Quasiparticle Random Phase Approximation Research Articles

Half-life prediction of some neutron-rich exotic nuclei prior to peak A = 130

β-decay is amongst the key properties of nuclei required for the modeling of r-process nucleosynthesis. It also governs the flow of abundances among neighboring isotopic chains of high-mass elements. In the present work, a simple proton-neutron quasi particle random phase approximation (p–n-QRPA) model has been used for the calculation of β-decay half-lives of Rb, Sr, Y and Zr neutron-rich isotopes. For 97−103Rb, 98−107Sr, 101−109Y and 104−112Zr, where the experimental data were available, the half-life values are reproduced with reasonable accuracy. The same set of model parameters are later used to predict half-lives for few neutron-rich nuclei (104−112Rb, 108−113Sr, 110−114Y and 113−115Zr) where measured data is not available. The p–n-QRPA results (including only allowed transitions) are compared with previous calculations (allowed plus forbidden) and exhibit agreement within a factor of 2.0 when compared with the recent available experimental 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.

Experimental observation of the M1 scissors mode in 254No

We present the first experimental evidence of the scissors mode in the superheavy nucleus 254No produced in the 208Pb(48Ca, 2nγ))254No reaction. The spectrum of γ rays emitted by the excited 254No nuclei shows an enhanced γ-ray yield for transition energies of ≈2.5 MeV. By measuring the linear polarization properties of the emitted γ rays, we confirm that the transitions in the enhancement region are predominantly of magnetic-dipole character, characteristic for the scissors mode. To further characterize the enhanced γ-ray yield, simulations of the electromagnetic decay of 254No were performed. The observed enhancement is reproduced by including an M1 component in the γ strength function with total strength B(M1↑)=11.8(19)μN2. This is in good agreement with the integrated M1 strength from sum-rule estimates and new calculations within the quasi-particle random-phase approximation presented here. Our results provide a stringent test of phenomenological formulae for the scissors mode currently used in stellar nucleosynthesis calculations. We find that those formulae are not satisfactory, and we recommend using sum-rule estimates assuming a rigid-body moment of inertia instead for describing the scissors mode in superheavy nuclei.

Comprehensive Analysis of the Neutrino Process in Core-collapsing Supernovae

We investigate the neutrino flavor change effects due to neutrino self-interaction and shock wave propagation, as well as the matter effects on the neutrino process in core-collapsing supernovae (CCSNe). For the hydrodynamics, we use two models: a simple thermal bomb model and a specified hydrodynamics model for SN1987A. For the presupernova model, we take an updated model, adjusted to explain SN1987A, which employs recent developments in the (n, γ) reaction rates for nuclei near the stability line (A ∼ 100). As for the neutrino luminosity, we adopt two different models: equivalent neutrino luminosity and nonequivalent luminosity models. The latter is taken from a synthetic analysis of CCSN simulation data, which quantitatively presented the results obtained by various neutrino transport models. Relevant neutrino-induced reaction rates are calculated using a shell model for light nuclei and a quasiparticle random phase approximation model for heavy nuclei. For each model, we present abundances of the light nuclei (7Li, 7Be, 11B, and 11C) and the heavy nuclei (92Nb, 98Tc, 138La, and 180Ta) produced by the neutrino process. The light nuclei abundances turn out to be sensitive to the Mikheyev–Smirnov–Wolfenstein (MSW) region around O-Ne-Mg layer while the heavy nuclei are mainly produced prior to the MSW region. Through detailed analyses, we find that neutrino self-interaction becomes a key ingredient, in addition to the MSW effect, for understanding the neutrino process and the relevant nuclear abundances. The normal mass hierarchy is shown to be more compatible with the meteorite data. The main nuclear reactions for each nucleus are also investigated in detail.

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.

