Gamow-Teller strengths and electron-capture rates forpf-shell nuclei of relevance for late stellar evolution

Abstract

Background: Electron-capture reaction rates on medium-heavy nuclei are an important ingredient for modeling the late evolution of stars that become core-collapse or thermonuclear supernovae. The estimation of these rates requires the knowledge of Gamow-Teller strength distributions in the ${\ensuremath{\beta}}^{+}$ direction. Astrophysical models rely on electron-capture rate tables largely based on theoretical models, which must be validated and tested against experimental results.Purpose: This paper presents a systematic evaluation of the ability of theoretical models to reproduce experimental Gamow-Teller transition strength distributions measured via ($n$,$p$)-type charge-exchange reactions at intermediate beam energies. The focus is on transitions from stable nuclei in the $pf$ shell ($45\ensuremath{\le}A\ensuremath{\le}64$). In addition, the impact of deviations between experimental and theoretical Gamow-Teller strength distributions on derived stellar electron-capture rates is investigated.Method: Data on Gamow-Teller transitions from 13 nuclei in the $pf$ shell measured via charge-exchange reactions and supplemented with results from $\ensuremath{\beta}$-decay experiments where available, were compiled and compared with strength distributions calculated in shell models (using the GXPF1a and KB3G effective interactions) and quasiparticle random-phase approximation (QRPA) using ground-state deformation parameters and masses from the finite-range droplet model. Electron-capture rates at relevant stellar temperatures and densities were derived for all distributions and compared.Results: With few exceptions, shell-model calculations in the $pf$ model space with the KB3G and GXPF1a interactions qualitatively reproduce experimental Gamow-Teller strength distributions of 13 stable isotopes with $45\ensuremath{\le}A\ensuremath{\le}64$. Results from QRPA calculations exhibit much larger deviations from the data and overestimate the total experimental Gamow-Teller strengths. For stellar densities in excess of ${10}^{7}$ g/cm${}^{3}$, ground-state electron-capture rates derived from the shell-model calculations using the KB3G (GXPF1a) interaction deviate on average less than 47$%$ (31$%$) from those derived from experimental data for which the location of daughter states at low excitation energies are well established. For electron-capture rates derived from Gamow-Teller strengths calculated in QRPA, the deviations are much larger, especially at low stellar densities.Conclusions: Based on the limited set of test cases available for nuclei in the $pf$ shell, shell-models using the GXPF1a and KB3G interactions can be used to estimate electron-capture rates for astrophysical purposes with relatively good accuracy. Measures of the uncertainties in these rates can serve as input for sensitivity studies in stellar evolution models. Ground-state electron-capture rates based on the QRPA formalism discussed in the paper exhibit much larger deviations than those based on the shell-model calculations and should be used with caution, especially at low stellar densities.