pn-QRPA Model Research Articles

Nuclear structure model for double-charge-exchange processes

A new model, based on the BCS approach, is specially designed to describe nuclear phenomena $(A,Z)\rightarrow (A,Z\pm 2)$ of double-charge exchange (DCE). After being proposed, and applied in the particle-hole limit, by one of the authors (F. Krmpoti\'c [1]), so far it was never been applied within the BCS mean-field framework, nor has its ability to describe DCE processes been thoroughly explored. It is a natural extension of the pn-QRPA model, developed by Halbleib and Sorensen [2] to describe the single $\beta$-decays $(A,Z)\rightarrow (A,Z\pm 1)$, to the DCE processes. As such, it exhibits several advantages over the pn-QRPA model when is used in the evaluation of the double beta decay (DBD) rates. For instance, i) the extreme sensitivity of the nuclear matrix elements (NMEs) on the model parametrization does not occur, ii) it allows to study NMEs, not only for the fundamental state in daughter nuclei, as the pn-QRPA model does, but also for all final $0^+$ and $2^+$ states, accounting at the same time their excitation energies and the corresponding DBD Q-values, iii) together with the DBD-NMEs it provides also the energy spectra of Fermi and Gamow-Teller DCE transition strengths, as well as the locations of the corresponding resonances and their sum rules, iv) the latter are relevant for both the DBD and the DCE reactions, since the involved nuclear structure is the same; this correlation does not exist within the pn-QRPA model. As an example, detailed numerical calculations are presented for the $(A,Z)\rightarrow (A,Z+ 2)$ process in $^{48}$Ca $\rightarrow ^{48}$Ti and the $(A,Z)\rightarrow (A,Z- 2)$ process in $^{96}$Ru $\rightarrow ^{96}$Mo, involving all final $0^+$ states and $2^+$ states.

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.

Nuclear structure properties and decay rates of molybdenum isotopes

Electron capture and $\beta ^{-}$ decay are the dominant decay processes during late phases of evolution of heavy stars. Previous simulation results show that weak rates on isotopes of Molybdenum (Mo) have a meaningful contribution during the development of phases of stars before they go supernova. The relative abundance coupled with the stellar weak rates on Mo isotopes may change the lepton-to-baryon content of the core material. Here we report on the calculation of nuclear structure properties of 82−138Mo isotopes employing the RMF model. Later we calculate the weak decay rates of these isotopes. We use the pn-QRPA model to compute these rates. In the first step, the ground-state nuclear properties of Mo isotopes such as binding energy per nucleon, neutron and proton separation energies, charge radii, total electric quadrupole moments and deformation parameter of electric quadrupole moments have been calculated using density dependent version of RMF model with DD-PC1 and DD-ME2 functionals. The calculated electric quadrupole deformation parameters have been used in a deformed pn-QRPA calculation in the second phase of this work to calculate half-lives and weak decay rates for these Mo isotopes in stellar matter. We calculate the electron capture and $\beta $-decay rates over an extensive range of temperature ($0.01\times 10^{9}$ K to $30\times 10^{9}$ K) and density (10 to $10^{11}$) g/cm3. Our study can prove useful for simulation of presupernova evolution processes of stars.

β−-Decay Half-Lives of Even-Even Nuclei Using the Recently Introduced Phase Space Recipe

In this paper, we present the β -decay half-lives calculation for selected even-even nuclei that decay through electron emission. The kinematical portion of the half-life calculation was performed using a recently introduced technique for computation of phase space factors (PSFs). The dynamical portion of our calculation was performed within the proton-neutron quasiparticle random phase approximation (pn-QRPA) model. Six nuclei ( 20 O, 24 Ne, 34 Si, 54 Ti, 62 Fe and 98 Zr) were selected for the present calculation. We compare the calculated PSFs for these cases against the traditionally used recipe. In our new approach, the Dirac equation was numerically solved by employing a Coulomb potential. This potential was adopted from a more realistic proton distribution of the daughter nucleus. Thus, the finite size of the nucleus and the diffuse nuclear surface corrections are taken into account. Moreover, a screened Coulomb potential was constructed to account for the effect of atomic screening. The power series technique was used for the numerical solution. The calculated values of half-lives, employing the recently developed method for computation of PSFs, were in good agreement with the experimental data.