Original e− Capture Cross Sections for Hot Stellar Interior Energies

The nuclear electron capture reaction possesses a prominent position among other weak interaction processes occurring in explosive nucleosynthesis, especially at the late stages of evolution of massive stars. In this work, we perform exclusive calculations of absolute e−-capture cross sections using the proton–neutron (pn) quasi-particle random phase approximation. Thus, the results of this study can be used as predictions for experiments operating under the same conditions and in exploring the role of the e−-capture process in the stellar environment at the pre-supernova and supernova phase of a massive star. The main goal of our study is to provide detailed state-by-state calculations of original cross sections for the e−-capture on a set of isotopes around the iron group nuclei (28Si, 32S, 48Ti, 56Fe, 66Zn and 90Zr) that play a significant role in pre-supernova as well as in the core–collapse supernova phase in the energy range 0≤E≤50 MeV.

Towards a Predictive HFB+QRPA Framework for Deformed Nuclei: Selected Tools and Techniques

Reliable predictions of the static and dynamic properties of a nucleus require a fully microscopic description of both ground and excited states of this complicated many-body quantum system. Predictive calculations are key to understanding such systems and are important ingredients for simulating stellar environments and for enabling a variety of contemporary nuclear applications. Challenges that theory has to address include accounting for nuclear deformation and the ability to describe medium-mass and heavy nuclei. Here, we perform a study of nuclear states in an Hartree-Fock-Bogoliubov (HFB) and Quasiparticle Random Phase Approximation (QRPA) framework that utilizes an axially-symmetric deformed basis. We present some useful techniques for testing the consistency of such calculations and for interpreting the results.

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.

Chebyshev kernel polynomial method for efficient calculation of the quasiparticle random phase approximation response function

Efficient and accurate algorithms for the calculation of the multipole response of deformed atomic nuclei are very important tools in nuclear structure, especially for large scale calculations. In this paper we present an implementation of the algorithm based on the expansion of the response function in terms of the Chebyshev polynomials in conjunction with the kernel polynomial method for a very efficient calculation of the quasiparticle random phase approximation response function. Several test calculations are performed in order to asses the applicability and feasibility of this algorithm, already used successfully in the field of computational solid state physics, in various nuclear structure calculations.

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.

Symmetry breaking of Gamow-Teller and magnetic-dipole transitions and its restoration in calcium isotopes

Nuclear magnetic-dipole (M1) and Gamow-Teller (GT) transitions provide insight into the spin-isospin properties of atomic nuclei. By considering them as unified spin-isospin transitions, the M1/GT transition strengths and excitation energies are subject to isospin symmetry. The excitation properties associated to the M1/GT symmetry need to be clarified within consistent theoretical approach. In this work, the relationship between the M1 and GT transitions in Ca isotopes is investigated in a unified framework based on the relativistic energy-density functional (REDF) with point-coupling interactions, using the relativistic quasi-particle random-phase approximation (RQRPA). It is shown that the isovector-pseudovector (IV-PV) residual interaction affects both transitions, and the symmetry of M1 and giant-GT transitions is disrupted by this interaction in closed-shell nuclei. In open-shell Ca isotopes, the proton-neutron pairing in the residual RQRPA interaction also plays a role in GT transitions. Due to the interplay between these interactions, the M1/GT symmetry can be restored especially in the $^{42}$Ca nucleus, i.e., the giant-GT strength can become comparable to that of the M1 mode in terms of the unified spin-isospin transitions by adjusting the PN-pairing strength to reproduce the experimental low-lying GT-excitation energies. The mirror symmetry of both M1 and GT transitions is also demonstrated for open-shell mirror partners, $^{42}$Ca and $^{42}$Ti. Further improvements are required to achieve simultaneous reproduction of M1 and GT-transition energies in the REDF framework.

Role of the quadrupole deformation in γ-soft nuclei: The case of 124−134Xe

Observation of the scissors mode in the γ-soft and transition nuclei provides the reasoning for investigating the possibility of quadrupole deformation in such nuclei. Using a deformed-based model for an investigation of the scissors mode, the goal of this work was to analyze the effects associated with quadrupole deformation for the so-called “γ-soft” nuclei in the example of even-even 124−134Xe isotopes. Here, the well-known properties of the scissors mode were investigated using just the quadrupole deformed-based rotational, invariant quasiparticle random phase approximation (QRPA) method. The properties of the scissors mode were clearly seen for all the investigated xenon isotopes, demonstrating that quadrupole deformed-based models can easily explain the nature of the low-lying M1 strength for γ-soft nuclei and indicating that quadrupole deformation plays a non-negligible role in the formation of the low-lying dipole strength for such nuclei.

