernova-neutrino scattering off116Cd

The interest in studies of neutrino–nucleus interactions goes beyond the study of the intrinsic properties of the neutrino extending to a variety of topics in astro-, nuclear and hadronic physics. We report in this paper the results of the calculations of the cross sections of inelastic neutrino–nucleus scattering off 116Cd, focusing on the incoherent neutral-current and charged-current processes, at energies typical of supernova neutrinos. The required nuclear wave functions for the participant initial and final states are constructed using the quasiparticle random-phase approximation in its charge-conserving mode and charge-changing mode. The response of 116Cd to supernova neutrinos and a…

Analysis of the intermediate-state contributions to neutrinoless double beta-minus decays

A comprehensive analysis of the structure of the nuclear matrix elements (NMEs) of neutrinoless double beta-minus decays to the 0^+ ground and first excited states is performed in terms of the contributing multipole states in the intermediate nuclei of neutrinoless double beta-minus transitions. We concentrate on the transitions mediated by the light (l-NMEs) Majorana neutrinos. As nuclear model we use the proton-neutron quasiparticle random-phase approximation (pnQRPA) with a realistic two-nucleon interaction based on the Bonn one-boson-exchange G matrix. In the computations we include the appropriate short-range correlations, nucleon form factors, higher-order nucleonic weak currents and …

Nuclear structure solving problems of fundamental physics

Nuclear-structure calculations are important inputs for solving problems of fundamental physics. Such problems are related with, e.g., neutrinos and dark-matter particles and their interactions with atomic nuclei. In this article the focus is directed to the important problem of the renormalization of the weak axial coupling gA and accurate treatment of β spectrum shapes. As particular applications of the spectral shapes the spectrum-shape method (SSM) and the hot topic of “reactor antineutrino anomaly” are introduced. peerReviewed

Neutrinoless ββ decays to excited 0+ states and the Majorana-neutrino mass

The nuclear matrix elements (NMEs) corresponding to the neutrinoless double-β (0νββ) decays to excited 0+ states of major experimental interest are calculated. All these decay transitions are electron emitting (0νβ−β− decays) and take place in the mass A = 76,82,96,100,110,116,124,130,136 nuclei. This work is an extension of our previous work [Phys. Rev. C 91, 024613 (2015)], where 0νββ decays to the ground states of the same nuclei were treated. We calculate the NMEs for transitions mediated by both the light (l-NMEs) and the heavy (h-NMEs) Majorana neutrinos. A higher-QRPA (quasiparticle random-phase approximation) framework, the multiple-commutator model, is adopted for the calculations,…

NUCLEAR-STRUCTURE EFFECTS ON DOUBLE BETA DECAYS TO 0+ STATES IN 76Ge

Neutrinoless double beta (0νββ) decay of 76 Ge to the ground state and first excited 0+ state in 76 Se is discussed in terms of the associated nuclear matrix elements. The effects arizing from the size of the single-particle model space and the occupancies of the individual orbits are discussed in the framework of the (higher) quasiparticle random-phase approximation with effective, G -matrix-derived nuclear forces. It is found that the orbital occupancies play a role for the size of the nuclear matrix element. Contrary to the ground-state transition the transition to the first excited 0+ state does not depend sensitively on the size of the model space.

The mass-hierarchy and CP-violation discovery reach of the LBNO long-baseline neutrino experiment.

The next generation neutrino observatory proposed by the LBNO collaboration will address fundamental questions in particle and astroparticle physics. The experiment consists of a far detector, in its first stage a 20 kt LAr double phase TPC and a magnetised iron calorimeter, situated at 2300 km from CERN and a near detector based on a high-pressure argon gas TPC. The long baseline provides a unique opportunity to study neutrino flavour oscillations over their 1st and 2nd oscillation maxima exploring the $L/E$ behaviour, and distinguishing effects arising from $\delta_{CP}$ and matter. In this paper we have reevaluated the physics potential of this setup for determining the mass hierarchy (M…

Second-forbidden nonunique β− decays of Na24 and Cl36 assessed by the nuclear shell model

We have performed a systematic study of the $logft$ values, shape factors, and electron spectra for the second-forbidden nonunique ${\ensuremath{\beta}}^{\ensuremath{-}}$ decays of $^{24}\mathrm{Na}({4}^{+})\ensuremath{\rightarrow}^{24}\mathrm{Mg}({2}^{+})$ and $^{36}\mathrm{Cl}({2}^{+}){\ensuremath{\rightarrow}}^{36}\mathrm{Ar}({0}^{+})$ transitions under the framework of the nuclear shell model. We have performed the shell model calculations in the $sd$ model space, using more recent microscopic effective interactions such as Daejeon16, chiral N3LO, and JISP16. These interactions are derived from the no-core shell model wave functions using Okubo-Lee-Suzuki transformation. For comparison,…

Calculated solar-neutrino capture rate for a radiochemical 205Tl-based solar-neutrino detector

Radiochemical experiments for low-energy solar-neutrino detection have been making headlines by exploiting the isotopes 37Cl and 71Ga. Such a very low-threshold measurement of this type can also be performed using 205Tl, which has been considered for decades for this purpose. A unique feature of this detector nucleus is the integration in the solar-neutrino flux over 106 of years owing to its long-living daughter 205Pb. In this Rapid Communication, we have calculated for the first time the cross section for the charged-current solar-neutrino scattering off 205Tl. Taking into account the solar-model-predicted neutrino fluxes and the electron-neutrino survival probabilities, a solar-neutrino …

Two-neutrinoββdecays and low-lying Gamow-Tellerβ−strength functions in the mass rangeA=70–176

Strength ofJπ=1+Gamow-Teller and isovector spin monopole transitions in double-β-decay triplets

In this work we study systematically the energetics and intensity distributions of Gamow-Teller (GT${}^{\ifmmode\pm\else\textpm\fi{}}$) and isovector spin monopole (IVSM${}^{\ifmmode\pm\else\textpm\fi{}}$) transitions from the ground states of the pairs ($^{76}\mathrm{Ge}$,$^{76}\mathrm{Se}$), ($^{82}\mathrm{Se}$,$^{82}\mathrm{Kr}$), ($^{100}\mathrm{Mo}$,$^{100}\mathrm{Ru}$), ($^{116}\mathrm{Cd}$,$^{116}\mathrm{Sn}$), ($^{128}\mathrm{Te}$,$^{128}\mathrm{Xe}$), ($^{130}\mathrm{Te}$,$^{130}\mathrm{Xe}$), and ($^{136}\mathrm{Xe}$,$^{136}\mathrm{Ba}$), of double-beta-decay initial and final nuclei, to the ${J}^{\ensuremath{\pi}}={1}^{+}$ excited states of the intermediate odd-odd nuclei $^{76}\…

Effects of orbital occupancies and spin–orbit partners II: decays of 76Ge, 82Se and 136Xe to first excited states

Abstract The neutrinoless double beta ( 0 ν β β ) decays of 76Ge, 82Se and 136Xe to the first excited 0 + states ( 0 1 + ) in 76Se, 82Kr and 136Ba are studied in calculations using different sizes of the single-particle model spaces and different occupancies of the individual orbits. This is a continuation of a similar study [J. Suhonen, O. Civitarese, Effects of orbital occupancies and spin–orbit partners on 0 ν β β -decay rates, Nucl. Phys. A 847 (2010) 207–232] of the 0 ν β β decays of 76Ge, 82Se, 128Te, 130Te and 136Xe to the ground states of 76Se, 82Kr, 128Xe, 130Xe and 136Ba. The nuclear matrix elements and half-lives of the decays to the 0 1 + states are calculated by the use of the …

Quenching of the weak axial-vector coupling strength in β decays

The quenching of the weak axial-vector coupling strength, gA, in nuclear β decays is reviewed. The quenching is discussed for both the Gamow–Teller decays and the forbidden β decays of different variants. Both the historical background and the present status are reviewed and compared with each other. Possible new measurements are urged, whenever relevant for determining the amount of gA quenching. peerReviewed

Value of the axial-vector coupling strength in $\beta$ and $\beta\beta$ decays: A review

In this review the quenching of the weak axial-vector coupling strength, $g_{\rm A}$, is discussed in nuclear $\beta$ and double-$\beta$ decays. On one hand, the nuclear-medium and nuclear many-body effects are separated, and on the other hand the quenching is discussed from the points of view of different many-body methods and different $\beta$-decay and double-$\beta$-decay processes. Both the historical background and the present status are reviewed and contrasted against each other. The theoretical considerations are tied to performed and planned measurements, and possible new measurements are urged, whenever relevant and doable. Relation of the quenching problem to the measurements of …

Detailed study of the neutral-current neutrino–nucleus scattering off the stable Mo isotopes

Abstract For neutrino detection and for various applications in astrophysics the knowledge of the nuclear responses to astrophysical neutrinos is crucial. Recent studies of neutrino interactions with the 100 Mo nucleus and the other stable molybdenum isotopes are important for the planned MOON (Mo Observatory of Neutrinos) detector. To this aim, in the present work we perform detailed nuclear structure calculations for the neutral-current neutrino–nucleus scattering off the stable molybdenum isotopes. We focus on the differential and total neutrino–nucleus cross sections as well as on flux averaged cross sections to various supernova neutrino spectra. We also propose a more efficient method…

Second-forbidden nonunique $$\beta ^-$$ decays of $$^{59,60}$$Fe:possible candidates for $$g_{\mathrm{A}}$$ sensitive electron spectral-shape measurements

In this work, we present a theoretical study of the electron spectral shapes for the second-forbidden nonunique $\beta^-$-decay transitions $^{59}\textrm{Fe}(3/2^-)\to\,^{59}\textrm{Co}(7/2^-)$ and $^{60}\textrm{Fe}(0^+)\to\,^{60}\textrm{Co}(2^+)$ in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete $0\hbar\omega$ calculation in the full $fp$ model space using the KB3G and GXPF1A effective interactions. When compared with the available data, these interactions predict the low-energy spectra and electromagnetic properties of the involved nuclei quite successfully. This success paves the way for the computations of the $\beta$-de…

Extended shell model calculation for even N = 82 isotones with a realistic effective interaction

The shell model within the $2s1d0g_{7/2}0h_{11/2}$ shell is applied to calculate nuclear structure properties of the even Z=52 - 62, N=82 isotones. The results are compared with experimental data and with the results of a quasiparticle random-phase approximation (QRPA) calculation. The interaction used in these calculations is a realistic two-body G-matrix interaction derived from modern meson-exchange potential models for the nucleon-nucleon interaction. For the shell model all the two-body matrix elements are renormalized by the $\hat{Q}$-box method whereas for the QRPA the effective interaction is defined by the G-matrix.

Neutrinoless ββ nuclear matrix elements using isovector spin-dipole Jπ = 2− data

Ground-state-to-ground-state neutrinoless double-beta (0νββ) decays in nuclei of current experimental interest are revisited. In order to improve the reliability of the nuclear matrix element (NME) calculations for the light Majorana-neutrino mode, the NMEs are calculated by exploiting the newly available data on isovector spin-dipole (IVSD) Jπ=2− giant resonances. In order to correctly describe the IVSD up to and beyond the giant-resonance region, the present computations are performed in extended no-core single-particle model spaces using the spherical version of the proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-…

Study of several double-beta-decaying nuclei using the renormalized proton-neutron quasiparticle random-phase approximation

The renormalized proton-neutron quasiparticle random-phase approximation model (RQRPA) has been used to calculate double-\ensuremath{\beta}-decay matrix elements and associated transition half-lives for two-neutrino double \ensuremath{\beta} decay of parent nuclei ${}^{76}\mathrm{Ge},$ ${}^{78}\mathrm{Kr},$ ${}^{82}\mathrm{Se},$ ${}^{96}\mathrm{Zr},$ ${}^{106}\mathrm{Cd},$ and ${}^{130}\mathrm{Te}$ to the ground state and excited one- and two-phonon states of their daughter nuclei. The results are compared to ordinary proton-neutron QRPA and experiments. In addition, the violation of the Ikeda sum rule in the RQRPA is examined and discussed.

High-Precision Q -Value Measurement Confirms the Potential of Cs135 for Absolute Antineutrino Mass Scale Determination

The ground-state-to-ground-state $\ensuremath{\beta}$-decay $Q$ value of $^{135}\mathrm{Cs}(7/{2}^{+})\ensuremath{\rightarrow}^{135}\mathrm{Ba}(3/{2}^{+})$ has been directly measured for the first time. The measurement was done utilizing both the phase-imaging ion-cyclotron resonance technique and the time-of-flight ion-cyclotron resonance technique at the JYFLTRAP Penning-trap setup and yielded a mass difference of 268.66(30) keV between $^{135}\mathrm{Cs}(7/{2}^{+})$ and $^{135}\mathrm{Ba}(3/{2}^{+})$. With this very small uncertainty, this measurement is a factor of 3 more precise than the currently adopted $Q$ value in the Atomic Mass Evaluation 2016. The measurement confirms that the f…

Impact of the quenching of gA on the sensitivity of 0νββ experiments

Detection of the neutrinoless $\ensuremath{\beta}\ensuremath{\beta}$ ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay is of high priority in the particle- and neutrino-physics communities. The detectability of this decay mode is strongly influenced by the value of the weak axial-vector coupling constant ${g}_{A}$. The recent nuclear-model analyses of $\ensuremath{\beta}$ and $\ensuremath{\beta}\ensuremath{\beta}$ decays suggest that the value of ${g}_{A}$ could be dramatically quenched, reaching ratios of ${g}_{A}^{\mathrm{free}}/{g}_{A}\ensuremath{\approx}4$, where ${g}_{A}^{\mathrm{free}}=1.27$ is the free, neutron-decay, value of ${g}_{A}$. The effects of this quenching ap…

Inelastic WIMP-nucleus scattering to the first excited state in125Te

The direct detection of dark matter constituents, in particular the weakly interacting massive particles (WIMPs), is considered central to particle physics and cosmology. In this paper we study transitions to the excited states, possible in some nuclei, which have sufficiently low lying excited states. Examples considered previously were the first excited states of $^{127}$I and $^{129}$Xe and $^{83}$Kr. Here we examine $^{125}$Te, which offers some advantages and is currently being considered as a target.In all these cases the extra signature of the gamma rays following the de-excitation of these states has definite advantages over the purely nuclear recoil and, in principle, such a signat…

Double-β decay within a consistent deformed approach

In this paper we present a timely application of the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA), designed to describe in a consistent way the 1+ Gamow-Teller states in oddodd deformed nuclei. For this purpose we apply a projection before variation procedure by using a singleparticle basis with projected angular momentum, provided by the diagonalization of a spherical mean field plus quadrupole-quadrupole interaction. The residual Hamiltonian contains pairing plus proton-neutron dipole terms in particle-hole and particle-particle channels, with constant strengths. As an example we describe the two-neutrino double-beta (2νββ) decay of 150Nd to the ground state…

In-beam γ -ray spectroscopy of low- and medium-spin levels in Po211

The structure of the low- and medium-spin levels of the $^{211}\mathrm{Po}$ nucleus have been studied with in-beam $\ensuremath{\gamma}$-ray spectroscopy with the $^{208}\mathrm{Pb}(\ensuremath{\alpha},n)^{211}\mathrm{Po}$ fusion-evaporation reaction. The level scheme was further extended with levels of the configurations $\ensuremath{\pi}{({h}_{9/2})}_{{2}^{+}\ensuremath{-}{4}^{+}}^{2}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{9/2}$, $\ensuremath{\pi}{({h}_{9/2})}_{{8}^{+}}^{2}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{9/2}$, $\ensuremath{\pi}{({h}_{9/2})}_{{2}^{+}\ensuremath{-}{4}^{+}}^{2}\ensuremath{\bigotimes}\ensuremath{\nu}{i}_{11/2}$, $\ensuremath{\pi}{({h}_{9/2})}_{{2}^{+}\ensurem…

Charged-current neutrino and antineutrino scattering offCd116described by Skyrme forces

We perform calculations of the cross sections for charged-current neutrino and antineutrino scattering off Cd-116 using ten different Skyrme interactions, at energies typical of supernova neutrinos. We use the quasiparticle random-phase approximation in its charged-changing mode (pnQRPA) to construct the required nuclear wave functions for the participant initial and final states. We compare the results of these calculations with the results of calculations based on the Bonn one-boson-exchange potential. The response of Cd-116 to supernova neutrinos is calculated by folding the obtained cross sections with suitably parametrized Fermi-Dirac distributions of the electron-neutrino and electron…

Structure of the (EC) decay strength function of Tb ( h)

The strength function for the (EC)-decay of ( h) is measured by the method of total -rays absorption. The same strength function is deduced from the analysis of the decay scheme and level scheme. The thus derived strength functions are in quite good agreement with each other. Also, theoretical calculation of by the microscopic quasiparticle-phonon model is carried out. The most characteristic properties of both the experimental and theoretical strength functions are pronounced resonances in .

