Proton-neutron Quasiparticle Random-phase Approximation Research Articles

Higher forbidden unique β− decay transitions and shell-model interpretation

In the present work, we have predicted the half-lives for the β− decay for higher forbidden unique transitions in the mass range of nuclei from A = 40-138. For these transitions, the experimental data for half-lives are not available except for a few cases. The calculations for half-lives are performed within the framework of the nuclear shell model (SM). We have used the effective interactions sdpf-mu, gxpf1a, gwbxg, G-matrix, snet, sn100pn, and jj56pnb to perform the SM calculations in different mass regions. A comprehensive discussion has been made between the SM predicted half-lives and the scaled half-lives from proton-neutron quasiparticle random-phase approximation (pnQRPA). The results of the present study will be useful to plan new experiments to measure half-lives for these higher forbidden unique β− transitions.

Re-examination of nuclear structure properties and shape co-existence of nuclei around A ∼ 70

We re-examine the nuclear structure properties of waiting point nuclei around A ∼ 70 using the interacting boson model-1 (IBM-1) and the relativistic mean field (RMF) model. Effective density-dependent meson-exchange functional (DD-ME2) and density-dependent point-coupling functional (DD-PC1) were used for the RMF calculations. We calculated the energy levels, the geometric shapes, binding and separation energies of nucleons and quadrupole deformation parameters (β2). The shape co-existence phenomena in A ∼ 70 nuclei (68Se, 70Se, 70Br, 70Kr, 72Kr, 74Kr, 74Rb and 74Sr) was later investigated. Spherical and deformed shapes of the selected waiting point nuclei were computed using the IBM-1 and RMF models, respectively. The proton-neutron quasiparticle random phase approximation (pn-QRPA) model was used to calculate β-decay properties (Gamow-Teller strength distributions, β-decay half-lives and branching ratios) of selected nuclei as a function of β2. The results revealed a significant variation in calculated half-lives and Gamow-Teller strength distributions as the shape parameter was changed. The β2 computed via DD-ME2 functional resulted in half-lives in best agreement with the measured data.

Re-examination of effects of pairing gaps on charge-changing transitions

We re-examine the effects of pairing gaps on charge-changing transitions and the associated β-decay half-lives. Calculations are performed using the proton-neutron quasiparticle random phase approximation (pn-QRPA) model for 250 nuclei possessing astrophysical significance. Pairing gaps between like nucleons are key model parameters in the pn-QRPA approach. Three different values of empirically computed pairing gaps were used as input parameters in our nuclear model. Changing the pairing gap values significantly altered the Gamow-Teller distributions including the total strength and centroid values. The β-decay half-lives also changed substantially. The half-lives computed via the three-term pairing formula, based on separation energies of nucleons, were in best agreement with the measured data.

Nuclear structure properties and weak interaction rates of even–even Fe isotopes

Nuclear structure properties and weak interaction rates of neutron-rich even–even iron (Fe) isotopes (A = 50 – 70) are investigated using the Interacting Boson Model-1 (IBM-1) and the proton–neutron Quasiparticle Random Phase Approximation (pn-QRPA) model. The IBM-1 is used for the calculation of energy levels and the B(E2) values of neutron-rich Fe isotopes. Later their geometry was predicted within the potential energy formalism of the IBM-1 model. Weak interaction rates on neutron-rich nuclei are needed for the modeling and simulation of presupernova evolution of massive stars. In the current study, we investigate the possible effect of nuclear deformation on stellar rates of even–even Fe isotopes. The pn-QRPA model is applied to calculate the weak interaction rates of selected Fe isotopes using three different values of deformation parameter. It is noted that, in general, bigger deformation values led to smaller total strength and larger centroid values of the resulting Gamow–Teller distributions. This later translated to smaller computed weak interaction rates. The current finding warrants further investigation before it may be generalized. The reported stellar rates are up to 4 orders of magnitude smaller than previous calculations and may bear astrophysical significance.

