Deformed Quasiparticle Random-phase Approximation Research Articles

Competition of deformation and neutron–proton pairing in Gamow–Teller transitions for 56,58Ni and 62,64Ni

We investigate effects of unlike-pairing correlations by neutron–proton (np) pairs on Gamow–Teller strength distributions for even–even Ni isotopes, 56,58,60,62,64Ni, by taking into account nuclear deformation in a deformed Woods–Saxon mean field. Our calculations based on a deformed Bardeen–Cooper–Schriffer approach which preserves the axial and the time-reversal symmetry are performed within a deformed quasiparticle random phase approximation, in which we explicitly include the deformation and the unlike-pairing as well as the like-pairing correlations by neutron–neutron and proton–proton pairs. Competition of these two effects, the deformation and the pairing correlations, is shown to be able to affect more or less the GT strength distributions of the even–even Ni isotopes.

The Gogny-HFB+QRPA dipole strength function and its application to radiative neutron capture cross section

Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we extend our large-scale calculations of the E1 and M1 absorption γ-ray strength function obtained in the framework of the axially-symmetric deformed quasiparticle random phase approximation (QRPA) based on the finite-range D1M Gogny force to the determination of the de-excitation strength function. To do so, shell-model calculations of the de-excitation dipole strength function as well as experimental data are considered to provide insight in the low-energy limit and to complement the QRPA estimate phenomenologically. We compare our final prediction of the E1 and M1 strengths with available experimental data at low energies and show that a relatively good agreement can be obtained. Its impact on the average radiative width as well as radiative neutron capture cross section is discussed.

A study of Gamow-Teller transitions for N = Z nuclei, 24Mg, 28Si, and 32S, by a deformed QRPA

We investigated Gamow-Teller (GT) transitions and strength distributions of s-d shell N = Z nuclei, 24Mg, 28Si, and 32S, by a deformed quasi-particle random phase approximation (DQRPA). In the DQRPA, we included particle model space up to p-f shell and considered explicitly the deformation as well as the like- and unlike-pairing correlations. Shell evolution by deformation and attractive force by unlike-pairing correlations turned out to play vital roles to reproduce the experimental GT data. Correlations between the deformation and the pairing correlations are also discussed with the comparison to the experimental data shape.

Competition between α and β decays for heavy deformed neutron-deficient Pa, U, Np, and Pu isotopes

The competition between $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ decays is investigated for neutron-deficient Pa, U, Np, and Pu isotopes. ${\ensuremath{\beta}}^{+}$/electron-capture (EC) decay rates are calculated within the deformed quasiparticle random-phase approximation with realistic nucleon-nucleon $(NN)$ interactions. Contributions from allowed Gamow-Teller and Fermi transitions as well as first-forbidden transitions are considered. $\ensuremath{\alpha}$-decay calculations are performed within the generalized density-dependent cluster model. Effects of differences between neutron and proton distributions and nuclear deformation are taken into account. In the calculations, Reid-93 $NN$ interactions are used for ${\ensuremath{\beta}}^{+}/\mathrm{EC}$ decays, while Michigan three-range Yukawa effective interactions, based on the $G$-matrix elements of Reid $NN$ potentials, are used for $\ensuremath{\alpha}$ decay. The calculated $\ensuremath{\beta}$-decay half-lives show good agreement with the experimental data over a range of magnitude from ${10}^{2}$ to ${10}^{5}$ s. The resulting total half-lives including $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ contributions are found to be in good agreement with the experimental data, together with the $\ensuremath{\alpha}/\ensuremath{\beta}$-decay branching ratios.

Effects of deformation and neutron-proton pairing on the Gamow-Teller transitions forMg24,26in a deformed quasiparticle random-phase approximation

We investigate effects of neutron-proton ($np$) pairing correlations on the Gamow-Teller (GT) transition of $^{24,26}\mathrm{Mg}$ by explicitly taking into account deformation effects. Our calculation is performed by a deformed quasiparticle random phase approximation (DQRPA) which includes the deformation at the Bardeen-Cooper-Schrieffer and RPA stage. In this paper, we include the $np$ pairing as well as neutron-neutron ($nn$) and proton-proton ($pp$) paring correlations to the DQRPA. Our new formalism is applied to the GT transition of well-known deformed Mg isotopes. The $np$ pairing effect is found to affect more or less the GT distribution of $^{24}\mathrm{Mg}$ and $^{26}\mathrm{Mg}$. But the deformation effect turns out to be much larger than the $np$ paring effect because the Fermi surfaces smear more widely by the deformation rather than the $np$ pairing correlations. Correlations between the deformation and the $np$ pairing effects and their ambiguities are also discussed with the comparison to experimental GT strength data by triton and $^{3}\mathrm{He}$ beams.