Test of the proton-neutron random-phase approximation method within an extended Lipkin-type model

An extended Lipkin-Meshkov-Glick model for testing the proton-neutron random-phase approximation $(pn\mathrm{RPA})$ method is developed, taking into account explicitly proton and neutron degrees of freedom. Besides the proton and neutron single-particle terms two types of residual proton-neutron interactions, one simulating a particle-particle and the other a particle-hole interaction, are included in the model Hamiltonian so that the model is exactly solvable in an isospin $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{SU}(2)$ basis. The behavior of the first excited (collective) state obtained by (i) exact diagonalization of the Hamiltonian matrix and (ii) with the $\mathrm{pn}\mathrm{RPA}…

β-decay half-life of V 50 calculated by the shell model

In this work we survey the detectability of the β− channel of 50 23V leading to the first excited 2+ state in 50 24Cr. The electron-capture (EC) half-life corresponding to the transition of 50 23V to the first excited 2+ state in 50 22Ti had been measured earlier. Both of the mentioned transitions are 4th-forbidden non-unique. We have performed calculations of all the involved wave functions by using the nuclear shell model with the GXPF1A interaction in the full f-p shell. The computed half-life of the EC branch is in good agreement with the measured one. The predicted half-life for the β− branch is in the range ≈2 × 1019 yr whereas the present experimental lower limit is 1.5 × 1018 yr. We…

The gallium anomaly revisited

The gallium anomaly, i.e. the missing electron-neutrino flux from $^{37}$Ar and $^{51}$Cr electron-capture decays as measured by the GALLEX and SAGE solar-neutrino detectors, has been among us already for about two decades. We present here a new estimate of the significance of this anomaly based on cross-section calculations using nuclear shell-model wave functions obtained by exploiting recently developed two-nucleon interactions. The gallium anomaly of the GALLEX and SAGE experiments is found to be smaller than that obtained in previous evaluations, decreasing the significance from 3.0σ to 2.3σ. This result is compatible with the recent indication in favor of short-baseline ν¯e disappeara…

Renormalization of the weak hadronic current in the nuclear medium

The renormalization of the weak charge-changing hadronic current as a function of the reaction energy release is studied at the nucleonic level. We have calculated the average quenching factors for each type of current (vector, axial vector and induced pseudoscalar). The obtained quenching in the axial vector part is, at zero momentum transfer, 19% for the sd shell and 23% in the fp shell. We have extended the calculations also to heavier systems such as $^{56}$Ni and $^{100}$Sn, where we obtain stronger quenchings, 44% and 59%, respectively. Gamow--Teller type transitions are discussed, along with the higher order matrix elements. The quenching factors are constant up to roughly 60 MeV mom…

Solar neutrino detection in liquid xenon detectors via charged-current scattering to excited states

We investigate the prospects for real-time detection of solar neutrinos via the charged-current neutrino-nucleus scattering process in liquid xenon time projection chambers. We use a nuclear shell model, benchmarked with experimental data, to calculate the cross sections for populating specific excited states of the caesium nuclei produced by neutrino capture on $^{131}$Xe and $^{136}$Xe. The shell model is further used to compute the decay schemes of the low-lying $1^{+}$ excited states of $^{136}$Cs, for which there is sparse experimental data. We explore the possibility of tagging the characteristic de-excitation $\gamma$-rays/conversion electrons using two techniques: spatial separation…

Unified description of 2+_1 states within the deformed quasiparticle random-phase approximation

We describe low-lying collective states in deformed even-even nuclei within a deformed quasiparticle randomphase approximation (dQRPA) by using a single-particle basis with good angular momentum. The statistical factors, accounting for the level occupancy, appear in the dQRPA in a natural way as rotation coefficients that take the intrinsic system to the laboratory system. We have used our model by performing a systematic analysis of E2 transitions from the first 2+ state to the ground state for all superfluid nuclei in the range 50 < Z 100 by using a common charge polarization parameter χ = 0.2. In spite of its similarity to the QRPA, this method is able to describe in an unified way gross…

Mesonic enhancement of the weak axial charge and its effect on the half-lives and spectral shapes of first-forbidden J+↔J− decays

The effects of the enhancement of the axial-charge matrix element γ5 were studied in medium heavy and heavy nuclei for first-forbidden J+↔J− decay transitions using the nuclear shell model. Noticeable dependence on the enhancement ϵMEC of the axial-charge matrix element, as well as on the value of the axial-vector coupling constant gA was found in the spectral shapes of $^{93}$Y, $^{95}$Sr, and $^{97}$Y. The importance of the spectrum of $^{138}$Cs in the determination of gA is discussed. Half-life analyses in the A≈95 and A≈135 regions were done, and consistent results gA≈0.90, 0.75, and 0.65, corresponding to the three enhancement scenarios ϵMEC=1.4, 1.7, and 2.0, were obtained. Connectio…

Charge-exchange reactions on double-βdecaying nuclei populatingJπ=2−states

The $(\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{He},t)$ charge-exchange reaction populating ${J}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ states has been examined at 420 MeV incident energy for a series of double-$\ensuremath{\beta}$ decaying nuclei, i.e., $^{76}\mathrm{Ge}$, $^{82}\mathrm{Se}$, $^{96}\mathrm{Zr}$, $^{100}\mathrm{Mo}$, $^{128}\mathrm{Te}$, $^{130}\mathrm{Te}$, and $^{136}\mathrm{Xe}$. The measurements were carried out at the Grand Raiden spectrometer of the Research Center for Nuclear Physics at the University Osaka with typical spectral resolution of 30--40 keV. It is found that the charge-exchange reaction leading to ${2}^{\ensuremath{-}}$ spin-dipole states is selective to…

Nuclear matrix elements for neutrinoless ββ decays and spin-dipole giant resonances

Nuclear matrix element (NME) for neutrinoless ββ decay (DBD) is required for studying neutrino physics beyond the standard model by using DBD. Experimental information on nuclear excitation and decay associated with DBD is crucial for theoretical calculations of the DBD-NME. The spin-dipole (SD) NME for DBD via the intermediate SD state is one of the major components of the DBD-NME. The experimental SD giant-resonance energy and the SD strength in the intermediate nucleus are shown for the first time to be closely related to the DBD-NME and are used for studying the spin-isospin correlation and the quenching of the axial-vector coupling, which are involved in the NME. So they are used to he…

Search for double-\beta decay of \{106}Cd by using isotopically enriched \{106}CdWO_{4} crystal scintillator

A search for double β processes in 106Cd was carried out at the Gran Sasso National Laboratories of the INFN (Italy) by using a CdWO4 crystal scintillator (mass of 215 g) enriched in 106Cd up to 66%. After 6590 h of data taking, half-life limits on double beta processes in 106Cd were set at level of 1019 −1021 yr. A possible resonant enhancement of the 0ν2ε processes has also been estimated in the framework of the QRPA approach. peerReviewed

Nuclear matrix elements and the neutrinoless double beta decay

Systematics of the nuclear matrix elements related to the neutrinoless double beta ( 0 ν β β ) decay are discussed. The calculation of the related nuclear matrix elements in the framework of the proton-neutron quasiparticle random-phase approximation (pnQRPA) is analyzed. In particular, the extraction of a proper value of the proton-neutron particle-particle interaction parameter in this theory is addressed. The relevance of different multipoles in the multipole decomposition of the 0 ν β β matrix element is also discussed.

Unified description of 2+_1 states within the deformed quasiparticle random-phase approximation

We describe low-lying collective states in deformed even-even nuclei within a deformed quasiparticle random-phase approximation (dQRPA) by using a single-particle basis with good angular momentum. The statistical factors, accounting for the level occupancy, appear in the dQRPA in a natural way as rotation coefficients that take the intrinsic system to the laboratory system. We have used our model by performing a systematic analysis of E2 transitions from the first ${2}^{+}$ state to the ground state for all superfluid nuclei in the range $50lZ\ensuremath{\le}100$ by using a common charge polarization parameter $\ensuremath{\chi}=0.2$. In spite of its similarity to the QRPA, this method is a…

gA-driven shapes of electron spectra of forbidden β decays in the nuclear shell model

The evolution of the shape of the electron spectra of 16 forbidden β− decays as a function of gA was studied using the nuclear shell model in appropriate single-particle model spaces with established, well-tested nuclear Hamiltonians. The β spectra of 94Nb(6+)→94Mo(4+) and 98Tc(6+)→98Ru(4+) were found to depend strongly on gA, which makes them excellent candidates for the determination of the effective value of gA with the spectrum-shape method (SSM). A strong gA dependence is also seen in the spectrum of 96Zr(0+)→96Nb(6+). This decay could be used for determining the quenching of gA in sixth-forbidden decays in the future, when the measurement of the spectrum becomes experimentally feasibl…

Calculation of the neutrinoless ββ decay of 76Ge using a quark model with harmonic confinement

Abstract The half-life of the neutrinoless double beta decay of 76Ge into the ground state of 76Se is calculated in a relativistic quark confinement model. The proton-neutron quasi-particle random-phase approximation is used to evaluate the s- and p-wave nuclear matrix elements contained in the decay amplitude. We avoid the closure approximation and calculate the effective vector and axial-vector coupling constants of the hadronic currents using our quark model. In our formulation the recoil matrix element arises from the quark recoil in the decaying neutrons. The recoil and the p-wave effect are discussed and compared with other calculations. From the experimental lower bound for the decay…

Nuclear matrix elements of double beta decay from beta decay

The evaluation of the nuclear matrix elements (NME) of the two-neutrino double beta ($2\nu\beta\beta$) decay and neutrinoless double beta ($0\nu\beta\beta$) decay using the proton-neutron quasiparticle random-phase approximation (pnQRPA) is addressed. In particular, the extraction of a proper value of the proton-neutron particle-particle interaction parameter, $g_{\rm pp}$, of this theory is analyzed in detail. Evidence is shown, that it can be misleading to use the experimental half-life of the $2\nu\beta\beta$ decay to extract a value for $g_{\rm pp}$. Rather, arguments are given in favour of using the available data on single beta decay for this purpose.

Neutrino-nuclear responses for astro-neutrinos, single beta decays and double beta decays

Abstract Neutrino–nuclear responses associated with astro-neutrinos, single beta decays and double beta decays are crucial in studies of neutrino properties of interest for astro-particle physics. The present report reviews briefly recent studies of the neutrino–nuclear responses from both experimental and theoretical points of view in order to obtain a consistent understanding of the many facets of the neutrino–nuclear responses. Subjects discussed in this review include (i) experimental studies of neutrino–nuclear responses by means of single beta decays, charge-exchange nuclear reactions, muon- photon- and neutrino–nuclear reactions, and nucleon-transfer reactions, (ii) implications of a…

Occupation Number Representation

The first two chapters of this book presented angular momentum algebra as the basic tool of nuclear theory. That includes angular momentum coupling coefficients, spherical tensor operators and reduced matrix elements. In the preceding chapter we introduced the mean-field concept, along with associated many-nucleon wave functions, Slater determinants, describing configurations of non-interacting particles in mean-field single-particle orbitals.

The Mean-Field Shell Model

Chapter 3 introduced the notion of a nuclear mean field with associated singleparticle orbitals. It was explained how the single-particle energies can be obtained either by using an empirical Woods-Saxon potential or by the selfconsistent Hartree-Fock approach, extensively discussed in Chap. 4.

Review of the properties of the 0νβ−β−nuclear matrix elements

In this work we investigate general properties of the nuclear matrix elements (NMEs) related to the neutrinoless double ?? decays (0????? decays) of several nuclei of interest for double-beta-decay experiments. A summary of the values of the NMEs calculated along the years by the Jyv?skyl??La Plata collaboration is given. These NMEs are compared with those of the other available calculations and general conclusions are drawn based on these comparisons.

Systematics of the α-decay to rotational states

We analyze \ensuremath{\alpha} decays to rotational states in even-even nuclei by using the stationary coupled channels approach. Collective excitations are described by the rigid rotator model. The \ensuremath{\alpha}-nucleus interaction is given by a double folding procedure using M3Y plus Coulomb nucleon-nucleon forces. We use a harmonic oscillator repulsive potential with one independent parameter, to simulate the Pauli principle. The decaying state is identified with the first resonance inside the resulting pocketlike potential. The energy of the resonant state is adjusted to the experimental Q value by using the depth of the repulsion. We obtained a good agreement with existing experi…

Shell Model Description of Spin-Dependent Elastic and Inelastic WIMP Scattering off 119Sn and 121Sb

In this work, we calculate the spin structure functions for spin-dependent elastic and inelastic WIMP scattering off 119Sn and 121Sb. Estimates for detection rates are also given. 119Sn and 121Sb are amenable to nuclear structure calculations using the nuclear shell model (NSM). With the possible exception of 201Hg, they are the only such nuclei still unexplored theoretically for their potential of inelastic WIMP scattering to a very low excited state. The present calculations were conducted using a state-of-the-art WIMP–nucleus scattering formalism, and the available effective NSM two-body interactions describe the spectroscopic properties of these nuclei reasonably well. Structure functio…

Second-forbidden nonunique β− decays of 59,60Fe:possible candidates for gA sensitive electron spectral-shape measurements

In this work, we present a theoretical study of the electron spectral shapes for the second-forbidden nonunique β−-decay transitions 59Fe(3/2−)→59Co(7/2−) and 60Fe(0+)→60Co(2+) in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete 0ℏω calculation in the full fp model space using the KB3G and GXPF1A effective interactions. When compared with the available data, these interactions predict the low-energy spectra and electromagnetic properties of the involved nuclei quite successfully. This success paves the way for the computations of the β-decay properties, and comparison with the available data. We have computed the electron spec…

$^{113}$Cd $\beta$-decay spectrum and $g_{\rm A}$ quenching using spectral moments

We present an alternative analysis of the $^{113}$Cd $\beta$-decay electron energy spectrum in terms of spectral moments $\mu_n$, corresponding to the averaged values of $n^{\rm th}$ powers of the $\beta$ particle energy. The zeroth moment $\mu_0$ is related to the decay rate, while higher moments $\mu_n$ are related to the spectrum shape. The here advocated spectral-moment method (SMM) allows for a complementary understanding of previous results, obtained using the so-called spectrum-shape method (SSM) and its revised version, in terms of two free parameters: $r=g_{\rm A}/g_{\rm V}$ (the ratio of axial-vector to vector couplings) and $s$ (the small vector-like relativistic nuclear matrix e…

Q values of the 76Ge and 100Mo double-beta decays

Abstract Penning trap measurements using mixed beams of 76Ge–76Se and 100Mo–100Ru have been utilized to determine the double-beta decay Q-values of 76Ge and 100Mo with uncertainties less than 200 eV. The value for 76Ge, 2039.04(16) keV is in agreement with the published SMILETRAP value, 2039.006(50) keV. The new value for 100Mo, 3034.40(17) keV is 30 times more precise than the previous literature value, sufficient for the ongoing neutrinoless double-beta decay searches in 100Mo. Moreover, the precise Q-value is used to calculate the phase-space integrals and the experimental nuclear matrix element of double-beta decay.

