Calculations of Allowed Beta Decay in the (0d,1s) Shell

Abstract

Allowed $\beta$-decay transition rates and half-lives have been calculated for ($0d,1s$) shell nuclei with $A=17-22,23-24,27-29,30-34, \mathrm{and} 35-39$. For nuclei with $A=17-22\mathrm{} \mathrm{and} 34-39$, the calculated $log\mathrm{ft}$ values have a rms deviation of 5% from experiment, with no discrepancies greater than 12%. For nuclei nearer the middle of the shell there are more significant discrepancies between experiment and theory. The calculated $log\mathrm{ft}$ values are used to predict the half-lives of some light elements. The predicted half-lives for which there are no experimental measurements are: ${}_{}{}^{20}{}_{}{}^{}\mathrm{Mg}$ (0.1 sec), ${}_{}{}^{21}{}_{}{}^{}\mathrm{O}$ (1.2 sec), and ${}_{}{}^{22}{}_{}{}^{}\mathrm{O}$ (0.15 sec). The $log\mathrm{ft}$ values relevant to the solar neutrino experiment are discussed.