Proton-neutron Quasiparticle Random-phase Approximation Research Articles

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.

Global calculation of two-neutrino double- β decay within the finite amplitude method in nuclear density functional theory

Two-neutrino double-beta ($2\nu\beta\beta$) decay has been used to constrain the neutron-proton part of effective interactions, which in turn is used to compute the nuclear matrix elements for neutrinoless double-beta decay, the observation of which would have important consequences for fundamental physics. We carefully examine $2\nu\beta\beta$ matrix elements within the proton-neutron quasiparticle random-phase approximation with nuclear energy density functionals. We work with functionals that are fit globally to single-beta-decay half-lives and charge-exchange giant-resonance energies, but not to $2\nu\beta\beta$ half-lives themselves, to evaluate the $2\nu\beta\beta$ nuclear matrix elements for all important nuclei, including those whose half-lives have not yet been measured. Such a comprehensive evaluation in large model spaces without configuration truncation requires an efficient computational scheme; we employ a double contour integration within the finite amplitude method. The results generally reproduce the nuclear matrix element extracted from half-lives well, without the use of any of those half-lives in the fitting procedure. We present predictions of the matrix elements in a total of 27 nuclei with half-lives that are still unmeasured.

Description of weak-interaction rates within the relativistic energy density functional theory

A new theoretical framework has been established and applied in the calculation of electron capture (EC) and β-decay rates in stellar environment, characterized by high density and temperature. For the description of the nuclear properties, the finite-temperature Hartree Bardeen-Cooper-Schrie_er (FTHBCS) theory based on the relativistic derivative-coupling D3C* interaction is employed. In order to describe the charge-exchange transitions, the finitetemperature proton-neutron quasi-particle random-phase approximation is developed (FT-PNRQRPA) which includes both temperature and pairing correlations. In the FT-HBCS calculations, only the isovector pairing is included, while in the residual interaction of the FT-PNRQRPA both the isovector and isoscalar pairing contribute. In this work, results for EC and β-decay rates are presented in the temperature interval T = 0–1.5 MeV and stellar density ρYe = 107 and 109 g/cm3. Both allowed 0+, 1+ and first-forbidden transitions 0−, 1− and 2− are included in the calculations. It is shown that interplay between pairing correlations and finite-temperature effects can lead to significant changes in rates. It is also important to include de-excitations, i.e. transitions with negative Q-value, that become increasingly significant at higher temperatures especially for p f -shell nuclei.

β-Decay properties of neutron-rich yttrium isotopes

In this study, we have reported key nuclear properties of weak β-decay processes on Yttrium isotopes for the mass number range A = 101 − 108. This mass region has importance while dealing with astrophysical r-process abundances. Our study might be helpful in r-process simulations. We have computed charge-changing strength distributions, β-decay half-lives, β-delayed neutron emission probabilities and β − (EC) weak rates under stellar conditions. We have performed microscopic calculations based on deformed proton-neutron quasi-particle random phase approximation (p–n-QRPA) over a wide temperature (107 − 3 × 1010) K and density (10 − 1011) g/cm3 domain. Unique first-forbidden (U1F) transitions have been included in the calculations in addition to the allowed transitions. A significant decrease in calculated half-lives in ceratin cases, e.g., in 107Y (108Y) by about 67% (42%), has been observed because of the contribution from U1F transitions. We have compared present results with measured and theoretical works. A good agreement of our half-lives with experimental data is observed.

β -delayed neutron-emission and fission calculations within relativistic quasiparticle random-phase approximation and a statistical model