Double beta decay: an interface between nuclear, particle and atomic physics

General properties of the nuclear matrix elements (NMEs) related to the various modes of neutrinoless double β decays are examined and analyzed. The decays include the electron-emitting double beta-minus decays β−β− and the various positron-emitting/electron capture decays. Special interest is devoted to the neutrinoless double electron capture decay with a resonance condition.

Electron spectra in forbidden β decays and the quenching of the weak axial-vector coupling constant gA

Evolution of the electron spectra with the effective value of the weak axial-vector coupling constant gA was followed for 26 first-, second-, third-, fourth- and fifth-forbidden β− decays of odd-A nuclei by calculating the involved nuclear matrix elements (NMEs) in the framework of the microscopic quasiparticle-phonon model (MQPM). The next-to-leading-order terms were included in the β-decay shape factor of the electron spectra. The spectrum shapes of third- and fourth-forbidden nonunique decays were found to depend strongly on the value of gA, while first- and second-forbidden decays were mostly unaffected by the tuning of gA. The gA-driven evolution of the normalized β spectra was found t…

Analysis of the Intermediate-State Contributions to Neutrinoless Double β− Decays

A comprehensive analysis of the structure of the nuclear matrix elements (NMEs) of neutrinoless double beta-minus (0νβ-β-) decays to the0+ground and first excited states is performed in terms of the contributing multipole states in the intermediate nuclei of0νβ-β-transitions. We concentrate on the transitions mediated by the light (l-NMEs) Majorana neutrinos. As nuclear model we use the proton-neutron quasiparticle random-phase approximation (pnQRPA) with a realistic two-nucleon interaction based on the Bonn one-boson-exchangeGmatrix. In the computations we include the appropriate short-range correlations, nucleon form factors, and higher-order nucleonic weak currents and restore the isospi…

Nuclear matrix elements for 0νββ decays with light or heavy Majorana-neutrino exchange

We compute the nuclear matrix elements (NMEs) corresponding to the neutrinoless double beta (0νββ) decays of nuclei which attract current experimental interest. We concentrate on ground-state-to-ground-state decay transitions mediated by light (l-NMEs) or heavy (h-NMEs) Majorana neutrinos. The computations are done in realistic single-particle model spaces using the proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange G matrix. Both the l-NMEs and the h-NMEs include the appropriate short-range correlations, nucleon form factors, and higher-order nucleonic weak currents. In addition, both types of NMEs are correct…

Particle-Hole Excitations and the Tamm-Dancoff Approximation

This chapter describes the configuration mixing of particle-hole excitations in doubly magic nuclei. The discussion is confined to one-particle-one-hole excitations within the simplest scheme of configuration mixing, namely the Tamm-Dancoff approximation (TDA). We show that the TDA arises from a variational principle and leads to diagonalization of the residual Hamiltonian in a basis of particle-hole excitations of the particle-hole vacuum.

SEMICLASSICAL DESCRIPTION OF SPIN EXCITATIONS OF THE PARTICLE-CORE INTERACTION SYSTEM

A model Hamiltonian describing a nucleon moving in a shifted oscillator well and inter-acting with a harmonic core through a quadrupole-quadrupole term is semiclassically treated. The solutions of the linearised equations of motion are quantised by the Bohr-Sommerfeld procedure. Among the four RPA modes, there is one which corresponds to the harmonic vibration of the spin degree of freedom. This mode is analogous to the spin wave mode describing a system of interacting spins placed in a magnetic field. The state describes a harmonic wobbling motion around a stationary state belonging to the ground rotational band.

Confirmation of gA quenching using the revised spectrum-shape method for the analysis of the 113Cd β-decay as measured with the COBRA demonstrator

In this article we present an updated spectrum-shape analysis of the $^{113}$Cd fourfold forbidden non-unique $\beta$-decay transition in order to address the quenching of the weak axial-vector coupling $g_{\rm A}$ in low-momentum exchange nuclear processes. The experimental data were collected in a dedicated low-threshold run with the COBRA demonstrator at the LNGS and resulted in 44 individual $^{113}$Cd spectra. These data are evaluated in the context of three nuclear model frameworks based on a revised version of the spectrum-shape method and the conserved vector current hypothesis. The novel idea devised in the present work is to fit the value of the small relativistic nuclear matrix e…

Search for2βdecays of96Ru and104Ru by ultralow-background HPGeγspectrometry at LNGS: Final results

An experiment to search for double-$\ensuremath{\beta}$ decay processes in ${}^{96}$Ru and ${}^{104}$Ru, which are accompanied by $\ensuremath{\gamma}$ rays, has been realized in the underground Gran Sasso National Laboratories of the I.N.F.N. (Italy). Ruthenium samples with masses of $\ensuremath{\approx}$0.5--0.7 kg were measured with the help of ultralow-background high-purity Ge $\ensuremath{\gamma}$-ray spectrometry. After 2162 h of data taking the samples were deeply purified to reduce the internal contamination of ${}^{40}$K. The last part of the data has been accumulated over 5479 h. New improved half-life limits on $2{\ensuremath{\beta}}^{+}/\ensuremath{\varepsilon}{\ensuremath{\be…

Microscopic description of low-lying two-phonon states: Electromagnetic transitions

Microscopic description of low-lying two-phonon states in even-even nuclei is introduced. The main building blocks are the quasiparticle random-phase approximation (QRPA) phonons. A realistic microscopic nuclear Hamiltonian, based on the Bonn one-boson-exchange potential, is diagonalized in a basis containing one-phonon and two-phonon components, coupled to a given angular momentum and parity. The QRPA equations are directly used in deriving the equations of motion for the two-phonon states. The Pauli principle is taken into account by diagonalizing the metric matrix and discarding the zero-norm states. The electromagnetic transition matrix elements are derived in terms of the metric matrix…

Possible detection of the doubleβ+/electron-capture decay

The two-neutrino double [beta] decay matrix elements of [sup 58]Ni, [sup 96]Ru, [sup 106]Cd, and [sup 136]Ce are calculated in the framework of the quasiparticle random phase approximation and the corresponding double [beta][sup +]/electron-capture (EC) decay ([beta][sup +][beta][sup +]/[beta][sup +]EC/ECEC) half-lives are estimated. The calculated ground-state-to-ground-state half-lives range from 3.9[times]10[sup 23] to 6.4[times]10[sup 19] yr indicating that the double [beta][sup +]/EC decay could, in principle, be detected using currently known experimental techniques.

Comparative analysis of muon-capture and 0νββ -decay matrix elements

Average matrix elements of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of current experimental interest are computed and compared with the corresponding energy and multipole decompositions of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements (NMEs). The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ NMEs include the appropriate short-range correlations, nuclear form factors, and higher-order nucleonic weak cu…

Simultaneous analysis of neutrinoless double beta decay and LHC pp-cross sections: limits on the left-right mixing angle

The extension of the Standard Model of electroweak interactions, to accommodate massive neutrinos and/or right-handed currents, is one of the fundamental questions to answer in the cross-field of particle and nuclear physics. The consequences of such extensions would reflect upon nuclear decays, like the very exotic nuclear double-beta-decay, as well as upon high-energy proton-proton reactions of the type performed at the LHC accelerator. In this talk we shall address this question by looking at the results reported by the ATLAS and CMS collaborations, where the excitation and decay of a heavy-mass boson may be mediated by a heavy-mass neutrino in proton-proton reactions leading to two jets…

On the decay of theJπ= 11/2−,T1/2= 38.9 h isomer in133Ba: search for the E5 transition and verification of the EC branch

International audience; This paper presents a search for the competing 11/2 − → 1/2 + E5 branch to the main 11/2 − → 3/2 + M4 transition from the T 1/2 = 39 h, J π = 11/2 − isomeric state in 133 Ba. An upper limit of 1.8 * 10 −5 could be established for the E5/M4 intensity ratio. In addition a long-standing controversy in the EC-decay of the same isomer was resolved: only one EC branch to the 11/2 + state in 133 Cs was observed. The shell-model structures of the involved states in 133 Ba and 133 Cs were studied with the microscopic quasiparticle-phonon model (MQPM). Good agreement with the decay rates B(λ) was obtained. In particular, the B(M4) value is well reproduced and further only one …

Systematic QRPA study of β− and decay transitions to excited states of 110–114Cd and 114–122Sn

Abstract A systematic study of the β− and β + EC decay transitions of odd-odd nuclei into the ground state, first excited quadrupole state (21+) and the two-quadrupole-phonon triplet (02ph+, 22ph+ and 42ph+) of the final even-even nuclei 110–114Cd and 114–122Sn is performed. In these cases the states of the even-even nucleus are fed both by β− as well as β + EC decay transitions of the two adjacent double-odd nuclei. Such exceptional circumstances help to study the β− and β + EC Gamow-Teller decay on equal footing starting from the predictions of the combined QRPA and pn-QRPA theories. In addition, the differences between the QRPA and the QTDA predictions are discussed. The present approach…

Renormalized Proton-Neutron Quasiparticle Random-Phase Approximation and Its Application to Double Beta Decay

A self-consistent method of treating excitations of the proton-neutron quasiparticle random-phase approximation is presented. The non-self-consistent methods violate the Pauli exclusion principle and lead to an eventual collapse of the ground state. This behavior renders a reliable calculation of the nuclear matrix elements, relevant for the prediction of double-beta-decay half-lives, difficult. The present formalism promotes the Pauli exclusion principle and avoids the collapse of the double-beta-decay matrix elements. We have applied this formalism to the double beta decay of ${}^{100}$Mo.

Value of the Axial-Vector Coupling Strength in β and ββ Decays : A Review

In this review the quenching of the weak axial-vector coupling constant, $g_{\rm A}$, is discussed in nuclear $\beta$ and double-$\beta$ decays. On one hand, the nuclear-medium and nuclear many-body effects are separated, and on the other hand the quenching is discussed from the points of view of different many-body methods and different $\beta$-decay and double-$\beta$-decay processes. Both the historical background and the present status are reviewed and contrasted against each other. The theoretical considerations are tied to performed and planned measurements, and possible new measurements are urged, whenever relevant and doable. Relation of the quenching problem to the measurements of …

Measurement of theββDecay Half-Life ofTe130with the NEMO-3 Detector

This Letter reports results from the NEMO-3 experiment based on an exposure of 1275 days with 661g of 130Te in the form of enriched and natural tellurium foils. With this data set the double beta decay rate of 130Te is found to be non-zero with a significance of 7.7 standard deviations and the half-life is measured to be T1/2 = (7.0 +/- 0.9(stat) +/- 1.1(syst)) x 10^{20} yr. This represents the most precise measurement of this half-life yet published and the first real-time observation of this decay.

Competition Between Beta and Double Beta Decay in 48Ca and 96Zr

Highly forbidden beta decays of 48Ca and 96Zr are studied and their relative importance as compared to the double beta decay of these nuclei is evaluated. 48Ca and 96Zr are the only naturally occurring nuclei in which these processes can occur simultaneously. Although usually ordinary beta decay overwhelms double beta decay unless the former is energetically forbidden, in these cases the high degree of forbiddenness and small release of kinetic energy makes the half-lives of these modes comparable to each other.

Charge-exchange reactions on double-β decaying nuclei populating Jπ=2− states

The (3He,t) charge-exchange reaction populating Jπ=2− states has been examined at 420 MeV incident energy for a series of double-β decaying nuclei, i.e., 76Ge, 82Se, 96Zr, 100Mo, 128Te, 130Te, and 136Xe. The measurements were carried out at the Grand Raiden spectrometer of the Research Center for Nuclear Physics at the University Osaka with typical spectral resolution of 30–40 keV. It is found that the charge-exchange reaction leading to 2− spin-dipole states is selective to the στ part of the interaction much similar to the observed selectivity to Gamow-Teller transitions. In the present case, the ΔL=1 peak cross sections at finite momentum transfers are used to extract the spin-isospin pa…

Nuclear Two-Body Interaction and Configuration Mixing

In previous chapters the nucleus was described as a collection of non-interacting nucleons in a mean-field potential. The wave function of a nuclear state was taken to be a Slater determinant corresponding to a definite way of placing the valence nucleons in the mean-field single-particle orbitals. In this way the energy of a nuclear state was fully determined by the energies of the occupied single-particle orbitals.

Neutrinoless ββ nuclear matrix elements using isovector spin-dipole Jπ=2− data

Level structure of 99Nb

The β decay of 97Sr to 97Y has been investigated using ion-guide on-line mass separation and a 10 Ge-detector array to record γ−γ coincidences to a detection limit well below that of former studies. Similarities are found in the β-decay patterns of 99Zr and of its isotone 97Sr and also in the γ-ray decay rates and branchings of the corresponding levels in their respective daughters 99Nb and 97Y. This indicates a persisting influence of the d5/2 neutron shell closure for 99Nb. The level structure of 99Nb and the β-feeding pattern are discussed in the frame of the interacting boson-fermion plus broken pair model and the microscopic quasiparticle phonon model.