Effect of nuclear deformation on electron capture cross-section on chromium isotopes

The electron capture plays significant role in the presupernova and supernova evolutions of massive stars which in turn are of great importance in synthesizing heavy elements beyond iron. In this paper, we study the effect of nuclear deformation on the computed electron capture cross-section on selected even–even chromium isotopes ([Formula: see text]Cr). The nuclear deformation parameters were computed using two different theoretical models: Interacting Boson Model (IBM-1) and Macroscopic (Yukawa-plus-exponential)–microscopic (Folded–Yukawa) model (Mac–mic model). A third value of deformation parameter was adopted from experimental data. We chose the pn-QRPA model to perform our calculations. The predictive power of the chosen model was first tested by calculating Gamow–Teller (GT) strength distributions of selected [Formula: see text]-shell nuclei where measured GT data was available. The calculated GT strength distributions were well-fragmented over the energy range 0–12[Formula: see text]MeV and were noted to be in decent agreement with experimental data. The total GT strength was found to increase (decrease) with decrease (increase) in the value of deformation parameter for the three chromium isotopes. The computed GT strength distributions satisfied the model-independent Ikeda sum rule. The ECC were calculated as a function of the deformation parameter at core temperature 1.0[Formula: see text]MeV. Our results show that the calculated ECC increased with increasing value of nuclear deformation.

Electron capture cross sections and nuclear partition functions for fp-shell nuclei

We present calculation of electron capture cross sections (ECC), in the limit of zero momentum transfer, using the pn-QRPA model in stellar matter. Towards this aim we make use of our recently introduced recipe for estimation of nuclear partition functions. For low momentum transfer (), the nuclear matrix elements of the operator provide the leading contribution to the total cross section which we estimate using the pn-QRPA model in a multi-shell single-particle space with a schematic interaction. Key fp-shell nuclei (odd-A, even–even and odd–odd) bearing astrophysical importance were selected for the calculation of ECC in stellar environment. These fp-shell nuclei play a crucial role in presupernova evolution of massive stars and core collapse. We further present microscopic calculation of ground and excited states Gamow–Teller strength distributions and stellar electron capture rates on these suite of nuclei. We used two different sets of empirically determined pairing gaps to calculate the ECC and electron capture rates. Results are compared with experimental data and previous computations. Our calculated ECC are systematically smaller at low electron incident energies as compared to the shell-model results.

Neutrino cooling rates due to nickel isotopes for presupernova evolution of massive stars

As per simulation studies, the weak reaction rates on nickel isotopes play a substantial role in affecting the ratio of electron-to-baryon content of stellar interior during the late stages of core evolution. (Anti)neutrinos are produced in weak-decay processes, and escape from the stellar content having densities less than 1011 g cm−3. They take away energy and reduce the stellar core entropy. In this paper we report on the microscopic calculation of neutrino and antineutrino cooling rates due to weak rates on nickel isotopes in mass range 56 ≤ A ≤ 71. The calculations are accomplished by employing the deformed pn-QRPA model. Recent studies on GT strength properties of nickel isotopes show that the deformed pn-QRPA model well explained the experimental charge-changing transitions. Our calculated beta decay half-lives for selected nickel isotopes are in excellent comparison with experimental data. The (anti)neutrino cooling rates are determined over temperatures in the range of 0.01 × 109 – 30 × 109 K and densities in the range of 10 – 1011 g cm−3 domain. The computed rates are compared with previous theoretical calculations. For neutron rich nuclide, at high temperatures, our computed cooling rates are enhanced as compared to previous calculations.

Allowed Gamow-Teller strength distributions and stellar electron capture rates on odd-A nuclei

The allowed Gamow-Teller (GT) strength distributions and associated weak interaction rates on fp-shell nuclei play crucial role in several astrophysical processes, particularly in nucleosynthesis, stellar evolution and supernova explosions. Results from simulation show that the electron capture (EC) rates on medium-heavy nuclei have a significant impact on decreasing the electron-to-baryon ratio of the stellar matter during the late stages of star formation. In this work we present the computation of allowed charge-changing transitions for odd-A fp-shell nuclei by using the deformed pn-QRPA model. The calculated GT strength distributions are compared with previous calculations (including shell and other QRPA models) and measured charge-changing reaction results. The associated EC rates are computed in stellar environment and are compared with previous theoretical results. It is concluded that our results are in good accordance with measured data. For [Formula: see text]Sc, [Formula: see text]V and [Formula: see text]Co, at high stellar temperatures, our calculated EC rates are bigger than the independent-particle and shell model rates. For [Formula: see text]Mn we generally calculate smaller EC rates than previous calculations. The differences with previous calculations may have consequences for supernovae simulators.