Background: $\ensuremath{\beta}$-delayed neutron emission and fission are essential in $r$-process nucleosynthesis. Although the number of experimental studies covering $r$-process nuclei has recently increased, the uncertainties of $\ensuremath{\beta}$-delayed neutron emission and fission are still large for $r$-process simulations.Purpose: Our aim is to introduce a theoretical framework for the description of $\ensuremath{\beta}$-delayed neutron-emission and fission rates based on relativistic nuclear energy density-functional and statistical models and investigate their properties throughout the nuclide map.Methods: To obtain $\ensuremath{\beta}$ strength functions, the relativistic proton-neutron quasiparticle random-phase approximation is employed. Particle evaporations and fission from highly excited nuclear states are estimated by the Hauser-Feshbach statistical model. $\ensuremath{\beta}$-delayed neutron branching ratios ${P}_{n}$ are calculated and compared with experimental data, and the $\ensuremath{\beta}$-delayed fission branching ratio ${P}_{f}$ are also assessed by using different fission barrier data.Results: Calculated ${P}_{n}$ are in a good agreement with the experimental data and the root mean square deviation is comparable to results of preceding works. It is found that energy withdrawal by $\ensuremath{\beta}$-delayed neutron-emission sensitivity varies ${P}_{n}$, especially for nuclei near the neutron drip line. ${P}_{f}$ depend sensitively on fission barrier data. It is found that not only the barrier height but also the number of barrier humps is important to evaluate ${P}_{f}$.Conclusions: The framework introduced in this work provides an improved theoretical description of the $\ensuremath{\beta}$-delayed neutron emission and fission. Since ${P}_{f}$ as well as ${P}_{n}$ depend strongly on fission barrier information, four kinds of fission barrier data are used in this work to allow further sensitivity studies of the $r$-process nucleosynthesis on the nuclear fission. More studies on fission barrier are highly requested to assess the role of $\ensuremath{\beta}$-delayed fission in the $r$-process study. A complete set of calculated data for $\ensuremath{\beta}$-delayed neutron emission and fission are summarized as a table in supplemental material for its use in $r$-process studies as well as to complement a part of nuclear data in which no experimental data are available.

Impact of the leading-order short-range nuclear matrix element on the neutrinoless double-beta decay of medium-mass and heavy nuclei

We evaluate the leading-order short-range nuclear matrix element for the neutrinoless double-beta (0νββ) decay of the nuclei most relevant for experiments, including 76Ge, 100Mo, 130Te and 136Xe. In our calculations, performed with the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) methods, we estimate the coupling of this term by the contact charge-independence-breaking coupling of various nuclear Hamiltonians. Our results suggest a significant impact of the short-range matrix element, which is about 15%−50% and 30%−80% of the standard 0νββ-decay long-range matrix element for the shell model and pnQRPA, respectively. Combining the full matrix elements with the results from current 0νββ-decay experiments we find that, if both matrix elements carry the same sign, these searches move notably toward probing the inverted mass ordering of neutrino masses.

Beta decay logft values for zinc isotopes by using pn-QRPA

Allowed Fermi (F), Gamow-Teller (GT), and first forbidden (FF) transitions were simulated using Pyatov Method (PM) and Schematic Model (SM) for even-even neutron rich isotopes of Zinc. The Fermi beta-decay calculations were obtained by the pure the Pyatov Method without introducing effective values of coupling constants using the proton-neutron quasi-particle random phase approximation (pn-QRPA). The pn-QRPA was utilized in the particle-hole (ph) and particle-particle (pp) channels in the PM and SM for the GT transitions. For FF transitions, only the corresponding ph channel in the SM was considered in the calculations. We solved the secular equations of Fermi, Gamow-Teller, and first forbidden transitions for eigenvalues and eigenfunctions of corresponding Hamiltonians. A spherical shape was assigned for each Zn nuclei throughout all simulations. Compared to the experimental studies, in general, the calculated logft values of the allowed F and GT transitions of PM and SM simulations were found to be closer to the experimental values. Alongside logft values, simulated half-lives obtained in this work are also in excellent agreement with experimental counterparts for the FF excitations.

Isovector spin susceptibility: Isotopic evolution of collectivity in spin response