On the interdependence between ground and one-phonon RPA states

Working within a schematic model and in a boson formalism, we provide a descrip tion of the ground and first-excited states of a nuclear system in terms of two independent phonon operators. The description reveals itself quite effective in reproducing the energies of the states. A comparison between these two phonon operators allows us to localize a region where a correct description of these states is compatible with the Random Phase Approximation (RPA) requirement of a single phonon. This region is found to coincide approximately with that spanned by the standard RPA. Outside this region, the two phonons start differing rapidly therefore making the application of the RPA scheme impossible…

The response of (95,97)Mo to supernova neutrinos

Knowledge about nuclear responses to neutrinos is essential for both astrophysical applications and studies of neutrino properties. We perform in this paper calculations of the cross sections for neutral-current neutrino scattering off the odd A = 95,97 Mo isotopes for energies appropriate for the detection of supernova neutrinos. Both the incoherent and coherent contributions to the cross sections are evaluated. The prominently contributing nuclear final states are identified and analysed. We employ the microscopic quasiparticle-phonon model (MQPM) to construct the wave functions of the initial and final nuclear states. The response of the aforementioned nuclei to supernova neutrinos are c…

Neutrino-nuclear responses and the effective value of weak axial coupling

On-going measurements of the neutrinoless ββ decay are accompanied by the growing interest in computing the values of the associated nuclear matrix elements. In order to extract the neutrino mass from the potentially measured ββ half-lives one not only needs to know the values of the nuclear matrix elements but also the effective value of the weak axial-vector coupling constant gA since its value affects strongly the ββ half-lives. In order to gain knowledge of the possible quenching of gA in finite nuclei one can study, e.g., allowed Gamow-Teller β decays. A new promising tool to study the quenching are the measurements of ordinary muon capture transitions for which the range of momentum e…

Charged-current neutrino-nucleus scattering off 95,97^Mo

Background: Reliable cross sections for the neutrino-nucleus scattering off relevant nuclei for supernova neutrinos are essential for various applications in neutrino physics and astrophysics (e.g., supernova mechanisms). Studies of the nuclear responses for the stable molybdenum isotopes are of great interest for the planned MOON (Mo Observatory of Neutrinos) experiment.Purpose: The purpose of the present work is, thus, to perform a detailed study of the charged-current nuclear responses to supernova neutrinos for the stable odd molybdenum isotopes. A special effort will be devoted to discuss in detail the structures of the most relevant final states in the corresponding proton-odd nucleus…

Charged-current neutrino-nucleus scattering off Xe isotopes

Xenon detectors are used in the search for dark matter and neutrinoless double-beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta})$. As the next-generation detectors reach masses in the ton scale, neutrinos from astrophysical sources are soon predicted to become background in such detectors. Theoretical predictions of neutrino scattering cross sections and information of nuclear structure effects therein are crucial in accounting for the background. We perform calculations for differential and total cross sections of charged-current neutrino scattering off the most abundant xenon isotopes. The nuclear-structure calculations are made in the proton-neutron quasiparticle random…

Detailed studies of $^{100}$Mo two-neutrino double beta decay in NEMO-3

The full data set of the NEMO-3 experiment has been used to measure the half-life of the two-neutrino double beta decay of $^{100}$Mo to the ground state of $^{100}$Ru, $T_{1/2} = \left[ 6.81 \pm 0.01\,\left(\mbox{stat}\right) ^{+0.38}_{-0.40}\,\left(\mbox{syst}\right) \right] \times10^{18}$ y. The two-electron energy sum, single electron energy spectra and distribution of the angle between the electrons are presented with an unprecedented statistics of $5\times10^5$ events and a signal-to-background ratio of ~80. Clear evidence for the Single State Dominance model is found for this nuclear transition. Limits on Majoron emitting neutrinoless double beta decay modes with spectral indices of …

Microscopic study of muon-capture transitions in nuclei involved in double-beta-decay processes

Abstract Total and partial ordinary muon-capture (OMC) rates to 1 + and 2 − states are calculated in the framework of the proton–neutron quasiparticle random-phase approximation (pnQRPA) for several nuclei involved in double-beta-decay processes. The aim is to obtain information on intermediate states involved in double-beta-decay transitions having these nuclei as either daughter or parent nuclei. It is found that the OMC observables, just like the 2 νββ -decay amplitudes, strongly depend on the particle–particle part of the proton–neutron interaction. First experiments measuring the partial OMC rates for nuclei involved in double beta decays have recently been performed.

Neutrinoless Double-Electron Capture

Double-beta processes play a key role in the exploration of neutrino and weak interaction properties, and in the searches for effects beyond the Standard Model. During the last half century many attempts were undertaken to search for double-beta decay with emission of two electrons, especially for its neutrinoless mode ($0\nu2\beta^-$), the latter being still not observed. Double-electron capture (2EC) was not in focus so far because of its in general lower transition probability. However, the rate of neutrinoless double-electron capture ($0\nu2$EC) can experience a resonance enhancement by many orders of magnitude in case the initial and final states are energetically degenerate. In the re…

Double beta decay versus cosmology: Majorana CP phases and nuclear matrix elements

We discuss the relation between the absolute neutrino mass scale, the effective mass measured in neutrinoless double beta decay, and the Majorana CP phases. Emphasis is placed on estimating the upper bound on the nuclear matrix element entering calculations of the double beta decay half life. Consequently, one of the Majorana CP phases can be constrained when combining the claimed evidence for neutrinoless double beta decay with the neutrino mass bound from cosmology.

Nuclear matrix elements for resonant neutrinoless double electron capture

The resonant neutrinoless double electron-capture (R0νECEC) is discussed from the point of view of the resonance condition and the involved nuclear matrix elements. A brief outline of the involved theory framework is given. The present status of measurements of the involved atomic masses and possible R0νECEC candidates is reviewed. peerReviewed

Spin-multipole nuclear matrix elements in thepnquasiparticle random-phase approximation: Implications forβandββhalf-lives

Half-lives for 148 potentially measurable 2nd-, 3rd-, 4th-, 5th-, 6th-, and 7th-forbidden unique beta transitions are predicted. To achieve this, the ratio of the nuclear matrix elements (NMEs), calculated by the proton-neutron quasiparticle random-phase approximation (pnQRPA), ${M}_{\mathrm{pnQRPA}}$, and a two-quasiparticle (two-qp) model, ${M}_{\mathrm{qp}}$, is studied and compared with earlier calculations for the allowed Gamow-Teller (GT) ${1}^{+}$ and first-forbidden spin-dipole (SD) ${2}^{\ensuremath{-}}$ transitions. The present calculations are done using realistic single-particle model spaces and $G$-matrix based microscopic two-body interactions. In terms of the ratio $k={M}_{\m…

Light-neutrino mass spectrum, nuclear matrix elements, and the observability of neutrinoless ββ decay

Parameters which describe neutrino flavor oscillations and neutrino mixing mechanisms, obtained from the analysis of the Sudbury Neutrino Observatory (SNO), Super-Kamiokande (SK), CHOOZ, KamLAND and WMAP data, are used to calculate upper limits of the effective neutrino mass 〈mν〉 relevant for the neutrinoless double-beta decay (0νββ). The observability of planned 0νββ experiments, and the present status of the decay of 76Ge are discussed within different light-neutrino mass spectra and by presenting a systematics on the available nuclear matrix elements.

Two-neutrino double-beta decay of76Ge in an anharmonic vibrator approach

We have calculated the nuclear matrix element of two-neutrino double-beta (2???) decay of 76Ge by using the proton?neutron microscopic anharmonic vibrator approach (pnMAVA). In the pnMAVA the wavefunctions of the intermediate 1+ states in 76As have a one-phonon part containing the proton?neutron QRPA (pnQRPA) phonons and a two-phonon part built by coupling the pnQRPA and charge-conserving QRPA phonons. We compare the measured GT? and GT+ Gamow?Teller strength functions with the measured ones. The two-phonon components of the pnMAVA wavefunctions cause the pnQRPA strength to redistribute over a finite energy range. This has only a small effect on the value 2??? nuclear matrix element. This s…

Neutral-Current Neutrino-Nucleus Scattering off Xe Isotopes

Large liquid xenon detectors aiming for dark matter direct detection will soon become viable tools also for investigating neutrino physics. Information on the effects of nuclear structure in neutrino-nucleus scattering can be important in distinguishing neutrino backgrounds in such detectors. We perform calculations for differential and total cross sections of neutral-current neutrino scattering off the most abundant xenon isotopes. The nuclear structure calculations are made in the nuclear shell model for elastic scattering, and also in the quasiparticle random-phase approximation (QRPA) and microscopic quasiparticle phonon model (MQPM) for both elastic and inelastic scattering. Using suit…

Schematic and realistic model calculations of the isovector spin monopole excitations in 116In

The excitation of Gamow-Teller (GT) and isovector spin monopole (IVSM) Jπ=1+ modes in 116In by (p,n) and (n,p) charge-exchange reactions on 116Cd and on 116Sn, respectively, is studied within the framework of the quasiparticle random-phase approximation. The calculations have been performed both for schematic and realistic model situations. It appears that the calculated admixture of the IVSM and Gamow-Teller (GT) Jπ=1+ excitations is negligible and that the contribution to the strength above 20 MeV of excitation energy, in 116In, is due to the IVSM (σr2t ±) mode. This result is compared with the recent experimental work that reported a large amount of both (p,n) and (n,p) strength beyond 1…

Charge-changing transitions in an extended Lipkin-type model

Charge-changing transitions are considered in an extended Lipkin-Meshkov-Glick (LMG) model taking into account explicitly the proton and neutron degrees of freedom. The proton and neutron Hamiltonians are taken to be of the LMG form and, in addition, a residual proton-neutron interaction is included. Model charge-changing operators and their action on eigenfunctions of the model Hamiltonian are defined. Transition amplitudes of these operators are calculated using exact eigenfunctions and then the RPA approximation. The best agreement between the two kinds of calculation is obtained when the correlated RPA ground state, instead of the uncorrelated HF ground state, is employed and when the p…

Statistical analysis of β decays and the effective value of gA in the proton-neutron quasiparticle random-phase approximation framework

We perform a Markov chain Monte Carlo (MCMC) statistical analysis of a number of measured groundstate-to-ground-state single β+/electron-capture and β− decays in the nuclear mass range of A = 62–142. The corresponding experimental comparative half-lives (log f t values) are compared with the theoretical ones obtained by the use of the proton-neutron quasiparticle random-phase approximation (pnQRPA) with G-matrixbased effective interactions. The MCMC analysis is performed separately for 47 isobaric triplets and 28 more extended isobaric chains of nuclei to extract values and uncertainties for the effective axial-vector coupling constant gA in nuclear-structure calculations performed in the p…

Extended phonon projection model for nuclear collective motion

The subject of this work is the formulation and application of a geometrical collective model with comparison to experiment and with other models dealing with low energy nuclear structure. This model, called the EPM(= Extended Phonon-Projection Model) avoids the use of an extensive diagonalization basis in the deformednucleus region by cleverly choosing a three dimensional model space with capability of producing the gross features encountered in moving from spherical vibrator nuclei to almost rigid rotors of deformed shapes. The use of deformed oriented states calls for angular momentum projection to restore the broken angular momentum conservation in the oriented wavefunctions. After havi…

Microscopic calculation of the LSP detection rates for the 71Ga, 73Ge and 127I dark-matter detectors

Abstract We have investigated the nuclear-structure details of the cross sections for the elastic scattering of Lightest Supersymmetric Particles (LSPs) from the promising dark-matter detectors 71 Ga, 73 Ge and 127 I. The associated LSP detection sensitivities have been obtained by a folding procedure for several recently proposed SUSY models with different scalar and axial-vector characteristics. For the nuclear problem, a realistic microscopic Hamiltonian has been used within realistic model spaces. The diagonalization of this Hamiltonian has been done by using the Microscopic Quasiparticle–Phonon Model (MQPM), suitable for description of spectroscopic properties of medium-heavy and heavy…

Mixing of Two-Quasiparticle Configurations

In this chapter we discuss configuration mixing of two-quasiparticle states. It is caused by the residual interaction remaining beyond the quasiparticle mean field defined in Chap. 13. We derive the equations of motion by the EOM method developed in Sect. 11.1. To accomplish this we need to express the residual Hamiltonian in terms of quasiparticles.

Effective axial-vector strength within proton-neutron deformed quasiparticle random-phase approximation

We use the available experimental Gamow-Teller β− and β+/EC (electron-capture) decay rates between 0+ and 1+ ground states in neighboring even-even and odd-odd nuclei, combined with 2νββ half-lives, to analyze the influence of the nuclear environment on the weak axial-vector strength gA. For this purpose, the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA), with schematic dipole residual interaction is employed. The Hamiltonian contains particle-hole (ph) and particle-particle (pp) channels with mass-dependent strengths. In deriving the equations of motion we use a self-consistent procedure in terms of a single-particle basis with projected angular momentum provi…

Impact of the quenching of gA on the sensitivity of 0νββ experiments

Detection of the neutrinoless ββ (0νββ) decay is of high priority in the particle- and neutrino-physics communities. The detectability of this decay mode is strongly influenced by the value of the weak axial-vector coupling constant gA. The recent nuclear-model analyses of β and ββ decays suggest that the value of gA could be dramatically quenched, reaching ratios of gfree A /gA ≈ 4, where gfree A = 1.27 is the free, neutron-decay, value of gA. The effects of this quenching appear devastating for the sensitivity of the present and future 0νββ experiments since the fourth power of this ratio scales the 0νββ half-lives. This, in turn, could lead to some two orders of magnitude less sensitivit…

Two-neutrino ββ decay to excited states. The 0+ → 2+ decay of 136Xe

Abstract A method to calculate the two-neutrino double beta decay (2vββ) to one-phonon excited states is presented. The formalism, which is based on the quasiparticle random phase approximation, is applied to the description of the 2vββ transition 136Xe (0 g.e. + ) → 136 Ba (2 1 + ). It is shown that the participant matrix element is not suppressed by the inclusion of renormalized particle-particle interactions.

High-precision mass measurements and production of neutron-deficient isotopes using heavy-ion beams at IGISOL

An upgraded ion-guide system for the production of neutron-deficient isotopes with heavy-ion beams has been commissioned at the IGISOL facility with an $^{36}\mathrm{Ar}$ beam on a $^{\mathrm{nat}}\mathrm{Ni}$ target. It was used together with the JYFLTRAP double Penning trap to measure the masses of $^{82}\mathrm{Zr}, ^{84}\mathrm{Nb}, ^{86}\mathrm{Mo}, ^{88}\mathrm{Tc}$, and $^{89}\mathrm{Ru}$ ground states and the isomeric state $^{88}\mathrm{Tc}^{m}$. Of these, $^{89}\mathrm{Ru}$ and $^{88}\mathrm{Tc}^{m}$ were measured for the first time. The precision of measurements of $^{82}\mathrm{Zr}, ^{84}\mathrm{Nb}$, and $^{88}\mathrm{Tc}$ was significantly improved. The literature value for $^…

Neutrinoless double beta-plus/EC decays

The relation of neutrino masses to neutrino oscillations and the nuclear double beta decay is highlighted. In particular, the neutrinoless 𝛽+ 𝛽+, 𝛽+EC, and resonant ECEC decays are investigated using microscopic nuclear models. Transitions to the ground state and excited 0+ states are analyzed. Systematics of the related nuclear matrix elements are studied and the present status of the resonant ECEC decays is reviewed. peerReviewed

Extracting information on the decays from the decays

Abstract We have analyzed the relation between the two-neutrino ( 2 ν β β ) and neutrinoless ( 0 ν β β ) double beta decays of 76Ge, 82Se, 100Mo, and 116Cd. The relevant nuclear matrix elements have been calculated by using the proton–neutron quasiparticle random-phase approximation (pn-QRPA) with realistic two-body interactions. The dependence of the calculated matrix elements on the strength g pp of the particle–particle part of the proton–neutron two-body interaction is investigated. Recently a procedure was proposed where data on 2 ν β β -decay half-lives could be used to derive appropriate values of g pp for calculating the 0 ν β β -decay matrix elements. Following this procedure, we h…

Anomalies and sterile neutrinos : Implications of new theoretical results

The reactor antineutrino and the gallium anomalies have been long unexplained. Possible explanations for both of these anomalies include new physics, such as the existence of one or more eV-scale sterile neutrino. However, the previous theoretical calculations, which do not replicate the experimental results, rely on many simplifying approximations. We have performed shell model calculations in order to gain insights into these issues. In the reactor-antineutrino analysis the beta decays contributing to the cumulative electron spectrum are usually assumed to have allowed spectral shapes. However, many of these decays are actually first-forbidden. Moreover, these decays dominate the experime…

Searches for neutrinoless resonant double electron captures at LNGS

Several experiments were performed during last years at underground (3600 m w.e.) Laboratori Nazionali del Gran Sasso (LNGS) of the INFN (Italy) to search for resonant 2$\varepsilon0\nu$ captures in 96Ru, 106Cd, 136Ce, 156Dy, 158Dy, 180W, 184Os, 190Pt with the help of HP Ge semiconductor detectors, and ZnWO4 and 106CdWO4 crystal scintillators. No evidence for r-2$\varepsilon0\nu$ decays was found, and only T_{1/2} limits were established in the range of 10^{14}-10^{21} yr.