Re-Examination of the Effect of Pairing Gaps on Gamow–Teller Strength Distributions and β-Decay Rates

β-decay is one of the key factors for understanding the r-process and evolution of massive stars. The Gamow–Teller (GT) transitions drive the β-decay process. We employ the proton–neutron quasiparticle random phase approximation (pn-QRPA) model to calculate terrestrial and stellar β-decay rates for 50 top-ranked nuclei possessing astrophysical significance according to a recent survey. The model parameters of the pn-QRPA model affect the predicted results of β-decay. The current study investigates the effect of nucleon–nucleon pairing gaps on charge-changing transitions and the associated β decay rates. Three different values of pairing gaps, namely TF, 3TF, and 5TF, were used in our investigation. It was concluded that both GT strength distributions and half-lives are sensitive to pairing gap values. The 3TF pairing gap scheme, in our chosen nuclear model, resulted in the best prediction with around 80% of the calculated half-lives within a factor 10 of the measured ones. The 3TF pairing scheme also led to the calculation of the biggest β-decay rates in stellar matter.

Re-analysis of the Gamow-Teller distributions for [formula omitted] nuclei, 24Mg, 28Si, and 32S

The Gamow-Teller (GT) strength distributions of sd-shell N=Z nuclei (24Mg, 28Si, and 32S) are investigated within the framework of proton–neutron quasi-particle random phase approximation (pn-QRPA) using a deformed basis. The nuclear properties of these special nuclei were investigated by the Relativistic Mean Field (RMF) model. The RMF framework with density-dependent interactions (DD-PC1 and DD-ME2) was employed to compute ground-state deformation parameters (β2) using potential energy curves. The β2 values computed from the RMF and the finite range droplet model (FRDM) were employed as a free parameter in the pn-QRPA calculation to investigate the resulting GT strength distributions. The present model-based analyses compare well with the observed data.

Impact of the Brink-Axel hypothesis on unique first-forbidden β-transitions for r-process nuclei* *J.-U. Nabi is supported by the Higher Education Commission Pakistan through Project (0-15394/NRPU/R&D/HEC/2021)

Key nuclear inputs for the astrophysical r-process simulations are the weak interaction rates. Consequently, the accuracy of these inputs directly affects the reliability of nucleosynthesis modeling. The majority of the stellar rates, used in simulation studies are calculated by invoking the Brink-Axel (BA) hypothesis. The BA hypothesis assumes that the strength functions of all parent excited states are the same as for the ground state, only shifted in energies. However, the BA hypothesis has to be tested against microscopically calculated state-by-state rates. In this project, we study the impact of the BA hypothesis on calculated stellar -decay and electron capture rates. Our investigation include both unique first forbidden (U1F) and allowed transitions for 106 neutron-rich trans-iron nuclei ([27, 77] ≤ [Z, A] ≤ [82, 208]). The calculations were performed using the deformed proton-neutron quasiparticle random-phase approximation (pn-QRPA) model with a simple plus quadrupole separable and schematic interaction. Waiting-point and several key r-process nuclei lie within the considered mass region of the nuclear chart. We computed electron capture and -decay rates using two different prescriptions for strength functions. One was based on invoking the BA hypothesis and the other was the state-by-state calculation of strength functions, under stellar density and temperature conditions ([10, 1] ≤ [ ( ), T( )] ≤ [1011, 30]). Our results show that the BA hypothesis invoked U1F rates are overestimated by 4–5 orders of magnitude as compared to microscopic rates. For capture rates, more than two orders of magnitude differences were noted when applying the BA hypothesis. It was concluded that the BA hypothesis is not a reliable approximation, especially for -decay forbidden transitions.

