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 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 (,)-type charge-exchange reactions at intermediate beam energies. The focus is on transitions from stable nuclei in the shell (). 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 shell measured via charge-exchange reactions and supplemented with results from -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 model space with the KB3G and GXPF1a interactions qualitatively reproduce experimental Gamow-Teller strength distributions of 13 stable isotopes with . 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 g/cm, 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 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.
20 More- Received 9 April 2012
DOI:https://doi.org/10.1103/PhysRevC.86.015809
©2012 American Physical Society