Background: Response to spin-dependent operators has been investigated in the magnetic dipole and Gamow-Teller transitions, which provides magnetic properties of a nuclear system. Purpose: I investigate an isotopic dependence of the collectivity generated by the spin-dependent interactions in the Ca and Ni isotopes through the isovector (IV) spin-flip excitations. The responses in the neutral $(t_z)$ and charge-exchange $(t_{\pm})$ channels are considered in a unified way. Method: A nuclear energy-density functional approach is employed for calculating the response functions based on the Skyrme-Kohn-Sham-Bogoliubov method and the quasiparticle-random-phase approximation (QRPA). I adopt the like-particle QRPA and the proton-neutron QRPA for the neutral and charge-exchange channels, respectively. I consider the fluctuation of the proton-neutron pair fields. Results: The collective shift due to RPA correlations for the response in the neutral channel is explained by the occupation probability of neutrons in the $j_>=\ell+1/2$ orbital. Many particle-hole or two-quasiparticle excitations have a coherent contribution to form a giant resonance in neutron-rich nuclei for the charge-exchange channel. The IV spin susceptibility displays the isotopic evolution of the collectivity and the underlying shell structure. Conclusions: A repulsive character of the residual interaction in the spin-isospin channel diminishes the IV spin susceptibility due to the collectivity, while the dynamic ${}^{3}S$ pairing appearing in the charge-exchange channel opposes the reduction.

Lepton emission rates of [formula omitted]v isotopes under stellar conditions

In astrophysical conditions prevalent during the late times of stellar evolution, lepton (e− and e+) emission processes compete with the corresponding lepton capture processes. Prior to the collapse, lepton emissions significantly affect the cooling of the core and reduce its entropy. Therefore the lepton emission rates for Fe-group nuclei serve as an important input for core-collapse simulations of high-mass stars. From earlier simulation studies, isotopes of vanadium (V) have great astrophysical significance in regard to their weak-decay rates which substantially affect Ye (fraction of lepton to baryon number) during the final developmental stages of massive stars. The current study involves the computation of the weak lepton emission (LE) rates for V-isotopes by employing the improved deformed proton-neutron Quasi-particle Random Phase Approximation (pn-QRPA) model. The mass numbers of the selected isotopes range from 43 to 64. The LE rates on these isotopes have been estimated for a broad spectrum of density and temperature under astrophysical conditions. The ranges considered for density and temperature are 101 to 1011 (g/cm3) and 107 to 3 × 1011 (K), respectively. The lepton emission rates from the present study were also compared to the rates previously estimated by using the independent-particle model (IPM) and large-scale shell model (LSSM). IPM rates are generally bigger than QRPA rates, while LSSM rates are overall in good comparison with the reported rates. We attribute these differences to correct placement of GT centroid in LSSM and QRPA models.

Investigation of Important Weak Interaction Nuclei in Presupernova Evolution

Abstract This project aims to investigate the most important weak interaction nuclei in the presupernova evolution of massive stars. To achieve this goal, an ensemble containing 728 nuclei in the mass range of A = 1–100 was considered. We computed the mass fractions of these nuclei using Saha’s equation for predetermined values of T, ρ, and Y e and assuming nuclear statistical equilibrium. The nuclear partition functions were obtained using a newly introduced recipe where excited states, up to 10 MeV, were treated as discrete. The weak interaction rates (electron capture (ec) and β-decay (bd)) were calculated in a totally microscopic fashion using the proton–neutron quasiparticle random phase approximation model and without assuming the Brink–Axel hypothesis. The calculated rates were coupled with the computed mass fractions to investigate the time rate of change of lepton to baryon fraction of the stellar matter. We compare our results with the previous calculations reported in the literature. Noticeable differences up to orders of magnitude are reported with previous calculations. These differences may influence the evolution of the star in the later stages of presupernova. We present a list of the top 50 ec and bd nuclei, which have the largest effect on Y e for conditions after silicon core burning. The competition between the ec and bd rates in the stellar core was investigated and it was found that Y e = 0.424–0.455 is the interval where the bd results are bigger than the ec rates.

Comparative Analysis of Nuclear Matrix Elements of 0νβ+β+ Decay and Muon Capture in 106Cd

Comparative analyses of the nuclear matrix elements (NMEs) related to the 0νβ+β+ decay of 106Cd to the ground state of 106Pd and the ordinary muon capture (OMC) in 106Cd are performed. This is the first time the OMC NMEs are studied for a nucleus decaying via positron-emitting/electron-capture modes of double beta decay. All the present calculations are based on the proton-neutron quasiparticle random-phase approximation with large no-core single-particle bases and realistic two-nucleon interactions. The effect of the particle-particle interaction parameter gpp of pnQRPA on the NMEs is discussed. In the case of the OMC, the effect of different bound-muon wave functions is studied.