Validity of Brink-Axel Hypothesis for calculations of allowed stellar weak rates of heavy nuclei

The knowledge of beta-decay transitional probabilities and Gamow-Teller (GT) strength functions from highly excited states of nuclides is of particular importance for applications to astrophysical network calculations of nucleosynthesis in explosive stellar events. These quantities are challenging to achieve from measurements or computations using various nuclear models. Due to unavailability of feasible alternatives, many theoretical studies often rely on the Brink-Axel (BA) hypothesis, that is, the response of strength functions depends merely on the transition energy of the parent nuclear ground state and is independent of the underlying details of the parent state, for the calculation of stellar rates. BA hypothesis has been used in many applications from nuclear structure determination to nucleosynthesis yield in the astrophysical matter. We explore here the the validity of BA hypothesis in the calculation of stellar beta-decay (BD) and electron capture (EC) weak rates of fp- and fpg-shell nuclides for GT transitions. Strength functions have been computed employing the fully microscopic proton-neutron QRPA (quasi-particle random-phase approximation) within a broad density, ρY e = (10-1011) [g cm−3], and temperature, T = (1−30) [GK], grid relevant to the pre-collapse astrophysical environment. Our work provides evidence that the use of the approximation based on the BA hypothesis does not lead to reliable calculations of excited states strength functions under extreme temperature-density conditions characteristic of presupernova and supernova evolution of massive stars. Weak rates obtained by incorporating the BA hypothesis in the calculation of strength functions substantially deviate from the rates based on the state-by-state microscopically calculated strength functions. Deviation in the two calculations becomes significant as early as neon burning phases of massive stars. The deviation in the calculation of BD rates is even more pronounced, reaching up to three orders of magnitude.

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 136Ba, the daughter nucleus of 136Xe double beta decay (DBD). The OMC rates at low-lying nuclear states (below 1 MeV of excitation energy) in 136Cs 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 136Cs, the intermediate nucleus of the 136Xe DBD. At the same time, OMC can be considered a powerful probe of the effective values of weak axial-type couplings in a 100 MeV momentum exchange region, which is relevant for neutrinoless DBD. The present work represents the first attempt to compare the ISM and pnQRPA results for OMC on a heavy nucleus while also including the exact muon wave function and the 2BC. The sensitivity estimates of the current and future neutrinoless DBD experiments will clearly benefit from future OMC measurements taken using OMC calculations similar to the one presented here.

Correlations between neutrinoless double- β , double Gamow-Teller, and double-magnetic decays in the proton-neutron quasiparticle random-phase approximation framework

We explore the relation between the nuclear matrix elements of neutrinoless double-beta ($0\nu\beta\beta$) decay and two other processes: double Gamow-Teller (DGT) and double-magnetic dipole (M1M1) transitions, with focus on medium-mass to heavy nuclei studied with the proton-neutron quasiparticle random-phase approximation (pnQRPA) framework. We explore a wide span of isoscalar proton-neutron pairing strengths covering the typical range of values that describe well $\beta$- and two-neutrino $\beta\beta$-decay data. Our results indicate good linear correlations between $0\nu\beta\beta$ and both DGT and M1M1 matrix elements. Together with future measurements of DGT and M1M1 transitions, these correlations could help constrain the values of the $0\nu\beta\beta$-decay nuclear matrix elements.

Neutrinoless ββ -decay nuclear matrix elements from two-neutrino ββ -decay data

We study two-neutrino ($2\nu\beta\beta$) and neutrinoless double-$\beta$ ($0\nu\beta\beta$) decays in the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) frameworks. Calculating the decay half-life of several dozens of nuclei ranging from calcium to xenon with the shell model, and of $\beta\beta$ emitters with a wide range of proton-neutron pairing strengths in the pnQRPA, we observe good linear correlations between $2\nu\beta\beta$- and $0\nu\beta\beta$-decay nuclear matrix elements for both methods. We then combine the correlations with measured $2\nu\beta\beta$-decay half-lives to predict $0\nu\beta\beta$-decay matrix elements with theoretical uncertainties based on our systematic calculations. Our results include two-body currents and the short-range $0\nu\beta\beta$-decay operator.

