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…

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…

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…

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…

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…

The M4 transitions of isomeric states

Tässä pro gradu -tutkielmassa tutkitaan isomeeristen tilojen magneettisten M4-gammasiirtymien redusoituja matriisielementtejä. Tutkittavat siirtymät ovat venyneitä M4-siirtymiä kaksoisbeetahajoamisten massa-alueilla A=85-115 ja A=135-143. Tutkielman tarkoituksena on verrata kokeellisia ydinmatriisielementtejä kvasihiukkasmatriisielementteihin ja MQPM-teorian avulla laskettuihin matriisielementteihin. Kokeelliset matriisielementi lasketaan kokeellisesti määritettyjen arvojen avulla ja kvasihiukkas- sekä MQPM-matriisielementit määritetään tietokoneohjelmien avulla. Kokeellisten ja kvasihiukkasmatriisielementtien välinen suhde osoittautui olevan noin 0,29 ja kokeellisten ja MQPM-matriisielemen…

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…

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-…

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…

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…

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

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

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…

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…

Konformikuvauksista

Tarkastelen työssä konformikuvauksia, sekä niihin liittyviä tärkeitä tuloksia. Esitän Riemannin kuvauslauseen todistuksen sekä todistan Schwarzin ja Christoffelin kaavan, joka karakterisoi konformikuvaukset puolitasolta monikulmiolle. Lisäksi tarkastelen työssä konformikuvausten soveltamista muutamiin fysiikan ongelmiin virtausmekaniikan, termodynamiikan ja sähköstatiikan aloilla. In the thesis I study conformal mappings and some important results related to them. I introduce a proof for Riemann mapping theorem and prove the Schwarz-Christoffel formula, which characterizes the conformal mappings from the half plane to a polygon. In addition, I study applying the conformal mappings to some p…