Calculated Electron Capture Rates Research Articles

Unblocking of stellar electron capture for neutron-rich N=50 nuclei at finite temperature

We have calculated electron capture rates for neutron-rich $N=50$ nuclei ($^{78}$Ni, $^{82}$Ge, $^{86}$Kr, $^{88}$Sr) within the Thermal QRPA approach at temperatures $T=0$, corresponding to capture on the ground-state, and at $T=10$ GK (0.86 MeV), which is a typical temperature at which the $N=50$ nuclei are abundant during a supernova collapse. In agreement with recent experiments, we find no Gamow-Teller (GT$_+$) strength at low excitation energies, $E<7$ MeV, caused by Pauli blocking induced by the $N=50$ shell gap. At the astrophysically relevant temperatures this Pauli blocking of the GT$_+$ strength is overcome by thermal excitations across the $Z=40$ proton and $N=50$ neutron shell gaps, leading to a sizable GT contribution to the electron capture. At the high densities, at which the $N=50$ nuclei are important for stellar electron capture, forbidden transitions contribute noticeably to the capture rate. Our results indicate that the neutron-rich $N=50$ nuclei do not serve as an obstacle of electron capture during the supernova collapse.

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.

Study of Gamow–Teller strength and associated weak-rates on odd-A nuclei in stellar matter

In a recent study by Cole et al. [A. L. Cole et al., Phys. Rev. C 86 (2012) 015809], it was concluded that quasi-particle random phase approximation (QRPA) calculations show larger deviations and overestimate the total experimental Gamow–Teller (GT) strength. It was also concluded that QRPA calculated electron capture rates exhibit larger deviation than those derived from the measured GT strength distributions. The main purpose of this study is to probe the findings of the Cole et al. paper. This study gives useful information on the performance of QRPA-based nuclear models. As per simulation results, the capturing of electrons that occur on medium heavy isotopes have a significant role in decreasing the ratio of electron-to-baryon content of the stellar interior during the late stages of core evolution. We report the calculation of allowed charge-changing transitions strength for odd-[Formula: see text] [Formula: see text]-shell nuclei ([Formula: see text]Sc and [Formula: see text]Mn) by employing the deformed pn-QRPA approach. The computed GT transition strength is compared with previous theoretical calculations and measured data. For stellar applications, the corresponding electron capture rates are computed and compared with rates using previously calculated and measured GT values. Our finding shows that our calculated results are in decent accordance with measured data. At higher stellar temperature, our calculated electron capture rates are larger than those calculated by independent particle model (IPM) and shell model. It was further concluded that at low temperature and high density regions, the positron emission weak-rates from [Formula: see text]Sc and [Formula: see text]Mn may be neglected in simulation codes.

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.

The nuclear structure and associated electron capture rates on odd-Z nucleus 51V in stellar matter

The Gamow-Teller strength distribution function, B(GT), for the odd Z parent $^{51}$V, $N-Z$ =5, up to 30 MeV of excitation energy in the daughter $^{51}$Ti is calculated in the domain of proton-neutron Quasiparticle Random Phase Approximation (pn-QRPA) theory. The pn-QRPA results are compared against other theoretical calculations, (n, p) and high resolution (d, $^{2}$He) reaction experiments. For the case of (d, $^{2}$He) reaction the calibration was performed for $0\leq E_{j} \leq 5.0$ MeV, where the authors stressed that within this excitation energy range the $\Delta L = 0$ transition strength can be extracted with high accuracy for $^{51}$V. Within this energy range the current pn-QRPA total B(GT) strength 0.75 is in good agreement with the (d, $^{2}$He) experiment's total strength of 0.9 $\pm$ 0.1. The pn-QRPA calculated Gamow-Teller centroid at 4.20 MeV in daughter $^{51}$Ti is also in good agreement with high resolution (d, $^{2}$He) experiment which placed the Gamow-Teller centroid at 4.1 $\pm$ 0.4 MeV in daughter $^{51}$Ti. The low energy detailed Gamow-Teller structure and Gamow-Teller centroid play a sumptuous role in associated weak decay rates and consequently affect the stellar dynamics. The stellar weak rates are sensitive to the location and structure of these low-lying states in daughter $^{51}$Ti. The calculated electron capture rates on $^{51}$V in stellar matter are also in good agreement with the large scale shell model rates.

Self-consistent theory of stellar electron capture rates

Recently a novel theory framework has been established for description of electron capture rates at temperatures and densities in stellar environment, based on the relativistic energy density functional. The model includes finite temperature relativistic mean field to determine single-particle basis and the corresponding thermal occupation factors of target nucleus, while relevant charge-exchange excitations are described by the self-consistent finite temperature relativistic random phase approximation (FTRRPA). The calculated electron capture rates for 54,56Fe are shown in comparison with other advanced theory approaches.