Investigation of Gamow Teller transition properties in [formula omitted]Ni isotopes using QRPA methods

Weak rates in nickel isotopes play an integral role in the dynamics of supernovae. Electron capture and β-decay of nickel isotopes, dictated by Gamow–Teller transitions, significantly alter the lepton fraction of the stellar matter. In this paper we calculate Gamow–Teller (GT) transitions for isotopes of nickel, Ni56–64, using QRPA methods. The GT strength distributions were calculated using four different QRPA models. Our results are also compared with previous theoretical calculations and measured strength distributions wherever available. Our investigation concluded that amongst all RPA models, the pn-QRPA(C) model best described the measured GT distributions (including total GT strength and centroid placement). It is hoped that the current investigation of GT properties would prove handy and may lead to a better understanding of the presupernova evolution of massive stars.

Allowed and unique first-forbidden stellar electron emission rates of neutron-rich copper isotopes

The allowed charge-changing transitions are the most common weak interaction processes of spin-isospin form that play a crucial role in several nuclear/astrophysical processes. The first-forbidden (FF) transition becomes important, in the circumstances where allowed Gamow-Teller (GT) transitions are unfavored, specifically for neutron-rich nuclei due to phase space considerations. In this paper deformed proton-neutron quasi-particle random phase approximation (pn-QRPA) model is applied, for the first time, for the estimation of allowed GT and unique first-forbidden (U1F) transitions ( $|\Delta J| = 2$ ) of neutron rich copper isotopes in mass range $72 \leq A \leq 82$ under stellar conditions. We compared our computed terrestrial $\beta$ -decay half-life values with previous calculations and experimental results. It was concluded that the pn-QRPA calculation is in good accordance with measured data. Our study suggests that the addition of rank (0 and 1) operators in FF transitions can further improve the comparison which remain unattended at this stage. The deformed pn-QRPA model was employed for the estimation of GT and U1F stellar electron emission ( $\beta^{-}$ -decay) rates over wide range of stellar temperature (0.01 GK–30 GK) and density ( $10\mbox{--}10^{11}\mbox{ g}/\mbox{cm}^{3}$ ) domains for astrophysical applications. Our study shows that, in high density and low temperature regions, the contribution of U1F rates to total electron emission rates of neutron-rich copper nuclei is negligible.

Nuclear structure properties and stellar weak rates for 76Se: Unblocking of the Gamow Teller strength

At finite temperatures (≥ 107K), 76Se is abundant in the core of massive stars and electron capture on 76Se has a consequential role to play in the dynamics of core-collapse. The present work may be classified into two main categories. In the first phase we study the nuclear structure properties of 76Se using the interacting boson model-1 (IBM-1). The IBM-1 investigations include the energy levels, B(E2) values and the prediction of the geometry. We performed the extended consistent-Q formalism (ECQF) calculation and later the triaxial formalism calculation (constructed by adding the cubic term to the ECQF). The geometry of 76Se can be envisioned within the formalism of the potential energy surface based on the classical limit of IBM-1 model. In the second phase, we reconfirm the unblocking of the Gamow–Teller (GT) strength in 76Se (a test case for nuclei having N>40 and Z<40). Using the deformed pn-QRPA model we calculate GT transitions, stellar electron capture cross section (within the limit of low momentum transfer) and stellar weak rates for 76Se. The distinguishing feature of our calculation is a state-by-state evaluation of stellar weak rates in a fully microscopic fashion. Results are compared with experimental data and previous calculations. The calculated GT distribution fulfills the Ikeda sum rule. Rates for β-delayed neutrons and emission probabilities are also calculated. Our study suggests that at high stellar temperatures and low densities, the β+-decay on 76Se should not be neglected and needs to be taken into consideration along with electron capture rates for simulation of presupernova evolution of massive stars.

