Shell-model description of theβ−decay of theN=21 and 22 isotones34Al,36Si, andP37

Abstract

The nuclear structure of the parent and daughter nuclei in the decays ${}_{}{}^{34}{}_{}{}^{}\mathrm{Al}$(${\beta }^{\mathrm{-}}$ ${)}^{34}$Si, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Si}$(${\beta }^{\mathrm{-}}$ ${)}^{36}$P, and ${}_{}{}^{37}{}_{}{}^{}\mathrm{P}$(${\beta }^{\mathrm{-}}$ ${)}^{37}$S are considered in a spherical shell model comprising the (2s,1d,1f,2p) configuration space. Energy spectra and beta and gamma transition strengths are calculated. These predictions are used to construct decay schemes from recent ${\beta }^{\mathrm{-}}$-delayed γ-ray singles spectra for the three decaying nuclei. The predicted half-lives of ${}_{}{}^{34}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{37}{}_{}{}^{}\mathrm{P}$ are 0.037(7), 0.8(4), and 2.0(9) s, where the uncertainties are due to mass uncertainties of the decaying bodies. These predictions are in agreement with recent experimental results of 0.050(25), 0.54(15), and 2.31(13) s, respectively.