Investigation of β-decay properties of neutron-rich Cerium isotopes

Reliable and precise knowledge of the β-decay properties of neutron-rich nuclei is important for a better understanding of the r-process. We report the computation of β-decay properties of neutron-rich Cerium isotopes calculated within the proton-neutron quasiparticle random phase approximation (pn-QRPA) approach. A total of 34 isotopes of Ce in the mass range 120 ≤ A ≤ 157 were considered in our calculation. Pairing gaps are recognized amongst the key parameters in the pn-QRPA model to compute Gamow-Teller (GT) transitions. We employed two different values of the pairing gaps obtained from two different empirical formulae in our computation. The GT strength distributions changed considerably with a change in the pairing gap values. This in turn resulted in contrasting centroid and total strength values of the GT distributions and led to differences in calculated half-lives using the two schemes. The traditional pairing gaps resulted in significant fragmentation of GT strength. However, the pairing gaps, calculated employing the formula based on separation energies of neutron and proton, led to computed half-lives in better agreement with the measured data.

Double- β transition 0+→2+ within a fully renormalized proton-neutron quasiparticle random-phase approximation with the gauge symmetry restored

The $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay from the ground to the first excited ${2}^{+}$ state is considered for eight nuclei where experimental data are available. The transition amplitude is calculated with a projected spherical single-particle basis, a fully renormalized proton-neutron quasiparticle random-phase approximation (pnQRPA) for the Gamow-Teller (GT) dipole transition operator and a renormalized QRPA for charge conserving quadrupole operators. Also for the transition operator the first-order boson expansion expression is employed. Using the phase space integral corresponding to the transition ${0}^{+}\ensuremath{\rightarrow}{2}^{+}$ and the GT transition amplitude, the process half-life is readily obtained. The single-${\ensuremath{\beta}}^{\ensuremath{\mp}}$ transition strengths are studied as function of the energies of the fully renormalized pnQRPA with the gauge symmetry restored. The single-$\ensuremath{\beta}$ transition operators are used to calculate the ${log}_{10}ft$ values for the electron capture of the intermediate odd-odd nucleus to the mother nucleus as well as for the ${\ensuremath{\beta}}^{\ensuremath{-}}$ transition to the daughter nucleus. For the final state in the daughter nucleus the $B(E2)$ values for the transition ${2}^{+}\ensuremath{\rightarrow}{0}^{+}$ and the half-life of the electromagnetic decaying state are calculated. The Ikeda sum rule for the mother nucleus is satisfied. The mentioned results are compared with the corresponding available data and a reasonable agreement is shown. The gauge projection quenches the half-life in the case of $^{150}\mathrm{Nd}, ^{116}\mathrm{Cd}$, and $^{100}\mathrm{Mo}$ and enhances it for the remaining considered nuclei. Keeping the same parameters for the model Hamiltonian the ground to ground double-$\ensuremath{\beta}$ transition is also treated and a good agreement with the existing data is obtained.

Beta decay and electron capture rates of manganese isotopes in astrophysical environments

The isotopes of manganese in the mass range of A=53−63 are abundant in the core materials of high-mass stars and they are considered to be of prime importance in the progression of the pre-collapse phases. During these late evolutionary phases, nuclear processes associated with weak interactions, including β−-decay and electron capture (EC) of these isotopes, significantly alter the lepton to baryon ratio (Ye) in the core’s composition. The temporal change in this parameter is one of the basic elements used to simulate a successful explosion. Hence, the β−-decay and EC rates of manganese (Mn) nuclides may serve as important inputs in the simulation codes for core-collapse supernova. In this study, we investigated the weak decay characteristics of 55−63Mn nuclides. The strength distributions of Gamow–Teller transitions in the directions of β−-decay and EC were calculated for these isotopes using the proton–neutron quasi-particle random-phase approximation (pn-QRPA) model. The β-decay half-life values of Mn isotopes under terrestrial conditions were computed and compared with measured data and previous calculations. The pn-QRPA estimated half-lives were in good agreement with the experimental values. The β− and EC rates were then calculated over a large range of stellar temperatures (0.01−30)×109K and densities (10−1011) g/cm3. The computed rates were compared with previous calculations performed using the large-scale shell model (LSSM) and independent particle model (IPM). For most of the isotopes, in high temperature and density regimes, the pn-QRPA calculated β−-decay rates were smaller than the LSSM and IPM rates by up to an order of magnitude. By contrast, the EC rates were larger by up to an order of magnitude (factor of 3−10) at high temperature compared with the LSSM (IPM) results.