Gamow-Teller strength and lepton captures rates on 66−71Ni in stellar matter

Charge-changing transitions play a significant role in stellar weak-decay processes. The fate of the massive stars is decided by these weak-decay rates including lepton (positron and electron) captures rates, which play a consequential role in the dynamics of core collapse. As per previous simulation results, weak interaction rates on nickel (Ni) isotopes have significant influence on the stellar core vis-à-vis controlling the lepton content of stellar matter throughout the silicon shell burning phases of high mass stars up to the presupernova stages. In this paper, we perform a microscopic calculation of Gamow–Teller (GT) charge-changing transitions, in the [Formula: see text]-decay and electron capture (EC) directions, for neutron-rich Ni isotopes ([Formula: see text]Ni). We further compute the associated weak-decay rates for these selected Ni isotopes in stellar environment. The computations are accomplished by employing the deformed proton–neutron quasiparticle random phase approximation (pn-QRPA) model. A recent study showed that the deformed pn-QRPA theory is well suited for the estimation of GT transitions. The astral weak-decay rates are determined over densities in the range of 10–10[Formula: see text][Formula: see text]g/cm3and temperatures in the range of 0.01[Formula: see text]–30[Formula: see text][Formula: see text]K. The calculated lepton capture rates are compared with the previous calculation of Pruet and Fuller (PF). The overall comparison demonstrates that, at low stellar densities and high temperatures, our EC rates are bigger by as much as two orders of magnitude. Our results show that, at higher temperatures, the lepton capture rates are the dominant mode for the stellar weak rates and the corresponding lepton emission rates may be neglected.

The Total β-Half-Lives for Some Nickel Isotopes

Abstract . The first-forbidden transitions can play an important role in decreasing the calculated half-lives specially in environments. We calculate the allowed Gamow-Teller transitions in pn-QRPA model for even-even neutron-rich isotopes of nickel. The first forbidden transitions for even-even neutron-rich isotopes of nickel are calculated assuming the nuclei to be spherical. The Woods-Saxon potential basis has been used in our calculations. The calculated half-lives have been compared with the schematic model calculations and corresponding experimental data. Keywords: pn-QRPA approximation, Gamow-Teller, First forbidden transitions

Unique first-forbidden β-decay transitions in odd–odd and even–even heavy nuclei

The allowed Gamow–Teller (GT) transitions are the most common weak nuclear processes of spin–isospin (στ) type. These transitions play a key role in numerous processes in the domain of nuclear physics. Equally important is their contribution in astrophysics, particularly in nuclear synthesis and supernova-explosions. In situations where allowed GT transitions are not favored, first-forbidden transitions become significant, specifically in medium heavy and heavy nuclei. For neutron-rich nuclei, first-forbidden transitions are favored mainly due to the phase-space amplification for these transitions. In this work we calculate the allowed GT as well as unique first-forbidden (U1F) |ΔJ|=2 transitions strength in odd–odd and even–even nuclei in mass range 70≤A≤214. Two different pn-QRPA models were used with a schematic separable interaction to calculate GT and U1F transitions. The inclusion of U1F strength improved the overall comparison of calculated terrestrial β-decay half-lives in both models. The ft values and reduced transition probabilities for the 2−⟷0+ transitions were also calculated. We compared our calculations with the previously reported correlated RPA calculation and experimental results. Our calculations are in better agreement with measured data. For stellar applications we further calculated the allowed GT and U1F weak rates. These include β±-decay rates and electron/positron capture rates of heavy nuclei in stellar matter. Our study shows that positron and electron capture rates command the total weak rates of these heavy nuclei at high stellar temperatures.

β-Decay half-lives and nuclear structure of exotic proton-rich waiting point nuclei under rp-process conditions

We investigate even–even nuclei in the A∼70 mass region within the framework of the proton–neutron quasi-particle random phase approximation (pn-QRPA) and the interacting boson model-1 (IBM-1). Our work includes calculation of the energy spectra and the potential energy surfaces V(β,γ) of Zn, Ge, Se, Kr and Sr nuclei with the same proton and neutron number, N=Z. The parametrization of the IBM-1 Hamiltonian was performed for the calculation of the energy levels in the ground state bands. Geometric shape of the nuclei was predicted by plotting the potential energy surfaces V(β,γ) obtained from the IBM-1 Hamiltonian in the classical limit. The pn-QRPA model was later used to compute half-lives of the neutron-deficient nuclei which were found to be in very good agreement with the measured ones. The pn-QRPA model was also used to calculate the Gamow–Teller strength distributions and was found to be in decent agreement with the measured data. We further calculate the electron capture and positron decay rates for these N=Z waiting point (WP) nuclei in the stellar environment employing the pn-QRPA model. For the rp-process conditions, our total weak rates are within a factor two compared with the Skyrme HF+BCS+QRPA calculation. All calculated electron capture rates are comparable to the competing positron decay rates under rp-process conditions. Our study confirms the finding that electron capture rates form an integral part of the weak rates under rp-process conditions and should not be neglected in the nuclear network calculations.