Long-lived K isomer and enhanced γ vibration in the neutron-rich nucleus 172Dy: Collectivity beyond double midshell

The level structure of 172Dy has been investigated for the first time by means of decay spectroscopy following in-flight fission of a 238U beam. A long-lived isomeric state with T1/2 = 0.71(5) s and K π = 8 − has been identified at 1278 keV, which decays to the ground-state and γ-vibrational bands through hindered electromagnetic transitions, as well as to the daughter nucleus 172Ho via allowed β decays. The robust nature of the K π = 8 − isomer and the ground-state rotational band reveals an axially-symmetric structure for this nucleus. Meanwhile, the γ-vibrational levels have been identified at unusually low excitation energy compared to the neighboring well-deformed nuclei, indicating the significance of the microscopic effect on the non-axial collectivity in this doubly mid-shell region. The underlying mechanism of enhanced γ vibration is discussed in comparison with the deformed Quasiparticle Random-Phase Approximation based on a Skyrme energy-density functional.

Deformation effects on the gamow-teller transitions in 76Ge and 76Se by using the deformed Quasi-Particle Random-Phase Approximation

With the advent of high technology in analyzing the Gamow-Teller (GT) excited states beyond the one nucleon emission threshold, the quenching of the GT strength to the Ikeda sum rule can be recovered by using the high-lying GT states. Moreover, in some nuclei, GT peaks that are stronger than any other peaks appear explicitly in the high-lying excited states. In the current study, we have addressed these high-lying GT (–) excited states within a framework of the deformed quasi-particle random-phase approximation (DQRPA). These high-lying GT (–) excited states are generated due to an increase in particle numbers around the Fermi surface due to an increase in the chemical potential owing to a certain deformation of the nuclei. On the contrary, among the GT(+) excited states, the low-lying ones were favored by an increase in the deformation. The main GT(+/–) transitions were also changed drastically by the deformation. A detailed mechanism leading to the changes in the GT transitions is discussed by studying the shell evolution and the consequent change in the particle numbers in the smearing region caused by the deformation in typical doublebeta-decay nuclei, 76Ge and 76Se.

β-decay rates of odd-mass neutron-rich isotopes in the deformed quasiparticle random-phase approximation with realistic interactions

The deformed quasiparticle random-phase approximation with realistic nucleon-nucleon interactions is extended for the ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay of odd-mass neutron-rich Kr, Sr, Zr, and Mo isotopes, from their longest-lived isotopes to the experimentally unknown nuclei. The particle-particle and particle-hole channels of residual interactions are handled in large single-particle model spaces, based on the Br\"uckner $G$ matrix with charge-dependent Bonn nucleon-nucleon forces. Both allowed Gamow-Teller and first-forbidden transitions are considered and different treatments for odd-mass systems are emphasized. The sensitivity of the calculated results to the single-particle level scheme and the particle-particle strength is discussed. The calculated Gamow-Teller strengths are analyzed, together with the contributions from first-forbidden transitions. The calculated half-lives are found to agree well with the experimental data over the orders of magnitude from ${10}^{\ensuremath{-}2}$ to ${10}^{3}$ s.

Formula omitted]/EC decay rates of deformed neutron-deficient nuclei in the deformed QRPA with realistic interactions

The weak-decay (β+ and EC) rates of neutron-deficient Kr, Sr, Zr, and Mo isotopes are investigated within the deformed quasiparticle random-phase approximation with realistic nucleon–nucleon interactions. The particle–particle and particle–hole channels of residual interactions are handled in large single-particle model spaces, based on the Brückner G-matrix with charge-dependent Bonn nucleon–nucleon forces. Contributions from allowed Gamow–Teller and Fermi transitions as well as first-forbidden transitions are calculated. The calculated half-lives show good agreement with the experimental data over a wide range of magnitude, from 10−2 to 107 s. Moreover, predictions of β-decay half-lives are made for some extremely proton-rich isotopes, which could be useful for future experiments.