Bulk and decay properties of neutron-deficient odd-mass Hg isotopes near A=185

Ground and isomeric states of the neutron-deficient odd-$A$ isotopes $^{183}$Hg, $^{185}$Hg, and $^{187}$Hg are described from a microscopic calculation based on a self-consistent, axially-deformed Hartree-Fock mean field with the Skyrme functional and pairing within BCS approximation. For each equilibrium shape and different odd-neutron states, results on mean square charge radii and magnetic dipole moments are given and analyzed in the context of their sensitivity to the nuclear deformation and to the spin and parity. Spin-isospin correlations within proton-neutron quasiparticle random phase approximation are then introduced in the nuclear states to obtain the distributions of Gamow-Teller strength and the $\beta^+/EC$ half-lives of these isotopes, whose measurements are planned at ISOLDE-CERN using total absorption gamma-ray spectroscopy techniques.

Roles of tensor and isoscalar pairing interactions in β-decay calculations for possible r-process waiting point nuclei with N ~ 82 and 126* *Supported by the National Natural Science Foundation of China (11575120, 11822504), and Science Specialty Program of Sichuan University (2020SCUNL210)

In this study, we adopt the self-consistent Hartree-Fock-Bogoliubov (HFB) theory with the proton-neutron quasi-particle random phase approximation (pnQRPA) based on the Skyrme force for calculation of the β − decay half-lives for nuclei with N ~ 82 and 126 on possible r-process paths. In the calculations, the Skyrme interaction (e.g., SKO') is adopted, and the tensor interaction is added self-consistently in both HFB and QRPA calculations. We systematically study how the half-life is changed by varying the strength of the triplet-even (TE) and triplet-odd (TO) components as well as the IS pairing. We find that a variation in strength of the IS pairing of approximately 20% does not produce a substantial effect on β-decay rates with or without the tensor force, while a strength variation of the TO tensor force considerably affects the change in the β-decay half-lives for the very neutron rich N ~ 82 and 126 isotonic chains. In addition, with the inclusion of the tensor force, the GT decay becomes dominant for very neutron-rich nuclei.

Electron capture and β-decay rates for nuclei with A = 65–80

Recently a list of top 50 most important electron capture (ec) and β-decay (bd) nuclei, averaged throughout the stellar trajectory for 0.500 > Y e > 0.400, was published. The current study presents the calculation of ec and bd rates, from the published list with A = 65–80, on a detailed temperature-density grid. The ec and bd rates were calculated using the proton-neutron quasiparticle random phase approximation model (pn-QRPA). Our calculation did not employ the Brink-Axel hypothesis. A systematic comparison of the current calculation with the previous pn-QRPA and independent particle model (IPM) results is presented for the first time. The reported ec rates are almost the same when compared with the previous pn-QRPA calculation. On the other hand, the reported bd rates are generally smaller up to an order of magnitude. Comparison with IPM results show that our calculated rates are bigger, by two orders of magnitude. The current calculation may contribute to a more realistic simulation of late phases of stellar evolution and modeling of x-ray bursts.