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.

Single-state or low-lying-states dominance mechanism of 2νββ -decay nuclear matrix elements

The $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements (NMEs) for 11 nuclei are studied with the self-consistent quasiparticle random phase approximation (QRPA) based on the Skyrme Hartree-Fock-Bogoliubov (Skyrme HFB) model. As a common feature pointed out by \ifmmode \check{S}\else \v{S}\fi{}imkovic, Smetana, and Vogel [Phys. Rev. C 98, 064325 (2018)], negative contributions in the running sums of NMEs are found, and play important roles in the fulfillment of the single-state dominance or low-lying-states dominance hypothesis. By comparing the results of the QRPA model and the quasiparticle Tamm-Dancoff approximation (QTDA) model, we find that the negative contributions are due to the enhanced ground-state correlations, which are brought by the backward amplitude in the QRPA model and tuned by strong isoscalar pairing interaction. The enhancement of ground-state correlations will change the signs of ${\mathrm{GT}}^{+}$ (Gamow-Teller) transition amplitudes of higher-lying states and leads to the negative contributions in the running sum.

Many-body approach to superfluid nuclei in axial geometry

Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov's quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon's characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in nonspherical geometries. In this paper, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov's Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point-coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of $^{38}\mathrm{Si}$ and $^{250}\mathrm{Cf}$ are presented and discussed.

The β-decay of 70Kr into 70Br: Restoration of the pseudo-SU(4) symmetry

The β-decay of the even-even nucleus 70Kr with Z=N+2, has been investigated at the Radioactive Ion Beam Factory (RIBF) of the RIKEN Nishina Center using the BigRIPS fragment separator, the ZeroDegree Spectrometer, the WAS3ABI implantation station and the EURICA HPGe cluster array. Fifteen γ-rays associated with the β-decay of 70Kr into 70Br have been identified for the first time, defining ten populated states below Eexc=3300 keV. The half-life of 70Kr was derived with increased precision and found to be t1/2=45.19±0.14 ms. The β-delayed proton emission probability has also been determined as εp=0.545(23)%. An increase in the β-strength to the yrast 1+ state in comparison with the heaviest Z=N+2 system studied so far (62Ge decay) is observed that may indicate increased np correlations in the T=0 channel. The β-decay strength deduced from the results is interpreted in terms of the proton-neutron quasiparticle random-phase approximation (pnQRPA) and also with a schematic model that includes isoscalar and isovector pairing in addition to quadrupole deformation. The application of this last model indicates an approximate realization of pseudo-SU(4) symmetry in this system.

How effective is the Brink–Axel hypothesis for astrophysical weak rates?

Abstract We explore the effectiveness of the Brink–Axel hypothesis (BAH) for the computation of stellar electron capture (EC) and β-decay (BD) rates, namely that the transition strength function depends only upon the transition energy and not upon the details of the initial state. For this purpose, we calculated Gamow–Teller (GT) strength distributions for a selection of sd-shell nuclides, using two different microscopic models, namely the proton–neutron quasiparticle random phase approximation and the full configuration-interaction shell model, taking into account the first 100 states of both the initial and final nuclides. The GT transition strengths among these levels evolve with initial state energy. These transition strength functions we folded into weak-interaction mediated rates in stellar matter, specifically EC and BD rates, for a range of densities 10 g cm−3 ⩽ ρ ⩽ 1011 g cm−3 and range of temperatures 1 GK ⩽ T ⩽ 30 GK. When transitions from excited states were approximated using the BAH, augmented by so-called ‘back-resonance’ transitions, the rates were affected by up to three orders of magnitude or more at high temperatures and densities. Thus the BAH is not a reliable approximation for the calculation of stellar rates, especially in high temperature–density environments.