Systematic study of the single-state dominance in 2νββ decay transitions

Abstract The single-state-dominance hypothesis (SSDH) states that the decay rates of the two-neutrino double-beta decay are governed by a virtual two-step transition connecting the initial and final ground states through the first 1 + state, 1 l + , of the intermediate odd-odd nucleus, for those odd-odd nuclei where the 1 l + state is the ground state. To investigate the validity of the SSDH we have performed a systematical theoretical analysis of all known double-beta-decay transitions where the SSDH conditions are fulfilled. the calculations are based on the quasiparticle random-phase approximation (QRPA) and the results have been obtained by using realistic single-particle bases and real…

The neutrinoless double beta decay of 76Ge, 82Se, 86Kr, 114Cd, 128, 130Te and 134, 136Xe in the framework of a relativistic quark confinement model

The half-life of the 0+ → 0+ neutrinoless double beta decay is calculated for 76Ge, 82Se, 86Kr, 114Cd, 128, 130Te and 134, 136Xe and the upper limit for the effective neutrino mass of 3.0 eV is deduced from available experimental data. In addition, the contribution of the right-handed charged weak currents to the effective weak hamiltonian is estimated. The relevant parameters attain the values |〈Λ〉| < 4.1 × 10−6 and |〈ν〉| < 6.6 × 10−8. The nucleonic weak current is treated starting from the current quark level and evaluating the quark current using relativistic quark wave functions obtained from a Dirac equation with a harmonic confinement potential. The nuclear matrix elements of the thus…

Charged-current neutrino-nucleus scattering off the even molybdenum isotopes

Neutrinos from supernovae constitute important probes of both the currently unknown supernova mechanisms and of neutrino properties. Reliable information about the nuclear responses to supernova neutrinos is therefore crucial. In this work, we compute the cross sections for the charged-current neutrino-nucleus scattering off the even-even molybdenum isotopes. The nuclear responses to supernova neutrinos are subsequently calculated by folding the cross sections with a Fermi-Dirac distribution.

113Cdβ-decay spectrum and gA quenching using spectral moments

We present an alternative analysis of the 113Cdβ-decay electron energy spectrum in terms of spectral moments μn, corresponding to the averaged values of nth powers of the β particle energy. The zeroth moment μ0 is related to the decay rate, while higher moments μn are related to the spectrum shape. The here advocated spectral-moment method (SMM) allows for a complementary understanding of previous results, obtained using the so-called spectrum-shape method (SSM) and its revised version, in terms of two free parameters: r=gA/gV (the ratio of axial-vector to vector couplings) and s (the small vectorlike relativistic nuclear matrix element, s-NME). We present numerical results for three differ…

An extended Lipkin-type model with residual proton-neutron interaction

Abstract The Lipkin-Meshkov-Glick (LMG) model is extended to explicitly take into account the proton and neutron degrees of freedom. The proton and neutron Hamiltonians are taken to be of the LMG form, and, in addition, a residual proton-neutron interaction is include. Exact solutions in an SU (2) ⊗ SU (2) basis as well as the RPA solutions for the energy spectrum of the model Hamiltonian are obtained. The spectrum of the exact solutions is degenerate in the limit of no proton-neutron residual interaction, but this degeneracy is totally removed when this type of residual interaction is turned on. The spectrum obtained with RPA is compressed or expanded, as compared to the LMG model with the…

First microscopic evaluation of spin-dependent WIMP-nucleus scattering off 183W

We perform the first consistent calculation of elastic-scattering and inelastic-scattering structure functions for spin-dependent WIMP-nucleus scattering for 183W in a microscopic nuclear-theory framework. The nuclear structure calculations are performed in the microscopic interacting boson-fermion model (IBFM-2). Our results show that while 183W is very insensitive to spin-dependent elastic scattering, the structure function for inelastic scattering is quite sizable at small momentum transfers. Moreover, to our knowledge 183W provides the first studied case where inelastic scattering can compete with elastic scattering as the primary detection signal. peerReviewed

Double-beta-decay nuclear matrix elements in the QRPA framework

We review the recent work done by the Jyväskylä-La Plata collaboration on the calculation of nuclear matrix elements for various modes of double-beta decays. Whenever helpful, we connect our recent work to the historical background in order to highlight the progress achieved in the field of double-beta decay. At the same time, we introduce some new concepts and ideas to treat e.g. possible backgrounds in Gamow-Teller strength functions generated in (p,n) and (n,p) reactions. © 2012 IOP Publishing Ltd. Fil: Suhonen, J.. Universidad de Jyvaskyla; Finlandia Fil: Civitarese, Enrique Osvaldo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La P…

Theoretical investigation of the double-beta processes in 96Ru

The two-neutrino (2ν2β) and neutrinoless (0ν2β) double-β decays of 96Ru are investigated for the transitions to the ground state, 0+ gs, and 0+ and 2+ excited states in 96Mo by using the quasiparticle random-phase approximation combined with the multiple-commutator model. G-matrix-based nuclear forces are used in realistic single-particle model spaces. All the possible channels, β+β+, β+EC, and ECEC, are discussed for both the 2ν2β and 0ν2β decays. The associated half-lives are computed, in particular the one corresponding to the resonant neutrinoless double electron capture (R0νECEC) transition to the 2.712.68-MeV nuclear state in 96Mo. This work represents the most complete theoretical in…

Double β Decay and the Axial Strength

Quenching of the weak axial strength gA is discussed and relations of this quenching to the nuclear matrix elements of double beta decays are highlighted. An analysis of Gamow-Teller transitions in the mass range A = 62 − 142 is presented and its results are compared with those of many previous works. The enhancement of the axial charge is discussed for first-forbidden pseudoscalar β transitions. Higher-forbidden β transitions are introduced and their role in determining the effective value of gA is examined, in particular from the point of view of the β-decay half-lives and the shapes of electron spectra of forbidden non-unique β transitions. peerReviewed

Theoretical direct WIMP detection rates for transitions to the first excited state inKr83

The direct detection of dark matter constituents, in particular the weakly interacting massive particles (WIMPs), is central to particle physics and cosmology. In this paper we study transitions to the excited states, possible in some nuclei, which have sufficiently low lying excited states. Examples considered previously were the first excited states of $^{127}\mathrm{I}$ and $^{129}\mathrm{Xe}$. We examine here $^{83}\mathrm{Kr}$, which offers some kinematical advantages and is a possible target. We estimate appreciable rates for the inelastic scattering mediated by the spin cross sections, with an inelastic event rate of $4.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ …

Neutrino scattering off the stable cadmium isotopes: neutral-current processes

In this work we present computed cross sections for the incoherent neutral-current neutrino scattering off the stable cadmium isotopes. The main focus is on supernova neutrinos. The nuclear states of the even-mass and odd-mass cadmium isotopes have been constructed using the quasiparticle random-phase approximation and the microscopic quasiparticle-phonon model, respectively. The computed cross sections are folded with suitably parametrized Fermi–Dirac distributions of the supernova (anti)neutrinos energies to obtain realistic estimates of the nuclear responses to these neutrinos.

Second-forbidden nonunique $��^-$ decays of $^{59,60}$Fe: Possible candidates for $g_A$ sensitive electron spectral-shape measurements

In this work, we present a theoretical study of the electron spectral shapes for the second-forbidden nonunique $��^-$-decay transitions $^{59}\textrm{Fe}(3/2^-)\to\,^{59}\textrm{Co}(7/2^-)$ and $^{60}\textrm{Fe}(0^+)\to\,^{60}\textrm{Co}(2^+)$ in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete $0\hbar��$ calculation in the full $fp$ model space using the KB3G and GXPF1A effective interactions. When compared with the available data, these interactions predict the low-energy spectra and electromagnetic properties of the involved nuclei quite successfully. This success paves the way for the computations of the $��$-decay proper…

Improved calculations of beta decay backgrounds to new physics in liquid xenon detectors

We present high-precision theoretical predictions for the electron energy spectra for the ground-state to ground-state $\beta$ decays of $^{214}$Pb, $^{212}$Pb, and $^{85}$Kr most relevant to the background of liquid xenon dark matter detectors. The effects of nuclear structure on the spectral shapes are taken into account using large-scale shell model calculations. Final spectra also include atomic screening and exchange effects. The impact of nuclear structure effects on the $^{214}$Pb and $^{212}$Pb spectra below $\approx100$ keV, pertinent for several searches for new physics, are found to be comparatively larger than those from the atomic effects alone. We find that the full calculatio…

Neutrinoless double beta decays of 106Cd revisited

Abstract Neutrinoless double beta ( 0 ν 2 β ) decays of 106 Cd are studied for the transitions to the ground state, 0 gs + , and 0 + excited states in 106 Pd by using realistic many-body wave functions calculated in the framework of the quasiparticle random-phase approximation and its extensions. Effective, G-matrix-based nuclear forces are used in large single-particle model spaces. Both the β + β + and β + EC channels of the 0 ν 2 β decay are discussed and half-lives are computed. Particular attention is devoted to the study of the detectability of the resonant neutrinoless double electron capture ( R 0 ν ECEC ) process in 106 Cd. The calculations of the present article constitute the thu…

Charged-current neutrino-nucleus scattering off 95,97^Mo

Background: Reliable cross sections for the neutrino-nucleus scattering off relevant nuclei for supernova neutrinos are essential for various applications in neutrino physics and astrophysics (e.g., supernova mechanisms). Studies of the nuclear responses for the stable molybdenum isotopes are of great interest for the planned MOON (Mo Observatory of Neutrinos) experiment. Purpose: The purpose of the present work is, thus, to perform a detailed study of the charged-current nuclear responses to supernova neutrinos for the stable odd molybdenum isotopes. A special effort will be devoted to discuss in detail the structures of the most relevant final states in the corresponding proton-odd nucleu…

QRPA estimate for the Δ (1232) contribution to the Gamow-Teller decay of heavy nuclei

Abstract The contribution of the Δ (1232) isobars to the nuclear beta decay strength function is estimated in the framework of the charge-changing form of the QRPA. This procedure is applied to neutron-deficient tin isotopes. The results imply that the quenching of the low-energy Gamow-Teller decay strength cannot attributed to the presence of delta admixtures in the nuclear wave function.

Coexisting structures in 115Sn and 116Sn

Abstract Excited states up to I ≈ 20 in 115 Sn and 116 Sn, populated via the ( 18 O, αxn) reactions, have been studied using the DORIS Ge detector array in conjunction with charged particle detectors. In both nuclei, spherical as well as regular, deformed level structures were found. The spherical states are interpreted to arise from pure neutron configurations, while the deformed, intruder bands obviously involve proton 2p-2h excitations across the Z = 50 shell gap.

Analysis of double-beta transitions in 78^Kr

In this paper a comprehensive theoretical analysis of the two-neutrino (2ν2β) and neutrinoless (0ν2β) doublebeta decays of 78Kr is performed by evaluating the corresponding nuclear matrix elements by combining the quasiparticle random-phase approximation with the multiple-commutator model. Transitions to the ground state 0+ gs and 0+ and 2+ excited states in 78Se are investigated by using G-matrix-based nuclear forces. The channels β+β+, β+EC, and ECEC are discussed for the 2ν2β decays and the channels β+β+ and β+EC for the 0ν2β decays. The associated half-lives are computed to see if the detection of some of these transitions is experimentally feasible. peerReviewed

Microscopic nuclear-structure calculations for the solar-neutrino detector and close-lying isobars

In the present solar-neutrino experiments, mainly observing the pp contribution of the solar-neutrino flux, an important role is played by 71Ga. The structure of this detector nucleus and three of its isobars have been calculated by using the microscopic quasiparticle–phonon model. Using a realistic effective two-body interaction in a realistic valence space, the method yielded energy spectra in good agreement with experiments. The calculated logft values for a number of spontaneous and neutrino-induced Gamow–Teller transitions, when compared with the experimental results, gave qualitatively correct but overestimated transition-strength values in most cases.

Shell-model study on event rates of lightest supersymmetric particles scattering offKr83andTe125

We investigate the elastic and inelastic scattering of lightest supersymmetric particle (LSP) dark matter off two possible target nuclei, $^{83}\mathrm{Kr}$ and $^{125}\mathrm{Te}$. For the nuclear-structure calculations, we employ the nuclear shell model using recently generated realistic interactions. We have condensed the nuclear-physics contribution to a set of nuclear-structure factors that are independent of the adopted supersymmetric (SUSY) model. Total event rates are then easily calculated by combining the nuclear-structure factors with SUSY parameters of choice. In particular, $^{125}\mathrm{Te}$ shows promise as a detector material with both the elastic and inelastic channels yie…

Rare weak decays and nuclear structure

Abstract. Weak interactions cause the atomic nuclei to decay via beta and double beta decays. Double beta decays are extremely rare since they are weak-interaction processes of the second order. Also (single) beta decays can be extremely rare. This can be caused by either a large di ff erence between the spins of the initial and final state (the so-called “forbidden” beta decays) or an extremely small Q value (decay energy) of the decay. All these cases are discussed in this article, and particular emphasis is given to the neutrino- less double electron capture on the double beta side of decays. peerReviewed

Impact of the quenching of $g_{\rm A}$ on the sensitivity of $0\nu\beta\beta$ experiments

Detection of the neutrinoless $\beta\beta$ ($0\nu\beta\beta$) decay is of high priority in the particle- and neutrino-physics communities. The detectability of this decay mode is strongly influenced by the value of the weak axial-vector coupling constant $g_{\rm A}$. The recent nuclear-model analyses of $\beta$ and $\beta\beta$ decays suggest that the value of $g_{\rm A}$ could be dramatically quenched, reaching ratios of $g^{\rm free}_{\rm A}/g_{\rm A}\approx 4$, where $g^{\rm free}_{\rm A}=1.27$ is the free, neutron-decay, value of $g_{\rm A}$. The effects of this quenching appear devastating for the sensitivity of the present and future $0\nu\beta\beta$ experiments since the 4$th$ power …

Isovector spin-multipole strength distributions in double-β-decay triplets

In this work the energetics and strength distributions of isovector spin-dipole and spin-quadrupole transitions from the ground states of the pairs (76Ge, 76Se), (82Se, 82Kr), (96Zr, 96Mo), (100Mo, 100Ru), (116Cd, 116Sn), (128Te, 128Xe), (130Te, 130Xe), and (136Xe, 136Ba), of double-β-decay initial and final nuclei, to the Jπ=0−,1−,2−,1+,2+, and 3+ excited states of the intermediate odd-odd nuclei 76As, 82Br, 96Nb, 100Tc, 116In, 128,130I, and 136Cs are investigated. The calculations are performed using a proton-neutron quasiparticle random-phase approximation (pnQRPA) theory framework with the Bonn-A two-body interaction in no-core single-particle valence spaces. peerReviewed

Effective value of gA in β and ββ decays

Effective value of the weak axial-vector coupling strength, g A , in nuclear β and ββ (double beta) decays is discussed. Both Gamow-Teller and first-forbidden β decays are included in the analyses. Quenching of g A in β and two-neutrino ββ decays is reviewed and impact of this quenching on neutrinoless ββ decays is addressed. New measurements of β spectra of first-forbidden non-unique β decays are encouraged, to learn about the mesonic enhancement of the weak axial charge in these decays. peerReviewed

Quasimolecular resonances in terms of dipole and quadrupole interacting bosons

The energy spectrum of the /sup 12/C+ /sup 12/C resonances is described with the interacting boson (quadrupole) model. The Hamiltonians corresponding to the three dynamical symmetries and to the general case of the model are used. The results are compared with the similar calculations within the nuclear vibron (dipole) model. Based on the present experimental data no choice can be made between the dipole and quadrupole descriptions, but in both cases the best fit is quite close to the dynamical symmetry corresponding to a soft vibrator.