First-forbidden $ \beta$ -decay rates, energy rates of $ \beta$ -delayed neutrons and probability of $ \beta$ -delayed neutron emissions for neutron-rich nickel isotopes

First-forbidden (FF) transitions can play an important role in decreasing the calculated half-lives specially in environments where allowed Gamow-Teller (GT) transitions are unfavored. Of special mention is the case of neutron-rich nuclei where, due to phase-space amplification, FF transitions are much favored. We calculate the allowed GT transitions in various pn-QRPA models for even-even neutron-rich isotopes of nickel. Here we also study the effect of deformation on the calculated GT strengths. The FF transitions for even-even neutron-rich isotopes of nickel are calculated assuming the nuclei to be spherical. Later we take into account deformation of nuclei and calculate GT + unique FF transitions, stellar $\beta$-decay rates, energy rate of $\beta$-delayed neutrons and probability of $\beta$-delayed neutron emissions. The calculated half-lives are in excellent agreement with measured ones and might contribute in speeding-up of the $r$-matter flow.

First-forbidden transitions and stellar β-decay rates of Zn and Ge isotopes

First-forbidden (FF) charge-changing transitions become relatively important for nuclei as their proton number increases. This is because the strength of allowed Gamow–Teller (GT) transitions decreases with increasing Z. The FF transitions play an important role in reducing the half-lives compared to those calculated from taking the GT transitions alone into account. In this paper we calculate allowed GT as well as and transitions for neutron-rich Zn and Ge isotopes. Two different pn-QRPA models were used with a schematic separable interaction to calculate GT and FF transitions. Half-lives calculated after inclusion of FF transitions were in excellent agreement with the experimental data. Our calculations were also compared to previous QRPA calculations and were found to be in better agreement with measured data. Stellar β-decay rates were calculated for these nuclei including allowed GT and unique FF transitions for astrophysical applications. 86,88Ge has a sizeable contribution to the total stellar rate from unique FF transitions.

Charge-changing transitions and capture strengths of pf-shell nuclei with T z =−2 at proton drip-line

Charge-changing transitions, commonly referred to as Gamow-Teller (GT) transitions, and electron capture/β +-decay strengths for pf-shell nuclei with T z =−2 at proton drip-line have been calculated using the proton-neutron quasi-particle random phase approximation (pn-QRPA) model. The total GT+ strength values and electron capture/β +-decay rates are needed for the study of the late stages of the stellar evolution. The pn-QRPA theory is used for a microscopic calculation of GT strength distribution functions and associated stellar electron capture/β +-decay rates of proton-rich pf-shell nuclei with T z =−2 in the mass range 46≤A≤56 at proton drip-line. Standard quenching factor of 0.74, usually implemented in the shell model calculation, has been incorporated for the comparison with experimental data (wherever available). The calculated GT strength of the two proton-rich nuclei, 52Ni and 56Zn are compared with experimental data of corresponding mirror nuclei. It has been found that the pn-QRPA results are in good agreement with the experimental data as well as shell model result. It is noted that the total GT strength increases linearly with the increase of mass number. The electron capture/β +-decay rates for proton-rich nuclei are calculated on a temperature and density scale relevant to presupernova evolution of massive stars. The β + decay half-lives are compared with measured and other theoretical calculations.

Spin-isospin transitions in chromium isotopes within the quasiparticle random phase approximation

Beta decay and electron capture on isotopes of chromium are advocated to play a key role in the stellar evolution process. In this paper we endeavor to study charge-changing transitions for 24 isotopes of chromium (42–65Cr). These include neutron-rich and neutron-deficient isotopes of chromium. Three different models from the QRPA genre, namely the pn-QRPA, the Pyatov method (PM) and the Schematic model (SM), were selected to calculate and study the Gamow–Teller (GT) transitions in chromium isotopes. The SM was employed separately in the particle–particle (pp) and pp+particle-hole (ph) channels. To study the effect of deformation, the SM was first used assuming the nuclei to be spherical and later to be deformed. The PM was used both in pp and pp + ph channels but only for the case of spherical nuclei. The pn-QRPA calculation was done by considering both pp and ph forces and taking deformation of nucleus into consideration. A recent study proved this version of pn-QRPA to be the best for calculation of GT strength distributions amongst the QRPA models. The pn-QRPA model calculated GT distributions had low-lying centroids and small widths as compared to other QRPA models. Our calculation results were also compared with other theoretical models and measurements wherever available. Our results are in decent agreement with previous measurements and shell model calculations.