Stellar electron-capture rates based on finite-temperature relativistic quasiparticle random-phase approximation

The electron capture process plays an important role in the evolution of the core collapse of a massive star that precedes the supernova explosion. In this study, the electron capture on nuclei in stellar environment is described in the relativistic energy density functional framework, including both the finite temperature and nuclear pairing effects. Relevant nuclear transitions $J^\pi = 0^\pm, 1^\pm, 2^\pm$ are calculated using the finite temperature proton-neutron quasiparticle random phase approximation with the density-dependent meson-exchange effective interaction DD-ME2. The pairing and temperature effects are investigated in the Gamow-Teller transition strength as well as the electron capture cross sections and rates for ${}^{44}$Ti and ${}^{56}$Fe in stellar environment. It is found that the pairing correlations establish an additional unblocking mechanism similar to the finite temperature effects, that can allow otherwise blocked single-particle transitions. Inclusion of pairing correlations at finite temperature can significantly alter the electron capture cross sections, even up to a factor of two for ${}^{44}$Ti, while for the same nucleus electron capture rates can increase by more than one order of magnitude. We conclude that for the complete description of electron capture on nuclei both pairing and temperature effects must be taken into account.

Lepton capture rates due to isotopes of vanadium in astrophysical environment

Lepton (electron and positron) capture rates on iron-regime nuclei are an essential element for modeling the late stages of progression of massive stars that become core collapse and thermonuclear supernova. As per previous simulation studies, lepton capture (LC) rates on isotopes of vanadium are believed to have a substantial effect in regulating the Ye (lepton to baryon fraction) during the final evolutionary phases. The present work involves the calculation of lepton capture rates for 22 isotopes of vanadium by making use of the proton-neutron (pn-) quasiparticle random phase approximation (QRPA) model. The covered mass range is from A = 43 to 64. The LC rates have been computed over stellar densities ranging from $10^{1}$ to $10^{11}$ (g/cm3) and for the temperature range $10^{7} - 3 \times 10^{10}$ (K). A comparison of our calculated LC rates to the rates computed using other models (IPM and LSSM) has also been presented. As compared to the rates calculated by other models, pn-QRPA rates at high temperature ( $3 \times 10^{10}$ K) are larger by up to 1-2 orders of magnitude.

Comparative analysis of muon-capture and 0νββ -decay matrix elements

Average matrix elements of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of current experimental interest are computed and compared with the corresponding energy and multipole decompositions of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements (NMEs). The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ NMEs include the appropriate short-range correlations, nuclear form factors, and higher-order nucleonic weak currents. The nuclear wave functions are obtained in extended no-core single-particle model spaces using the spherical version of the proton-neutron quasiparticle random-phase approximation with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. Both the OMC and $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes involve 100-MeV-range momentum exchanges and hence similarities could be expected for both processes in the feeding of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ intermediate states. These similarities may help improve the accuracy of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ NME calculations by using the data from the currently planned OMC experiments.

Nuclear structure properties of even-even chromium isotopes and the effect of deformation on calculated electron capture cross sections

In this study, we investigate the role of the nuclear deformation on the calculated electron capture cross section (ECC) of even-even chromium (Cr) isotopes. We first determined the nuclear structure properties of these nuclei within the interacting boson model-1 (IBM-1). The energy spectra and E2 transition probabilities were calculated by fitting the parameters in the model formalism. The analysis of the potential energy surface were also performed to predict the geometric shape of the Cr nuclei by plotting their contour plot in the plane of (β, γ) deformation parameters. Later, we calculated the ECC within the proton-neutron quasiparticle random phase approximation (pn-QRPA) model. In particular we studied how the calculated ECC changed with different values of nuclear deformation parameter. The calculated Gamow-Teller (GT) strength distributions were widely spread among the daughter states. The total GT strength decreased with increasing value of the β parameter. The computed ECC values, however, increased with increase in the β value of the Cr isotopes.