Theoretical results on the double positron decay of 106Cd

Abstract Theoretical results for the double positron decay of 106 Cd are presented. The calculated values for the lateral single-beta-decay feeding patterns and electromagnetic transitions leading to states in 106 Cd and 106 Pd are discussed and compared to the data. The results on the double positron decay of 106 Cd are compared to new experimental limits. Based on the results of the present calculations, we report on the possibility of detecting the EC/EC or the β + /EC decay modes to final J π =0 + states using the improved sensitivity of the planned measurements.

First-forbidden transitions in the reactor anomaly

We study the dominant forbidden transitions in the antineutrino spectra of the fission actinides from 4 MeV onward using the nuclear shell model. Through explicit calculation of the shape factor, taking into account Coulomb corrections, we show the expected changes on cumulative electron and antineutrino spectra. Compared to the usual allowed approximation this results in a minor decrease of electron spectra from 4 MeV and onward, whereas an increase of several percent is observed in antineutrino spectra. We show that, despite their limited number, forbidden transitions dominate the spectral flux for most of the experimentally accessible range. Based on the shell model calculations we attem…

Neutrinoless double beta decay to excited collective 0+ states

Abstract The many recently performed experiments to study the two-neutrino double beta (2 νββ ) decay to the first excited 0 + final state encourage similar experiments to be done for the neutrinoless double beta (0 νββ ) decay. Based on the accumulated theoretical and experimental information on the 2 νββ decays one could hope that the 0 νββ decay to the excited 0 + state would be very efficient in restricting the parameter space of modern particle-physics theories. In this article the 0 νββ decays of 76 Ge and 82 Se to excited collective 0 + states are studied within a realistic nuclear model. It is found that the lower limits for the half-lives of these decays are of the order of 10 27 y…

Spectral shapes of forbidden argonβdecays as background component for rare-event searches

The spectral shape of the electrons from the two first-forbidden unique beta- decays of Ar-39 and Ar-42 were calculated for the first time to the next-to-leading order. Especially the spectral shape of the Ar-39 decay can be used to characterise this background component for dark matter searches based on argon. Alternatively, due to the low thresholds of these experiments, the spectral shape can be investigated over a wide energy range with high statistics and thus allow a sensitive comparison with the theoretical predictions. This might lead to interesting results for the ratio of the weak vector and axial-vector constants in nuclei.

Study of the low-lying collective states in 94–100Mo isotopes using the MAVA

Abstract A systematic investigation of reduced electric quadrupole decay strengths, B ( E 2 ) and level energies of even 94–100 Mo isotopes is performed using the microscopic anharmonic vibrator approach (MAVA). The MAVA is suited for dynamical microscopic description of two-phonon-like states and their energy splitting due to interaction with low-lying one-phonon states. The starting point for the model is a realistic single-particle valence space and a microscopic many-body Hamiltonian which is used to generate the one-phonon states by the use of the quasiparticle random-phase approximation (QRPA). The same Hamiltonian generates also the interaction between the one- and two-phonon states.…

Theory of double beta decay

Basic features of the two-neutrino double beta ( 2 ν β β ) decay and neutrinoless double beta ( 0 ν β β ) decay are discussed. A short review of the most important nuclear models, used to describe the ββ decay, is given. A deeper survey of the nuclear matrix elements, related to the above-mentioned decay modes, is performed using the proton-neutron quasiparticle random-phase approximation (pnQRPA). In particular, the extraction of a proper value of the proton-neutron particle-particle interaction parameter in this theory is addressed. The relevance of different multipoles in the multipole decomposition of the 0 ν β β matrix element is also discussed in the pnQRPA framework.

Ordinary muon capture studies for the matrix elements in ββ decay

High-purity germanium (HPGe) detectors were used to make a precise measurement of the γ-ray spectrum produced following ordinary (nonradiative) capture of negative muons by natural Se, Kr, Cd, and Sm. The measurement was repeated for isotopically enriched 48Ti, 76Se, 82Kr, 106Cd, and 150Smtargets. By investigating energy and time distributions, the lifetime of negative muons in the different isotopes was deduced. A detailed analysis of the intensity of the γ lines enabled the extraction of the relative yields of several daughter nuclei. The partial rates of (μ−,ν) capture to numerous excited levels of the 48Sc, 76As, 82Br, 106Ag, and 150Tc isotopes (considered to be virtual states of the in…

Forbidden nonunique β decays and effective values of weak coupling constants

Forbidden nonunique β decays feature shape functions that are complicated combinations of different nuclear matrix elements and phase-space factors. Furthermore, they depend in a very nontrivial way on the values of the weak coupling constants, gV for the vector part and gA for the axial-vector part. In this work we include also the usually omitted second-order terms in the shape functions to see their effect on the computed decay half-lives and electron spectra (β spectra). As examples we study the fourth-forbidden nonunique ground-state-to-ground-state β− decay branches of 113Cd and 115In using the microscopic quasiparticle-phonon model and the nuclear shell model. A striking new feature …

Consistent large-scale shell-model analysis of the two-neutrino $\beta\beta$ and single $\beta$ branchings in $^{48}\rm Ca$ and $^{96}\rm Zr$

Two-neutrino double-beta-decay matrix elements $M_{2\nu}$ and single beta-decay branching ratios were calculated for $^{48}$Ca and $^{96}$Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For $^{48}$Ca the matrix element $M_{2\nu}=0.0511$ is obtained, which is 5.5\% smaller than the previously reported value of 0.0539. For $^{96}$Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value $M_{2\nu}=0.0747$ with extreme single-state dominance. If the scenario where the first $1^+$ state in $^{96}$Nb is at 694.6 keV turns out to be correct, the matrix element is in…

Combining data from high-energy p p -reactions and neutrinoless double-beta decay: Limits on the mass of the right-handed boson

From the recently established lower-limits on the nonobservability of the neutrinoless double-beta decay of 76Ge (GERDA collaboration) and 136Xe (EXO-200 and KamLAND-Zen collaborations), combined with the ATLAS and CMS data, we extract limits for the left-right (LR) mixing angle, of the SU(2)L ×SU(2)R electroweak Hamiltonian. For the theoretical analysis, which is a model dependent, we have adopted a minimal extension of the Standard Model (SM) of Electroweak Interactions belonging to the SU(2)L ×SU(2)R representation. The nuclear-structure input of the analysis consists of a set of matrix elements and phase-space factors, and the experimental lower-limits for the half-lives. The other inpu…

Forbidden nonuniqueβdecays and effective values of weak coupling constants

Forbidden nonunique $\ensuremath{\beta}$ decays feature shape functions that are complicated combinations of different nuclear matrix elements and phase-space factors. Furthermore, they depend in a very nontrivial way on the values of the weak coupling constants, ${g}_{\mathrm{V}}$ for the vector part and ${g}_{\mathrm{A}}$ for the axial-vector part. In this work we include also the usually omitted second-order terms in the shape functions to see their effect on the computed decay half-lives and electron spectra ($\ensuremath{\beta}$ spectra). As examples we study the fourth-forbidden nonunique ground-state-to-ground-state ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay branches of $^{113}\ma…

Microscopic description ofα+40Caquasimolecular resonances

A multistep microscopic approach describing the dynamics of quasimolecular resonances is applied to the $\ensuremath{\alpha}{+}^{40}\mathrm{Ca}$ system. The lowest collective two-particle eigenmodes are used as building blocks of the four-particle states. The pair states are built on mean-field single-particle orbitals including also sharp resonances in continuum. The structure of ${}^{44}\mathrm{Ti}$ is analyzed and strong high-lying $\ensuremath{\alpha}$-like resonances are found in good agreement with the experimentally observed quasimolecular spectrum. The resonances turn out to be very collective and contain mostly proton-neutron pairs where the lowest proton single-particle resonance,…

Measurement of the Spectral Shape of the β -Decay of Xe137 to the Ground State of Cs137 in EXO-200 and Comparison with Theory

We report on a comparison between the theoretically predicted and experimentally measured spectra of the first-forbidden nonunique β-decay transition ^{137}Xe(7/2^{-})→^{137}Cs(7/2^{+}). The experimental data were acquired by the EXO-200 experiment during a deployment of an AmBe neutron source. The ultralow background environment of EXO-200, together with dedicated source deployment and analysis procedures, allowed for collection of a pure sample of the decays, with an estimated signal to background ratio of more than 99 to 1 in the energy range from 1075 to 4175 keV. In addition to providing a rare and accurate measurement of the first-forbidden nonunique β-decay shape, this work constitut…

Spin-multipole nuclear matrix elements in the pn quasiparticle random-phase approximation: Implications for β and ββ half-lives

Half-lives for 148 potentially measurable 2nd-, 3rd-, 4th-, 5th-, 6th-, and 7th-forbidden unique beta transitions are predicted. To achieve this, the ratio of the nuclear matrix elements (NMEs), calculated by the proton-neutron quasiparticle random-phase approximation (pnQRPA), MpnQRPA, and a two-quasiparticle (two-qp) model, Mqp, is studied and compared with earlier calculations for the allowed Gamow-Teller (GT) 1+ and first-forbidden spin-dipole (SD) 2− transitions. The present calculations are done using realistic single-particle model spaces and G-matrix based microscopic two-body interactions. In terms of the ratio k = MpnQRPA/Mqp the studied decays fall into two groups: for GROUP 1, w…

Angular Momentum Coupling

In nuclear physics, as also in atomic and molecular physics, the entities to be described consist of sub-entities with some orbital angular momentum and spin. The angular momentum of the entity is built, then, of the angular momenta of the sub-entities. This building process leads to quantum-mechanical angular momentum coupling. This chapter presents the basic machinery for treating angular momentum and its coupling. Clebsch-Gordan coefficients and 3j symbols are introduced. It is shown that Clebsch-Gordan coefficients and 3j symbols relate to the coupling of two angular momenta. Increasing the number of angular momenta to be coupled leads to more complicated coupling patterns. Transformati…

Proton-Neutron QRPA

We discussed proton—neutron two-quasiparticle excitations and their electromagnetic and beta decays in Chap. 15. In Chap. 17 we introduced the pn-QTDA, the simplest configuration mixing scheme of these excitations. The vacuum of the pnQTDA is the BCS vacuum, and the solutions of the pn-QTDA satisfy a variational principle.1

Charge-Changing Particle-Hole Excitations and the pnTDA

In this chapter we extend the Tamm-Dancoff approximation (TDA) to charge-changing particle-hole excitations. Such excitations consist of a proton particle and a neutron hole, or a neutron particle and a proton hole. These excitations of the doubly magic Hartree-Fock vacuum are nuclear states in the adjacent odd-odd nuclei. This formalism is well suited to describe beta-decay transitions from the states of one of the odd-odd nuclei to the ground and excited states of the even-even reference nucleus.

Study of odd-mass N = 82 isotones with realistic effective interactions

The microscopic quasiparticle-phonon model, MQPM, is used to study the energy spectra of the odd $Z=53 - 63$, N=82 isotones. The results are compared with experimental data, with the extreme quasiparticle-phonon limit and with the results of an unrestricted $2s1d0g_{7/2}0h_{11/2}$ shell model (SM) calculation. The interaction used in these calculations is a realistic two-body G-matrix interaction derived from modern meson-exchange potential models for the nucleon-nucleon interaction. For the shell model all the two-body matrix elements are renormalized by the $\hat{Q}$-box method whereas for the MQPM the effective interaction is defined by the G-matrix.

The Nuclear Mean Field and Many-Nucleon Configurations

After the two preceding chapters, throughout impregnated with messy-looking, though necessary mathematics, we are finally entering the realm of basic concepts of nuclear structure physics. While the preceding chapters may have been a shock to the reader not familiar with the fine details of angular momentum coupling, the present chapter should offer a soothing soft landing to the basic philosophy behind the nuclear shell model, namely the nuclear mean field.

Electromagnetic Multipole Moments and Transitions

In the preceding chapter we constructed and discussed the simplest possible nuclear wave functions. This construction was done at the mean-field level. No account was taken of configuration mixing caused by the nuclear residual interaction. These simple wave functions produce degeneracies in energy spectra. This is contrary to experimental data, so improved wave functions are called for.

