0000000000461315
AUTHOR
J. Toivanen
Spectroscopic Properties of Nuclear Skyrme Energy Density Functionals
We address the question of how to improve the agreement between theoretical nuclear single-particle energies (SPEs) and experiment. Empirically, in doubly magic nuclei, the SPEs can be deduced from spectroscopic properties of odd nuclei that have one more, or one less neutron or proton. Theoretically, bare SPEs, before being confronted with experiment, must be corrected for the effects of the particle-vibration-coupling (PVC). In the present work, we determine the PVC corrections in a fully self-consistent way. Then, we adjust the SPEs, with PVC corrections included, to empirical data. In this way, the agreement with experiment, on average, improves; nevertheless, large discrepancies still …
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…
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…
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…
Deformations and quasiparticle spectra of nuclei in the nobelium region
We have performed self-consistent Skyrme Hartree-Fock-Bogolyubov calculations for nuclei close to $^{254}$No. Self-consistent deformations, including $\beta_{2,4,6,8}$ as functions of the rotational frequency, were determined for even-even nuclei $^{246,248,250}$Fm, $^{252,254}$No, and $^{256}$Rf. The quasiparticle spectra for N=151 isotones and Z=99 isotopes were calculated and compared with experimental data and the results of Woods-Saxon calculations. We found that our calculations give high-order deformations similar to those obtained for the Woods-Saxon potential, and that the experimental quasiparticle energies are reasonably well reproduced.
Solution of self-consistent equations for the N3LO nuclear energy density functional in spherical symmetry. The program hosphe (v1.02)
Abstract We present solution of self-consistent equations for the N 3 LO nuclear energy density functional. We derive general expressions for the mean fields expressed as differential operators depending on densities and for the densities expressed in terms of derivatives of wave functions. These expressions are then specified to the case of spherical symmetry. We also present the computer program hosphe (v1.02), which solves the self-consistent equations by using the expansion of single-particle wave functions on the spherical harmonic oscillator basis. Program summary Program title: HOSPHE (v1.02) Catalogue identifier: AEGK_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGK_…
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…
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…
Propagation of uncertainties in the Skyrme energy-density-functional model
Parameters of nuclear energy-density-functionals (EDFs) are always derived by an optimization to experimental data. For the minima of appropriately defined penalty functions, a statistical sensitivity analysis provides the uncertainties of the EDF parameters. To quantify theoretical errors of observables given by the model, we studied the propagation of uncertainties within the UNEDF0 Skyrme-EDF approach. We found that typically the standard errors rapidly increase towards neutron rich nuclei. This can be linked to large uncertainties of the isovector coupling constants of the currently used EDFs.
Efficient matrix-vector products for large-scale nuclear Shell-Model calculations
A method to accelerate the matrix-vector products of j-scheme nuclear Shell-Model Configuration Interaction (SMCI) calculations is presented. The method takes advantage of the matrix product form of the j-scheme proton-neutron Hamiltonian matrix. It is shown that the method can speed up unrestricted large-scale pf-shell calculations by up to two orders of magnitude compared to previously existing related j-scheme method. The new method allows unrestricted SMCI calculations up to j-scheme dimension 10^10 to be made in more complex model spaces.
Finite-range separable pairing interaction within the new N3LO DFT approach
For over four decades, the Skyrme functional within various parametrizations has been used to calculate nuclear properties. In the last few years there was a number of attempts to improve its performance and introduce generalized forms. In particular, the most general phenomenological quasi-local energy density functional, which contains all combinations of density, spin-density, and their derivatives up to the sixth order (N3LO), was proposed in [1]. Since in the phenomenological-functional approaches, the particle-particle (pp) channel is treated independently of the particle-hole (ph) channel, there remains a question of what pairing interaction is suitable to use within the N3LO energy …
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.
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…
Collective vibrational states with fast iterative QRPA method
An iterative method we previously proposed to compute nuclear strength functions is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasi-particle-random-phase approximation (QRPA) and uses an iterative non-hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method gives substantial advantages over conventional QRPA calculations with regards to the computational cost. The method is used to calculate excitation energies and decay rates of the lowest lying 2+ and 3- states in Pb, Sn, Ni and Ca isotopes using three different Skyrme interactions and a separabl…
Linear response strength functions with iterative Arnoldi diagonalization
We report on an implementation of a new method to calculate RPA strength functions with iterative non-hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix. We discuss the treatment of spurious modes, numerical stability, and how the method scales as the used model space is enlarged. We perform the particle-hole RPA benchmark calculations for double magic nucleus 132Sn and compare the resulting electromagnetic strength functions against those obtained within the standard RPA.
Dependence of single-particle energies on coupling constants of the nuclear energy density functional
We show that single-particle energies in doubly magic nuclei depend almost linearly on the coupling constants of the nuclear energy density functional. Therefore, they can be very well characterized by the linear regression coefficients, which we calculate for the coupling constants of the standard Skyrme functional. We then use these regression coefficients to refit the coupling constants to experimental values of single-particle energies. We show that the obtained rms deviations from experimental data are still quite large, of the order of 1.1 MeV. This suggests that the current standard form of the Skyrme functional cannot ensure spectroscopic-quality description of single-particle energ…
Giant Monopole Resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions
Background: Following the 2007 precise measurements of monopole strengths in tin isotopes, there has been a continuous theoretical effort to obtain a precise description of the experimental results. Up to now, there is no satisfactory explanation of why the tin nuclei appear to be significantly softer than 208Pb. Purpose: We determine the influence of finite-range and separable pairing interactions on monopole strength functions in semi-magic nuclei. Methods: We employ self-consistently the Quasiparticle Random Phase Approximation on top of spherical Hartree-Fock-Bogolyubov solutions. We use the Arnoldi method to solve the linear-response problem with pairing. Results: We found that the dif…
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.