Gamow-Teller excitations at finite temperature: Competition between pairing and temperature effects

The relativistic and nonrelativistic finite temperature proton-neutron quasiparticle random phase approximation (FT-PNQRPA) methods are developed to study the interplay of the pairing and temperature effects on the Gamow-Teller excitations in open-shell nuclei, as well as to explore the model dependence of the results by using two rather different frameworks for effective nuclear interactions. The Skyrme-type functional SkM* is employed in the nonrelativistic framework, while the density-dependent meson-exchange interaction DD-ME2 is implemented in the relativistic approach. Both the isoscalar and isovector pairing interactions are taken into account within the FT-PNQRPA. Model calculations show that below the critical temperatures the Gamow-Teller excitations display a sensitivity to both the finite temperature and pairing effects, and this demonstrates the necessity for implementing both in the theoretical framework. The established FT-PNQRPA opens perspectives for the future complete and consistent description of astrophysically relevant weak interaction processes in nuclei at finite temperature such as $\beta$-decays, electron capture, and neutrino-nucleus reactions.

On the role of pairing correlations in calculation of β-decay half-lives within QRPA formalism

In this paper we show that the proton-neutron residual interaction can play an important role in the reliability of calculated β-decay half-lives. It may also improve the prediction power of the quasiparticle random phase approximation (QRPA) model. We further demonstrate that a reasonable choice of the particle-particle (attractive) and particle-hole force (repulsive) parameters can result in calculated half-lives in very good comparison with the measured ones. Pairing gaps have affect on calculated half-lives which we explore in this paper. We present our half-lives calculation using the proton-neutron QRPA (pn-QRPA) model possessing a multi-shell single-particle deformed space including a schematic interaction for some medium mass neutron-deficient nuclei undergoing β+/EC decay. Our study shows a better agreement with the available experimental data as compared to former calculations.

A proton-neutron QRPA Calculation of the β- Decay of Nd152 using the Fayans Energy Density Functional

This paper presents a calculation of the β– decay of the neutron-rich nucleus Nd152 using the proton-neutron Quasi-particle Random Phase Approximation (pnQRPA) model. The single-particle ground states are calculated self-consistently using the Fayans energy density functional in a Hartree-Fock-Bogoliubov (HFB) scheme for deformed nuclei. The quasi-particle states which are needed for the pnQRPA calculation are calculated from the HFB single-particle ground states using the Bardeen-Cooper-Schriefer (BCS) approximation. Only Gamow-Teller β– excitations are considered, and two kinds of excitation force are used to excite the daughter nucleus to produce the β– decay: (a) a pure Migdal force, and (b) a Migdal force plus a correction term obtained self-consistently from the BCS quasi-particle basis. The calculations with the pure Migdal force and the corrected Migdal force give half-lives of 5.92 min and 6.91 min, respectively, which are about one half of the experimental value of 11.6(7) min, and decay energies of 1.38 MeV and 1.33 MeV, respectively, both close to the experimental decay energy of 1.12 MeV. The correction to the Migdal excitation force turns out to improve the accuracy of the calculations.

Energy rates due to weak decay rates of vanadium isotopes in stellar environment

The neutrino cooling and gamma heating rates are considered as an important input needed to study the final phases of the evolution of high-mass stars. The weak-interaction mediated processes, namely the $\beta $-decay and electron capture, significantly change the lepton to baryon ratio and accelerate the contraction of the core. The emission of resulting neutrinos/antineutrinos tend to cool the stellar core. On the other hand gamma rays are produced because of electron capture and $\beta $-decay to excited states in daughter nuclei. These gamma rays heat the core and contribute to increase of entropy which may cause convection to occur. In the present work, the weak-interaction heating and cooling rates on a chain of twenty two isotopes of vanadium having mass in the range 43–64 have been estimated using the proton-neutron quasiparticle random phase approximation theory. The rates have been computed for the temperature ranging from ($10^{7}\mbox{--}3\times 10^{10}$) K and for the density range $(10\mbox{--}10^{11})~\mbox{g/cm}^{3}$. Our calculated neutrino energy loss rates have also been compared with the previously reported rates calculated using other theoretical models. At high stellar temperatures, our rates are larger by 1–2 orders of magnitude as compared to previous results.