Gamow-Teller decay of118Pd and of neighbouring even isotopes of palladium

Neutron-rich isotopes of palladium were produced via the fission of238U by 20 MeV protons. These isotopes were selected using the ion guide-fed on-line mass-separator facility IGISOL at Jyvaskyla. Their decays were studied byβ-ray,γ-ray and conversion-electron spectroscopy. For114Pd and116Pd, the decay schemes established previously were confirmed; additionally multipolarities were determined for a few transitions. In the case of118Pd, only an approximate half-life was known from a previous radiochemical experiment. In the present study, 15 gamma transitions were observed, most of which were placed in a decay scheme. The half-life and the decay energy were found to beT1/2=1.9±0.1 s andQβ=4.…

Double-beta decay Q values of 116Cd and 130Te

Abstract The Q values of the 116Cd and 130Te double-beta decaying nuclei were determined by using a Penning trap mass spectrometer. The new atomic mass difference between 116Cd and 116Sn of 2813.50(13) keV differs by 4.5 keV and is 30 times more precise than the previous value of 2809(4) keV. The new value for 130Te, 2526.97(23) keV is close to the Canadian Penning trap value of 2527.01 ± 0.32 keV (Scielzo et al., 2009) [1] , but differs from the Florida State University trap value of 2527.518 ± 0.013 keV (Redshaw et al., 2009) [2] by 0.55 keV (2σ). These values are sufficiently precise for ongoing neutrinoless double-beta decay searches in 116Cd and 130Te. Hence, our Q values were used to …

Single and double beta decays in the , and triplets of isobars

Abstract In this paper we analyze the ground-state-to-ground-state two-neutrino double beta ( 2 ν β β ) decays and single EC and β − decays for the A = 100 ( 100 Mo– 100 Tc– 100 Ru), A = 116 ( 116 Cd– 116 In– 116 Sn) and A = 128 ( 128 Te– 128 I– 128 Xe) triplets of isobars. We use the proton–neutron quasiparticle random-phase approximation (pnQRPA) with realistic G-matrix-derived effective interactions in very large single-particle bases. The purpose is to access the effective value of the axial-vector coupling constant g A in the pnQRPA calculations. We show that the three triplets of isobars represent systems with different characteristics of orbital occupancies and cumulative 2 ν β β nuc…

Two-neutrino ββ decays and low-lying Gamow-Teller β− strength functions in the mass range A=70–176

We apply the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA) to describe the low-lying (E 6 MeV) 1+ Gamow-Teller (GT) strength functions in odd-odd deformed nuclei which participate as intermediate nuclei in two-neutrino double-β-decay (2νββ) transitions within the mass range A = 70–176. In deriving equations of motion we use a single-particle basis with projected angular momentum, provided by the diagonalization of a spherical mean field furnished with a quadrupole-quadrupole interaction. The schematic residual Hamiltonian contains pairing and proton-neutron interaction terms in particle-hole (ph) and particle-particle (pp) channels, with constant strengths. By …

On the double-beta decays of 70Zn, 86Kr, 94Zr, 104Ru, 110Pd and 124Sn

Abstract Double-beta decays of 70Zn, 86Kr, 94Zr, 104Ru, 110Pd and 124Sn to the final ground states and the decays of 110Pd and 124Sn to the excited states in 110Cd and 124Te are studied in the framework of the proton–neutron quasiparticle random-phase approximation (pnQRPA) combined with the multiple-commutator model (MCM) for description of decays to the excited final states. Reasonably large single-particle model spaces and G-matrix-based effective nuclear forces are used to compute the relevant nuclear matrix elements and decay half-lives. The present study is among the very few that have been dedicated to double-beta decays of these nuclei, although the associated double-beta Q values e…

Neutrino-nuclear responses for astro-neutrinos, single beta decays and double beta decays

Neutrino–nuclear responses associated with astro-neutrinos, single beta decays and double beta decays are crucial in studies of neutrino properties of interest for astro-particle physics. The present report reviews briefly recent studies of the neutrino–nuclear responses from both experimental and theoretical points of view in order to obtain a consistent understanding of the many facets of the neutrino–nuclear responses. Subjects discussed in this review include (i) experimental studies of neutrino–nuclear responses by means of single beta decays, charge-exchange nuclear reactions, muon- photon- and neutrino–nuclear reactions, and nucleon-transfer reactions, (ii) implications of and discus…

Neutral-current supernova-neutrino cross sections for Pb204,206,208 calculated by Skyrme quasiparticle random-phase approximation

The present work constitutes a detailed study of neutral-current (NC) supernova-neutrino scattering off the stable even-even lead isotopes Pb204,206,208. This is a continuation of our previous work [Almosly et al., Phys. Rev. C. 94, 044614 (2016)10.1103/PhysRevC.94.044614] where we investigated charged-current processes on the same nuclei. As in the previous work, we have adopted the quasiparticle random-phase approximation (QRPA) as the theory framework and use three different Skyrme interactions to build the involved nuclear wave functions. We test the Skyrme forces by computing the location of the lowest-order isovector spin-multipole giant resonances and comparing with earlier calculati…

Quasiparticle Mean Field: BCS and Beyond

In the previous two chapters we have laid the foundation for the BCS theory to describe open-shell nuclei. The properties of BCS solutions were compared with exact results from schematic solvable models. In this chapter we go into the details of numerical solution of the BCS equations. The implications of these solutions are discussed through applications to ds- and pf-shell nuclei.

Investigation of the decay of to excited states in

The two-neutrino mode of double beta decay of is investigated both theoretically and experimentally. The calculations, using the quasiparticle random phase approximation approach, show that for the detection of transitions to the two first excited states in the daughter nuclide will be possible in the very near future. On the experimental side, new, most stringent limits on half-lives for the double beta decay of to excited states in have been obtained with a `well-type' germanium detector. They range between and years (90% CL).

Double-Beta-Decay Matrix Elements And The Effective Value Of Weak Axial Coupling

The neutrinoless double beta (0&nu;&beta;&beta;) decay of atomic nuclei is a possible way to access the nature and mass of the neutrino. These unknown features of the neutrino can be tackled by the 0&nu;&beta;&beta;-decay experiments. In a simplistic picture the rate of 0&nu;&beta;&beta; decay depends on the second power of the double Gamow-Teller nuclear matrix element, M(0&nu;)GTGT, containing virtual transitions through various multipole states J&pi; of the intermediate nucleus. The matrix element is multiplied by the second power of the effective (quenched) value, geffA, of the weak axial-vector coupling gA. The coupling geffA plays an extremely important role in determining the 0&nu;&b…

Second-forbidden nonunique $\beta^-$ decays of $^{24}$Na and $^{36}$Cl assessed by the nuclear shell model

We have performed a systematic study of the log$ft$ values, shape factors and electron spectra for the second-forbidden nonunique $\beta^-$ decays of $^{24}$Na$(4^+) \rightarrow ^{24}$Mg$(2^+)$ and $^{36}$Cl$(2^+) \rightarrow ^{36}$Ar$(0^+)$ transitions under the framework of the nuclear shell model. We have performed the shell model calculations in the $sd$ model space, using more recent microscopic effective interactions such as Daejeon16, chiral N3LO, and JISP16. These interactions are derived from the no-core shell model wave functions using Okubo-Lee-Suzuki transformation.For comparison, we have also shown the results obtain from the phenomenological USDB interaction. To test the predi…

Statistical analysis of beta decays and the effective value of g_A in the proton-neutron quasiparticle random-phase approximation framework

We perform a Markov Chain Monte Carlo (MCMC) statistical analysis of a number of measured ground-state-to-ground-state single $\beta^+$/electron-capture and $\beta^-$ decays in the nuclear mass range A = 62 - 142. The corresponding experimental comparative half-lives (log ft values) are compared with the theoretical ones obtained by the use of the proton-neutron quasiparticle random-phase approximation (pnQRPA) with G-matrix based effective interactions. The MCMC analysis is performed separately for 47 isobaric triplets and 28 more extended isobaric chains of nuclei to extract values and uncertainties for the effective axial-vector coupling constant g_A in nuclear-structure calculations per…

Effects of orbital occupancies and spin–orbit partners on -decay rates

Abstract Neutrinoless double beta ( 0 ν β β ) decay of the 76Ge, 82Se, 128Te, 130Te and 136Xe nuclei is discussed in terms of the associated nuclear matrix element (NME). The effects of the size of the single-particle model space and the occupancies of individual orbits on the NME are discussed by using the proton–neutron quasiparticle random-phase approximation (pnQRPA) with effective, G-matrix-derived nuclear forces. It is found that only in some cases the orbital occupancies play a decisive role for the size of the NME, whereas the inclusion of all the spin–orbit partners is essential to achieve a NME of reasonable quality. The obtained results are compared with published results of othe…

Muon-electron lepton-flavor-violating transitions : Shell-model calculations of transitions in 27Al

In this paper we present the results of large-scale shell-model calculations of muon-to-electron lepton-flavorviolating transitions for the case of the target nucleus 27Al. We extend the previous shell-model calculations, done in the sd model space, by including also the p orbitals in order to see whether the negative-parity states produce any significant effect in the conversion rate. The analysis of the results shows the dominance of coherent transitions mediated by isovector operators and going by the ground state of the target, with practically null influence of excited positive- or negative-parity states. peerReviewed

Statistical analysis ofβdecays and the effective value ofgAin the proton-neutron quasiparticle random-phase approximation framework

We perform a Markov chain Monte Carlo (MCMC) statistical analysis of a number of measured ground-state-to-ground-state single ${\ensuremath{\beta}}^{+}$/electron-capture and ${\ensuremath{\beta}}^{\ensuremath{-}}$ decays in the nuclear mass range of $A=62--142$. The corresponding experimental comparative half-lives ($logft$ values) are compared with the theoretical ones obtained by the use of the proton-neutron quasiparticle random-phase approximation $(pn\mathrm{QRPA})$ with $G$-matrix-based effective interactions. The MCMC analysis is performed separately for 47 isobaric triplets and 28 more extended isobaric chains of nuclei to extract values and uncertainties for the effective axial-vec…

The Random-Phase Approximation

In this chapter we extend the TDA particle-hole formalism of Chap. 9 to include correlations in the nuclear ground state. This sophisticated particle-hole formalism is called the random-phase approximation (RPA). In this description the simple Hartree-Fock particle-hole vacuum is replaced by a correlated ground state involving many-particle-many-hole excitations of the simple particle-hole vacuum. The resulting configuration mixing in excited states is more involved in the RPA than it is in the TDA. The ground-state correlations induce both particle-hole and hole-particle components in the RPA wave function.

Muon-capture strength functions in intermediate nuclei of 0νββ decays

Capture rates of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of current experimental interest are computed. The corresponding OMC (capture-rate) strength functions have been analyzed in terms of multipole decompositions. The computed low-energy OMC-rate distribution to $^{76}\mathrm{As}$ is compared with the available data of Zinatulina et al. [Phys. Rev. C 99, 024327 (2019)]. The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The participant nuclear wave functions are obtained in extended no-core singl…

Shell-model computed cross sections for charged-current scattering of astrophysical neutrinos off 40Ar

Charged-current (anti)neutrino- 40 Ar cross sections for astrophysical neutrinos have been calculated. The initial and final nuclear states were calculated using the nuclear shell model. The folded solar-neutrino scattering cross section was found to be 1.78 ( 23 ) × 10 − 42 cm 2 , which is higher than what the previous papers have reported. The contributions from the 1 − and 2 − multipoles were found to be significant at supernova-neutrino energies, confirming the random-phase approximation (RPA) result of a previous study. The effects of neutrino flavor conversions in dense stellar matter (matter oscillations) were found to enhance the neutrino-scattering cross sections significantly for …

Systematic study of neutrinoless double beta decay to excited 0+ states

Abstract A systematic study of neutrinoless double beta (0 νββ ) decay to excited 0 + states, described as monopole-vibrational states or as composed of two collective quadrupole-phonon states, has been performed. Both double β − and double β + /EC decays have been analyzed within the framework of the multiple commutator model (MCM) by using a realistic nuclear many-body Hamiltonian and realistic mean-field single-particle bases. It is found that the associated 0 νββ -decay transitions are suppressed relative to the decay to the final ground state both by the available phase space and especially by the smallness of the involved transition matrix elements. For completeness, also the double β…

Perturbative analysis of the 2νββ decays of 100Mo and 116Cd

We have performed a theoretical analysis of the ground-state-to-ground-state transitions in 100Mo and 116Cd, based on the quasiparticle random-phase approximation and on a straightforward perturbative scheme. The results show that the single-state dominance found in the realistic calculations of the nuclear matrix elements, which is consistent with data, can be viewed as a result of the interference between few two-quasiparticle configurations.

Shell-model computed cross sections for charged-current scattering of astrophysical neutrinos off 40Ar

Charged-current (anti)neutrino-$^{40}\mathrm{Ar}$ cross sections for astrophysical neutrinos have been calculated. The initial and final nuclear states were calculated using the nuclear shell model. The folded solar-neutrino scattering cross section was found to be $1.78(23)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}42}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$, which is higher than what the previous papers have reported. The contributions from the ${1}^{\ensuremath{-}}$ and ${2}^{\ensuremath{-}}$ multipoles were found to be significant at supernova-neutrino energies, confirming the random-phase approximation (RPA) result of a previous study. The effects of neutrino flavor conve…

Theoretical estimates of supernova-neutrino cross sections for the stable even-even lead isotopes: Charged-current reactions

A detailed study of the charged-current supernova electron neutrino and electron antineutrino scattering off the stable even-mass lead isotopes A = 204, 206, and 208 is reported in this work. The proton-neutron quasiparticle random-phase approximation (pnQRPA) is adopted to construct the nuclear final and initial states. Three different Skyrme interactions are tested for their isospin and spin-isospin properties and then applied to produce (anti)neutrino-nucleus scattering cross sections for (anti)neutrino energies below 80 MeV. Realistic estimates of the nuclear responses to supernova (anti)neutrinos are computed by folding the computed cross sections with a two-parameter Fermi-Dirac distr…

Direct measurement of the mass difference of As72−Ge72 rules out As72 as a promising β -decay candidate to determine the neutrino mass

We report the first direct determination of the ground-state to ground-state electron-capture $Q$ value for the $^{72}\mathrm{As}$ to $^{72}\mathrm{Ge}$ decay by measuring their atomic mass difference utilizing the double Penning trap mass spectrometer, JYFLTRAP. The $Q$ value was measured to be 4343.596(75) keV, which is more than a fiftyfold improvement in precision compared to the value in the most recent Atomic Mass Evaluation 2020. Furthermore, the new $Q$ value was found to be 12.4(40) keV (3.1 $\ensuremath{\sigma}$) lower. With the significant reduction of the uncertainty of the ground-state to ground-state $Q$ value combined with the level scheme of $^{72}\mathrm{Ge}$ from $\ensurem…

Elastic and inelastic LSP-nucleus scattering on medium-heavy nuclei

Elastic and inelastic scattering rates of the lightest supersymmetric particle (LSP) off nuclei are derived for the stable iodine, xenon and cesium detectors. The parameters of the supersymmetric theory are decoupled from the nuclear structure. The involved nuclear wave functions are calculated in the nuclear shell model by using a realistic effective two-nucleon interaction in a realistic valence space. By using fitted nuclear gyromagnetic factors we successfully reproduce the relevant spectroscopic data in the discussed nuclei.

Estimation of bounds for left-right mixing from nuclear double beta decay processes

Abstract Nuclear matrix elements, extracted from a systematic calculation of neutrinoless double beta decay rates for 0 + g.s →o + g.s transitions in 76 Ge, 82 Se, 128 Te, 130 Te and 136 Xe, have been used to compute bounds on the left-right mixing angle ζ of the weak currents. The parameters of the nuclear model have been fixed by calculating the corresponding two-neutrino double beta decay half lives. The present analysis favours a mixing of the order of |tanξ| −3 which is to be compared with those obtained in muon decay (|tan ξ | ⩽ 0.035) and in supernova (|tan ξ | ⩽ 10 −5 ) analysis. It shows that nuclear structure calculations yield estimates on ξ which complement the existing data.