β-decay rates of neutron-rich Kr and Sr isotopes in the deformed QRPA with realistic interactions

Deformed quasiparticle random phase approximation with realistic nucleon–nucleon interactions is employed to investigate β-decay half-lives and β-delayed neutron emission probabilities of neutron-rich Kr and Sr isotopes. The residual particle–particle and particle-hole interactions are obtained in terms of the Brückner G-matrix with the charge-dependent Bonn nucleon–nucleon force. Both allowed Gamow–Teller and first-forbidden transitions are taken into account. The available experimental half-lives are well reproduced with a factor of about three. Predictions on β-decay properties are made for more neutron-rich isotopes, which could be useful for future experiments.

β-decay rates of neutron-rich Zr and Mo isotopes in the deformed quasiparticle random-phase approximation with realistic interactions

The ${\ensuremath{\beta}}^{\ensuremath{-}}\mathrm{-decay}$ rates of neutron-rich Zr and Mo isotopes are investigated within the deformed quasiparticle random-phase approximation with realistic nucleon-nucleon interactions. Axially symmetric deformations are considered in the calculations from a mean-field description of a quasiparticle picture and of both particle-hole and particle-particle excitations. The Br\"uckner $G$ matrix obtained with charge-dependent Bonn nucleon-nucleon forces is employed for residual particle-particle and particle-hole interactions. Contributions from both allowed Gammow-Teller and first-forbidden transitions are calculated and the sensitivity of the calculated results to the particle-particle strength is discussed. The calculated $\ensuremath{\beta}$-decay half-lives show a good agreement with the available experimental data. Moreover, predictions of $\ensuremath{\beta}$-decay half-lives are made for some extremely neutron-rich isotopes, which could be useful for future experiments.

Shell evolution ofN=20nuclei and Gamow-Teller strengths of30,32,34Mg with deformed quasiparticle random-phase approximation

Gamow-Teller (GT) strength distributions of Mg isotopes are investigated within a framework of the deformed quasiparticle random-phase approximation. We found that the $N=20$ shell closure in ${}^{28\ensuremath{\sim}34}$Mg was broken by the prolate shape deformation originating from the $\mathit{fp}$-intruder states. The shell closure breaking gives rise to a shift of low-lying GT excited states into high-lying states. Discussions regarding the shell evolution trend of single-particle states around $N=20$ nuclei are also presented with the comparison to other approaches.

Unified description of 21+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 able to describe in an unified way gross features of electromagnetic transitions from vibrational to rotational nuclei.

Nuclear Structure of 12,14Be Within Deformed Quasi-Particle Random Phase Approximation (DQRPA)

We developed a deformed quasi-particle random phase approximation (DQRPA) to describe the Gamow–Teller (GT) transitions on even–even neutron-rich nuclei. To describe deformed nuclei, we exploited the deformed axially symmetric Woods–Saxon potential, the deformed BCS, and the deformed QRPA with realistic two-body interaction calculated by Brueckner G-matrix based on Bonn CD potential. The deformed single particle states are expanded in terms of the spherical harmonic oscillator basis in order to take the realistic G-matrix stored in the spherical basis. We calculated GT strength distributions, B(GT), of two nuclei 12,14Be for many different deformation parameter β 2 values as a function of the excitation energy E ex w.r.t. the ground state of a parent nucleus. Our results for 12Be predict to prefer a prolate shape and B(GT) results of 14Be turn out to be independent of the β 2 values.

Deformation effects on the Gamow-Teller strength distributions in the double-βdecay partners76Ge and76Se

A theoretical approach based on a deformed quasiparticle random phase approximation built on a Skyrme self-consistent mean field is used to describe the recent measurements of the Gamow-Teller GT${}^{\ensuremath{-}}$ strength distribution extracted from the charge-exchange reaction ${}^{76}$Ge(${}^{3}$He${,t)}^{76}$As with high energy resolution. The same analysis is made to describe the Gamow-Teller GT${}^{+}$ strength distribution measured in the ${}^{76}$Se$(d{,}^{2}$He)${}^{76}$As reaction. Combining these two branches, the nuclear matrix element for the two-neutrino double-$\ensuremath{\beta}$ decay process is evaluated and compared to experiment. The role of the nuclear deformation on those processes is emphasized and analyzed.