Calculation of β -decay half-lives within a Skyrme-Hartree-Fock-Bogoliubov energy density functional with the proton-neutron quasiparticle random-phase approximation and isoscalar pairing strengths optimized by a Bayesian method

Background: For data on radioactive nuclei, $\ensuremath{\beta}$ decay provides some of the most important information, applicable to various fields. However, some $\ensuremath{\beta}$-decay data are not available due to experimental difficulties. For this reason, theoretically calculated results have been embedded in the data on radioactive nuclear $\ensuremath{\beta}$ decay to compensate for the missing information.Purpose: It is necessary to treat various nuclear correlations as precisely as possible for theoretical $\ensuremath{\beta}$-decay calculations. In particular, the pairing correlation is one of the most important factors for reproducing $\ensuremath{\beta}$-decay half-lives correctly. Therefore, we first study the effect of zero- and finite-range isovector pairings on half-lives. Second, we investigate the isoscalar pairing strengths, which are determined through experimental data of half-lives. Finally, we predict the isoscalar pairing strengths and half-lives of neutron-rich nuclei.Methods: To calculate the $\ensuremath{\beta}$-decay half-lives, a proton-neutron quasiparticle random-phase approximation on top of a Skryme energy density functional is applied with an assumption of spherical symmetry. The half-lives are calculated by including the allowed and first-forbidden transitions. The isoscalar pairing strength is estimated by a Bayesian neural network (BNN). We verify the predicted isoscalar pairing strengths by preparing the training data and test data.Results: It was confirmed that the finite-range isovector pairing ensures that the $\ensuremath{\beta}$-decay half-lives are insensitive to the model space, while the zero-range one is largely dependent on it. The half-lives calculated with the BNN isoscalar pairing strengths reproduced most of the experimental data, although those of highly deformed nuclei were underestimated. We also studied the predictive performance on new experimental data that were not used for the BNN training and found that they were reproduced well.Conclusions: Our study demonstrates that the isoscalar pairing strengths determined by the BNN can reproduce experimental data with the same accuracy as other theoretical works. To achieve a more precise prediction, the nuclear deformation is important.

Two-neutrino double- β decay matrix elements based on a relativistic nuclear energy density functional

Nuclear matrix elements (NMEs) for two-neutrino double-beta decay ($2\nu\beta\beta$) are studied in the framework of relativistic nuclear energy density functional (REDF). The properties of nuclei involved in the decay are obtained using the relativistic Hartree-Bardeen-Cooper-Schrieffer theory and relevant nuclear transitions are described using the relativistic proton-neutron quasiparticle random phase approximation based on relativistic energy density functional (REDF-QRPA). Three effective interactions have been employed, including density-dependent meson-exchange (DD-ME2) and point coupling interactions (DD-PC1 and DD-PCX), and pairing correlations are described consistently both in $T=1$ and $T=0$ channels using a separable pairing interaction. The optimal values of $T=0$ pairing strength parameter $V_{0pp}$ are constrained by the experimental data on $\beta$-decay half lives. The $2\nu\beta\beta$ matrix elements and half-lives are calculated for several nuclides experimentally known to undergo this kind of decay: $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Xe, $^{128}$Te, $^{130}$Te, $^{136}$Xe and $^{150}$Nd. The model dependence of the NMEs and their sensitivity on $V_{0pp}$ is investigated, and the NMEs obtained using optimal values of $V_{0pp}$ are discussed in comparison to previous studies. The results of the present work represent an important benchmark for the future applications of the relativistic framework in studies of neutrinoless double-beta decay.

Investigation of Gamow–Teller strength of 186Hg within deformed pn-QRPA

Recently, the total absorption gamma spectroscopy technique was used to determine the Gamow–Teller (GT) distribution of β-decay of 186Hg. It was concluded that the best description of the measured data was obtained with dominantly prolate components for both parent 186Hg and daughter 186Au. Motivated by the recent findings, we investigate the effect of nuclear deformation on the energy distribution of the GT strength of the decay of 186Hg into 186Au within the framework of proton–neutron quasiparticle random phase approximation (pn-QRPA) based on the deformed Nilsson potential. To do the needful, we first calculate the energy levels and shape prediction of 186Hg within the interacting boson model. The computed GT strength distribution satisfied the model-independent Ikeda sum rule 100% (99.98%) for the prolate (oblate) case. Based on the strength distributions, the deformed pn-QRPA model with separable interaction prefers a prolate shape for the ground state of 186Hg and supports the shape coexistence for this nucleus.