Rp-process weak-interaction mediated rates of waiting-point nuclei

Electron capture and positron decay rates are calculated for neutron-deficient Kr and Sr waiting point nuclei in stellar matter. The calculation is performed within the framework of pn-QRPA model for rp-process conditions. Fine tuning of particle-particle, particle-hole interaction parameters and a proper choice of the deformation parameter resulted in an accurate reproduction of the measured half-lives. The same model parameters were used to calculate stellar rates. Inclusion of measured Gamow-Teller strength distributions finally led to a reliable calculation of weak rates that reproduced the measured half-lives well under limiting conditions. For the rp-process conditions, electron capture and positron decay rates on $^{72}$Kr and $^{76}$Sr are of comparable magnitude whereas electron capture rates on $^{78}$Sr and $^{74}$Kr are 1--2 orders of magnitude bigger than the corresponding positron decay rates. The pn-QRPA calculated electron capture rates on $^{74}$Kr are bigger than previously calculated. The present calculation strongly suggests that, under rp-process conditions, electron capture rates form an integral part of weak-interaction mediated rates and should not be neglected in nuclear reaction network calculations as done previously.

Ground and excited states Gamow-Teller strength distributions of iron isotopes and associated capture rates for core-collapse simulations

This paper reports on the microscopic calculation of ground and excited states Gamow-Teller (GT) strength distributions, both in the electron capture and electron decay direction, for 54,55,56Fe. The associated electron and positron capture rates for these isotopes of iron are also calculated in stellar matter. These calculations were recently introduced and this paper is a follow-up which discusses in detail the GT strength distributions and stellar capture rates of key iron isotopes. The calculations are performed within the framework of the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. The pn-QRPA theory allows a microscopic state-by-state calculation of GT strength functions and stellar capture rates which greatly increases the reliability of the results. For the first time experimental deformation of nuclei are taken into account. In the core of massive stars isotopes of iron, 54,55,56Fe, are considered to be key players in decreasing the electron-to-baryon ratio (Y e ) mainly via electron capture on these nuclide. The structure of the presupernova star is altered both by the changes in Y e and the entropy of the core material. Results are encouraging and are compared against measurements (where possible) and other calculations. The calculated electron capture rates are in overall good agreement with the shell model results. During the presupernova evolution of massive stars, from oxygen shell burning stages till around end of convective core silicon burning, the calculated electron capture rates on 54Fe are around three times bigger than the corresponding shell model rates. The calculated positron capture rates, however, are suppressed by two to five orders of magnitude.

Gamow-Teller strength distributions at finite temperatures and electron capture in stellar environments

We propose a new method to calculate stellar weak-interaction rates. It is based on the thermofield dynamics formalism and allows calculation of the weak-interaction response of nuclei at finite temperatures. The thermal evolution of the ${\mathrm{GT}}_{+}$ distributions is presented for the sample nuclei $^{54,56}\mathrm{Fe}$ and $^{76,78,80}\mathrm{Ge}$. For Ge we also calculate the strength distribution of first-forbidden transitions. We show that thermal effects shift the ${\mathrm{GT}}_{+}$ centroid to lower excitation energies and make possible negative- and low-energy transitions. In our model we demonstrate that the unblocking effect for ${\mathrm{GT}}_{+}$ transitions in neutron-rich nuclei is sensitive to increasing temperature. The results are used to calculate electron capture rates and are compared to those obtained from the shell model.

Unblocking of the Gamow-Teller strength in stellar electron capture on neutron-rich germanium isotopes

We propose a new model to calculate stellar electron capture rates for neutron-rich nuclei. These nuclei are encountered in the core-collapse of a massive star. Using the Shell Model Monte Carlo approach, we first calculate the finite temperature occupation numbers in the parent nucleus. We then use these occupation numbers as a starting point for calculations using the random phase approximation. Using the RPA approach, we calculate electron capture rates including both allowed and forbidden transitions. Such a hybrid model is particularly useful for nuclei with proton numbers Z<40 and neutron numbers N>40, where allowed Gamow-Teller transitions are only possible due to configuration mixing by the residual interaction and by thermal unblocking of $pf$-shell single-particle states. Using the even germanium isotopes Ge-68 to Ge-76 as examples, we demonstrate that the configuration mixing is strong enough to unblock the Gamow-Teller transitions at all temperatures relevant to core-collapse supernovae.

Supernova electron capture rates

We have calculated the Gamow-Teller strength distributions for the ground states and low lying states of several nuclei that play an important role in the precollapse evolution of supernova. The calculations reproduce the experimental GT distributions nicely. The GT distribution are used to calculate electron capture rates for typical presupernova conditions. The computed rates are noticeably smaller than the presently adopted rates. The possible implications for the supernova evolution are discussed.