Nuclear structure and neutrino-nucleus reactions at supernova energies

Supernova-(anti-)neutrino–nucleus scattering is discussed with reference to neutral-current (NC) and charged-current (CC) processes in heavy stable nuclei. The Donnelly-Walecka method with the associated multipole expansion of the nucleonic current has been adopted as the basic framework in deriving the neutrino-nucleus scattering cross sections. The needed nuclear wave functions are computed by using the quasiparticle random-phase approximation (QRPA) for the even-even target nuclei in the NC processes and the proton-neutron QRPA (pnQRPA) has been used to compute the CC processes for the mentioned nuclei. The wave functions of the stable odd-mass target nuclei have been obtained by the use…

GT neutrino–nuclear responses for double beta decays and astro neutrinos

Gamow–Teller nuclear matrix elements (NMEs) for pairs of ground-state-to-ground-state transitions, in particular their geometric mean NME , are studied. The observed means in the medium-heavy mass region are compared with the corresponding single-quasiparticle (qp) NMEs and the means calculated by the proton neutron qp random-phase approximation (pnQRPA). The NMEs turn out to be insensitive to the nucleon occupancy/vacancy amplitudes and to the particle–particle interaction parameter of the pnQRPA. The observed mean NMEs are found to be reduced by a coefficient relative to the effective qp NMEs and by a coefficient with respect to the pnQRPA NMEs. The reductions associated with the spin iso…

Effective axial-vector strength and β -decay systematics

We use the weak axial-vector coupling strength as a key parameter to reproduce simultaneously the available data for both the Gamow-Teller and decay rates in nine triplets of isobars with mass numbers . We use the proton-neutron quasiparticle random-phase approximation (pnQRPA) with schematic dipole interaction containing particle-particle and particle-hole parts with mass-dependent strengths. Our analysis points to a strongly quenched effective value , with a relative error of 28%. We then perform a systematic computation of 218 experimentally known and decays with quite a remarkable success. The presently extracted value of should be taken as an effective one, specific for a given nuclear…

Nucleon Pairing and Seniority

Until now we have been dealing with particle and hole aspects of nuclear structure. In this second part of the book we go farther away from a closed major shell. Still near the beginning or end of a major shell we encounter vibrational, spherical open-shell nuclei that cannot be described in terms of a few particles or holes. Farther towards the middle of the shell the spherical shape will give way to permanent deformation signalled by rotational bands analogous to those of diatomic molecules. Microscopic description of such nuclei requires a deformed mean field as the starting point. Deformed nuclei will not be considered in any detail in this book.

Spectrum-shape method and the next-to-leading-order terms of the β-decay shape factor

Effective values of the axial-vector coupling constant gA have lately attracted much attention due to the prominent role of gA in determining the half-lives of double β decays, in particular their neutrinoless mode. The half-life method, i.e., comparing the calculated half-lives to the corresponding experimental ones, is the most widely used method to access the effective values of gA. The present paper investigates the possibilities offered by a complementary method: the spectrum-shape method (SSM). In the SSM, comparison of the shapes of the calculated and measured β electron spectra of forbidden nonunique β decays yields information on the magnitude of gA. In parallel, we investigate the…

Ordinary Muon Capture on 136Ba : Comparative Study Using the Shell Model and pnQRPA

In this work, we present a study of ordinary muon capture (OMC) on 136136Ba, the daughter nucleus of 136136Xe double beta decay (DBD). The OMC rates at low-lying nuclear states (below 1 MeV of excitation energy) in 136136Cs are assessed by using both the interacting shell model (ISM) and proton–neutron quasiparticle random-phase approximation (pnQRPA). We also add chiral two-body (2BC) meson-exchange currents and use an exact Dirac wave function for the captured s-orbital muon. OMC can be viewed as a complementary probe of the wave functions in 136136Cs, the intermediate nucleus of the 136136Xe DBD. At the same time, OMC can be considered a powerful probe of the effective values of weak axi…

Doppler-broadening of gamma rays following muon capture: search for scalar coupling

Abstract A precision measurement of the 277 keV γ ray produced by capturing muons in gaseous oxygen was performed using high-resolution HPGe detectors. The Doppler-broadened shape of this line is sensitive to the possible admixture into muon capture of genuine scalar interaction. This experiment complements, in the muon sector, in principle, similar ones undertaken recently in nuclear β decay. Using a procedure discussed in earlier papers, a fit to the experimental line-shape allowed us to obtain for the recoil–gamma correlation coefficient the value of a 1 2 =0.096±0.041 (95% CL). The available evaluations of the contributing nuclear matrix elements, performed in the impulse approximation …

Systematic approach to β and 2vββ decays of mass A=100-136 nuclei

In this work we perform a systematic study of pairs of single-β-decaying nuclei in the mass region A = 100–136 to extract information on the effective value of the axial-vector coupling constant gA. As the many-body framework we use the quasiparticle random-phase approximation (QRPA) and its proton-neutron variant (pnQRPA) in singleparticle valence bases with Woods-Saxon-calculated single-particle energies. It is found that, to a reasonable approximation, gA is a linear function of the mass number A, with a slightly different parametrization below and above the mass A = 121. Using the values of gA extracted from the linear fit, as well as an average constant value of gA, we calculate the tw…

Search for 2-beta decays of 96^Ru and 104^Ru by ultralow-background HPGe gamma spectrometry at LNGS: Final Results

An experiment to search for double-β decay processes in 96Ru and 104Ru, which are accompanied by γ rays, has been realized in the underground Gran Sasso National Laboratories of the I.N.F.N. (Italy). Ruthenium samples with masses of ≈0.5–0.7 kg were measured with the help of ultralow-background high-purity Ge γ -ray spectrometry. After 2162 h of data taking the samples were deeply purified to reduce the internal contamination of 40K. The last part of the data has been accumulated over 5479 h. New improved half-life limits on 2β+/εβ+/2ε processes in 96Ru have been established on the level of 1020 yr, in particular for decays to the ground state of 96Mo: T 2ν2β+ 1/2 1.4 × 1020 yr, T 2νεβ+ 1/2…

Measurement of the 2+→0+ ground-state transition in the β decay of F20

We report the first detection of the second-forbidden, nonunique, 2+→0+, ground-state transition in the β decay of F20. A low-energy, mass-separated F+20 beam produced at the IGISOL facility in Jyvaskyla, Finland, was implanted in a thin carbon foil and the β spectrum measured using a magnetic transporter and a plastic-scintillator detector. The β-decay branching ratio inferred from the measurement is bβ=[0.41±0.08(stat)±0.07(sys)]×10-5 corresponding to logft=10.89(11), making this one of the strongest second-forbidden, nonunique β transitions ever measured. The experimental result is supported by shell-model calculations and has significant implications for the final evolution of stars tha…

β-decay half-life ofV50calculated by the shell model

In this work we survey the detectability of the ${\ensuremath{\beta}}^{\ensuremath{-}}$ channel of ${}_{23}^{50}\mathrm{V}$ leading to the first excited ${2}^{+}$ state in ${}_{24}^{50}\mathrm{Cr}$. The electron-capture (EC) half-life corresponding to the transition of ${}_{23}^{50}V$ to the first excited ${2}^{+}$ state in ${}_{22}^{50}\mathrm{Ti}$ had been measured earlier. Both of the mentioned transitions are 4th-forbidden non-unique. We have performed calculations of all the involved wave functions by using the nuclear shell model with the GXPF1A interaction in the full f-p shell. The computed half-life of the EC branch is in good agreement with the measured one. The predicted half-lif…

Search for neutrinoless double-beta decay ofMo100with the NEMO-3 detector

We report the results of a search for the neutrinoless double-$\beta$ decay (0$\nu\beta\beta$) of $^{100}$Mo, using the NEMO-3 detector to reconstruct the full topology of the final state events. With an exposure of 34.7 kg.y, no evidence for the 0$\nu\beta\beta$ signal has been found, yielding a limit for the light Majorana neutrino mass mechanism of $T_{1/2}(0\nu\beta\beta)>1.1 \times 10^{24}$ years (90% C.L.) once both statistical and systematic uncertainties are taken into account. Depending on the Nuclear Matrix Elements this corresponds to an upper limit on the Majorana effective neutrino mass of $ < 0.3-0.8$ eV (90% C.L.). Constraints on other lepton number violating mechanisms of 0$…

Search for double-βdecay processes in106Cd with the help of a106CdWO4crystal scintillator

A search for double $\ensuremath{\beta}$ processes in ${}^{106}$Cd was carried out at the Gran Sasso National Laboratories of the INFN (Italy) with the help of a ${}^{106}$CdWO${}_{4}$ crystal scintillator (215 g) enriched in ${}^{106}$Cd up to 66$%$. After 6590 h of data taking, new improved half-life limits on the double $\ensuremath{\beta}$ decay processes in ${}^{106}$Cd were established at the level of ${10}^{19}$--${10}^{21}$ yr; in particular, ${T}_{1/2}^{2\ensuremath{\nu}\ensuremath{\varepsilon}{\ensuremath{\beta}}^{+}}\ensuremath{\geqslant}2.1\ifmmode\times\else\texttimes\fi{}{10}^{20}$ yr, ${T}_{1/2}^{2\ensuremath{\nu}2{\ensuremath{\beta}}^{+}}\ensuremath{\geqslant}4.3\ifmmode\tim…

In-beam γ-ray spectroscopy of low- and medium-spin levels in 211Po

The structure of the low- and medium-spin levels of the 211Po nucleus have been studied with in-beam γ-ray spectroscopy with the 208Pb(α,n)211Po fusion-evaporation reaction. The level scheme was further extended with levels of the configurations π(h9/2)22+−4+⊗νg9/2, π(h9/2)28+⊗νg9/2, π(h9/2)22+−4+⊗νi11/2, π(h9/2)22+−4+⊗νj15/2, π(h9/2f7/2)8+⊗νg9/2, and π(h9/2)20+⊗ν(g9/2)20+(s1/2)−1. The single-particle neutron states νd5/2 and νs1/2 were also identified. Furthermore, a number of states feeding the low-spin structures were added. peerReviewed

Recursive method for computing matrix elements for two-body interactions

A recursive method for the efficient computation of two-body matrix elements is presented. The method consists of a set of recursion relations for the computationally demanding radial integral and adds one more tool to the set of computational methods introduced by Horie and Sasaki [H. Horie and K. Sasaki, Prog. Theor. Phys. 25, 475 (1961)]. The neutrinoless double-$\ensuremath{\beta}$ decay will serve as the primary application and example, but the method is general and can be applied equally well to other kinds of nuclear structure calculations involving matrix elements of two-body interactions.

Beta-spectrum shapes of forbidden β decays

The neutrinoless [Formula: see text] decay of atomic nuclei continues to attract fervent interest due to its potential to confirm the possible Majorana nature of the neutrino, and thus the nonconservation of the lepton number. At the same time, the direct dark matter experiments are looking for weakly interacting massive particles (WIMPs) through their scattering on nuclei. The neutrino-oscillation experiments on reactor antineutrinos base their analyses on speculations of [Formula: see text]-spectrum shapes of nuclear decays, thus leading to the notorious “reactor antineutrino anomaly.” In all these experimental efforts, one encounters the problem of [Formula: see text]-spectrum shapes of…

Search for double-\beta decay processes in \{106}Cd with the help of a \{106}CdWO_{4} crystal scintillator

A search for double β processes in 106Cd was carried out at the Gran Sasso National Laboratories of the INFN (Italy) with the help of a 106CdWO4 crystal scintillator (215 g) enriched in 106Cd up to 66%. After 6590 h of data taking, new improved half-life limits on the double β decay processes in 106Cd were established at the level of 1019–1021 yr; in particular, T 2νεβ+ 1/2 2.1 × 1020 yr, T 2ν2β+ 1/2 4.3 × 1020 yr, and T 0ν2ε 1/2 1.0 × 1021 yr. The resonant neutrinoless double-electron captures to the 2718-, 2741-, and 2748-keV excited states of 106Pd are restricted to T 0ν2K 1/2 4.3 × 1020 yr, T 0νKL1 1/2 9.5 × 1020 yr, and T 0νKL3 1/2 4.3 × 1020 yr, respectively (all limits at 90% confide…

Spin-dependent WIMP-nucleus scattering off 125Te, 129Xe, and 131Xe in the microscopic interacting boson-fermion model

We perform calculations of structure functions for elastic and inelastic spin-dependent scattering of weakly interacting massive particles (WIMPs) off 125Te, 129Xe, and 131Xe. The nuclear structure calculations are performed in the microscopic interacting boson-fermion model (IBFM-2). In our calculations we employ one-body and leading long-range two-body WIMP-nucleus currents derived from chiral effective field theory. We demonstrate that the relevant matrix elements can be reliably computed in the IBFM-2, which will allow investigation of heavy deformed nuclei previously inaccessible to theoretical calculations. peerReviewed

Physics of nuclear processes triggered by the interplay of strong and weak interactions

Neutrinoless double beta (0νββ) decay of nuclei is a process that requires the neutrino to be a massive Majorana particle and thus cannot proceed in the standard model of electro-weak interactions. Recent results of the neutrino-oscillation experiments have produced accurate information on the mixing of neutrinos and their squared mass differences. The 0νββ decay takes place in atomic nuclei where it can be observed, at least in principle, by underground neutrino experiments. The information about the weak-interaction observables, like the neutrino mass, has to be filtered from the data through the nuclear matrix elements (NMEs). In this article recent work of the Jyv¨askyl¨a group on the N…

AccurateQValue for theSn112Double-βDecay and its Implication for the Search of the Neutrino Mass

The $Q$ value of the $^{112}\mathrm{Sn}$ double-beta decay was determined by using a Penning trap mass spectrometer. The new atomic-mass difference between $^{112}\mathrm{Sn}$ and $^{112}\mathrm{Cd}$ of 1919.82(16) keV is 25 times more precise than the previous value of 1919(4) keV. This result removes the possibility of enhanced resonance capture of the neutrinoless double-EC decay to the excited ${0}^{+}$ state at 1871.00(19) keV in $^{112}\mathrm{Cd}$.

Spectrum-shape method and the next-to-leading-order terms of the β-decay shape factor

Effective values of the axial-vector coupling constant ${g}_{\mathrm{A}}$ have lately attracted much attention due to the prominent role of ${g}_{\mathrm{A}}$ in determining the half-lives of double $\ensuremath{\beta}$ decays, in particular their neutrinoless mode. The half-life method, i.e., comparing the calculated half-lives to the corresponding experimental ones, is the most widely used method to access the effective values of ${g}_{\mathrm{A}}$. The present paper investigates the possibilities offered by a complementary method: the spectrum-shape method (SSM). In the SSM, comparison of the shapes of the calculated and measured $\ensuremath{\beta}$ electron spectra of forbidden nonuniq…

Mean-field effects on neutrinoless double beta decay

Abstract Mean-field effects on the nuclear matrix elements involved in the neutrinoless double beta (0νββ) decay of several double-electron and double-positron emitters have been studied within the framework of the relativistic quark-confinement model and the quasiparticle random-phase approximation. The single-particle energies of the model space have been generated both by using the standard Woods-Saxon parametrization of the mean field and adjusting the quasiparticle spectra with the data from neutron- and proton-odd nuclei. The 0νββ rates are found to be much less affected by the energies of the mean-field orbitals than the rates of the two-neutrino double beta decay. The present study …

Weak-interaction and nuclear-structure aspects of nuclear double beta decay

Abstract Weak-interaction and nuclear-structure aspects of double beta decay are reviewed. Starting from effective electroweak lagrangians, decay rates for the two-neutrino and neutrinoless modes of the nuclear double beta decay transitions are defined and second-order perturbative expressions for the nuclear decay amplitudes are given. Nuclear matrix elements of the relevant operators are presented, as extracted from data and from shell-model and QRPA calculations as well as from other theoretical approximations. The analysis is performed both for the two-neutrino and neutrinoless modes of the decay. The expressions for ground-state-to-ground-state and ground-state-to-excited-state transit…

Confined quarks and the neutrinoless ββ decay

Abstract The half life of the neutrinoless double beta decay of 76Ge into the ground state of 76Se is calculated in a relativistic quark confinement model. The neutron-proton quasi-particle random phase approximation is used to evaluate the nuclear matrix elements involved in the decay amplitude. We avoid the closure approximation, but compare our results with this approximation. From the experimental half life we deduce an upper limit for the Majorana mass of the neutrino and estimate the right-handed contribution to the charged weak current.