Evaluation of the resonance enhancement effect in neutrinoless double-electron capture in152Gd,164Er, and180W atoms

We study the resonant neutrinoless double-electron capture ($0\ensuremath{\nu}$ECEC) in ${}^{152}\mathrm{Gd}$, ${}^{164}\mathrm{Er}$, and ${}^{180}\mathrm{W}$ atoms, associated with the ground-state to ground-state nuclear transitions. The corresponding matrix elements are calculated within the deformed quasiparticle random-phase approximation using the realistic charge-dependent Bonn (CD-Bonn) nucleon-nucleon interaction. The half-lives are estimated with the use of the most recent precision data on the $Q$ values of these processes. Perspectives of experimental search for the $0\ensuremath{\nu}$ECEC with the isotopes ${}^{152}\mathrm{Gd}$, ${}^{164}\mathrm{Er}$, and ${}^{180}\mathrm{W}$ are discussed.

β-decay properties of neutron-rich Zr and Mo isotopes

Gamow-Teller strength distributions, beta-decay half-lives, and beta-delayed neutron emission are investigated in neutron-rich Zr and Mo isotopes within a deformed quasiparticle random-phase approximation. The approach is based on a self-consistent Skyrme Hartree-Fock mean field with pairing correlations and residual separable particle-hole and particle-particle forces. Comparison with recent measurements of half-lives stresses the important role that nuclear deformation plays in the description of beta-decay properties in this mass region.

Pygmy dipole mode in deformed neutron-rich Mg isotopes close to the drip line

We investigate the microscopic structure of the low-lying isovector-dipole excitation mode in neutron-rich $^{36,38,40}\mathrm{Mg}$ close to the drip line by means of the deformed quasiparticle random-phase approximation employing the Skyrme and the local pairing energy-density functionals. It is found that the low-lying bump structure above the neutron emission-threshold energy develops when the drip line is approached, and that the isovector dipole strength at ${E}_{x}l10$ MeV exhausts about $6.0%$ of the classical Thomas-Reiche-Kuhn dipole sum rule in $^{40}\mathrm{Mg}$. We obtained the collective dipole modes at around $8\text{\ensuremath{-}}10$ MeV in Mg isotopes, that consist of many two-quasiparticle excitations of the neutron. The transition density clearly shows an oscillation of the neutron skin against the isoscalar core. We found significant coupling effects between the dipole and octupole excitation modes due to the nuclear deformation. It is also found that the responses for the compressional dipole and isoscalar octupole excitations are much enhanced in the lower energy region.

Shape mixing andβ-decay properties of neutron-deficient Kr and Sr isotopes

Gamow-Teller strength distributions and $\ensuremath{\beta}$-decay half-lives in neutron-deficient Kr and Sr isotopes are investigated within a deformed quasiparticle random phase approximation. The approach is based on a self-consistent Skyrme Hartree-Fock mean field with pairing correlations and residual separable particle-hole and particle-particle forces. A simple two-level model is used to mix the nuclear shapes into the physical ground state. Good agreement with experiment is found with shape mixing coefficients which are consistent with those obtained phenomenologically from mixing of rotational bands.

Nuclear shape dependence of Gamow-Teller distributions in neutron-deficient Pb isotopes

We study Gamow-Teller strength distributions in the neutron-deficient even isotopes (184-194)Pb in a search for signatures of deformation. The microscopic formalism used is based on a deformed quasiparticle random phase approximation (QRPA) approach, which involves a self-consistent quasiparticle deformed Skyrme Hartree-Fock (HF) basis and residual spin-isospin forces in both the particle-hole and particle-particle channels. By analyzing the sensitivity of the Gamow-Teller strength distributions to the various ingredients in the formalism, we conclude that the beta-decay of these isotopes could be a useful tool to look for fingerprints of nuclear deformation.