Low-lying states in near-magic odd-odd nuclei and the effective interaction
The iterative quasiparticle random-phase approximation (QRPA) method we previously developed [Phys. Rev. C 81, 034312 (2010); 86, 024303 (2012); 86, 014307 (2012)] to accurately calculate properties of individual nuclear states is extended so that it can be applied for nuclei with odd numbers of neutrons and protons. The approach is based on the proton-neutron QRPA (pnQRPA) and uses an iterative non-Hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method is used to calculate excitation energies of proton-neutron multiplets for several nuclei. The influence of a pairing interaction in the T = 0 channel is studied.
FINITE-RANGE SEPARABLE PAIRING INTERACTION WITHIN NEW N[sup 3]LO DFT APPROACH
For over four decades, the Skyrme functional within various parametrizations has been used to calculate nuclear properties. In the last few years there was a number of attempts to improve its performance and introduce generalized forms. In particular, the most general phenomenologi‐cal quasi‐local energy density functional, which contains all combinations of density, spin‐density, and their derivatives up to the sixth order (N3LO), was proposed in reference [1]. Since in the phe‐nomenological functional approaches the particle‐particle (pp) interaction channel is treated independently from the particle‐hole (ph) channel, there remains a question of what pairing interaction is suitable to us…
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…
Error analysis of nuclear mass fits
We discuss the least-square and linear-regression methods, which are relevant for a reliable determination of good nuclear-mass-model parameter sets and their errors. In this perspective, we define exact and inaccurate models and point out differences in using the standard error analyses for them. As an illustration, we use simple analytic models for nuclear binding energies and study the validity and errors of models' parameters, and uncertainties of its mass predictions. In particular, we show explicitly the influence of mass-number dependent weights on uncertainties of liquid-drop global parameters.
Continuity equation and local gauge invariance for the N3LO nuclear energy density functionals
Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required, as a step preliminary to the adjustment of the coupling constants. Purpose: Determine to which extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, to study the relations between the validity of the continuity equation and invari…
Polarization corrections to single-particle energies studied within the energy-density-functional and quasiparticle random-phase approximation approaches
Background: Models based on using perturbative polarization corrections and mean-field blocking approximation give conflicting results for masses of odd nuclei. Purpose: We systematically investigate the polarization and mean-field models, implemented within self-consistent approaches that use identical interactions and model spaces, to find reasons for the conflicts between them. Methods: For density-dependent interactions and with pairing correlations included, we derive and study links between the mean-field and polarization results obtained for energies of odd nuclei. We also identify and discuss differences between the polarization-correction and full particle-vibration-coupling (PVC) …
Polarization corrections to single-particle energies studied within the energy-density-functional and QRPA approaches
Background: Models based on using perturbative polarization corrections and mean-field blocking approximation give conflicting results for masses of odd nuclei. Purpose: Systematically investigate the polarization and mean-field models, implemented within self-consistent approaches that use identical interactions and model spaces, so as to find reasons for the conflicts between them. Methods: For density-dependent interactions and with pairing correlations included, we derive and study links between the mean-field and polarization results obtained for energies of odd nuclei. We also identify and discuss differences between the polarization-correction and full particle-vibration-coupling (PV…
Building blocks for odd–even multigrid with applications to reduced systems
Abstract Building blocks yielding an efficient implementation of the odd–even multigrid method for the Poisson problem in the reference domain (0,1) d , d=2,3, are described. Modifications needed to transform these techniques to solve reduced linear systems representing boundary value problems in arbitrary domains are given. A new way to define enriched coarser subspaces in the multilevel realization is proposed. Numerical examples demonstrating the efficiency of developed multigrid methods are included.
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.
Characterization of totally chlorine-free effluents from kraft pulp bleaching III
Abstract Chemical changes in the dissolved high-molecular-mass material from silver birch (Betula pendula) kraft pulp during the oxygen–alkali delignification stage (O) and the subsequent totally chlorine-free (TCF) bleaching sequence (X–Z–EOP–AZ–EP–S) were investigated by analytical pyrolysis (pyrolysis–gas chromatography/mass-sensitive detector (Py–GC/MSD)). In addition, the pyrolysis data were subjected to chemometric analysis, resulting in a rapid method for determining with reasonable accuracy, for example, the mass proportion of carbohydrates and lignin in the effluents from each of the treatment stages. The method was calibrated by chemical analysis on the same effluents.
Fluctuating parts of nuclear ground state correlation energies
Background: Heavy atomic nuclei are often described using the Hartree-Fock-Bogoliubov (HFB) method. In principle, this approach takes into account Pauli effects and pairing correlations while other correlation effects are mimicked through the use of effective density-dependent interactions. Purpose: Investigate the influence of higher order correlation effects on nuclear binding energies using Skyrme's effective interaction. Methods: A cut-off in relative momenta is introduced in order to remove ultraviolet divergences caused by the zero-range character of the interaction. Corrections to binding energies are then calculated using the quasiparticle-random-phase approximation (QRPA) and secon…
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.