Shell-model interpretation of the beta - decay of 212Big, 212Bim1, and 212Bim2.

Abstract

The ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ decay of the $^{212}\mathrm{Bi}$ ground state (${\mathit{T}}_{1/2}$=61 min) and the isomers $^{212}\mathrm{Bi}^{\mathit{m}1}$ (${\mathit{T}}_{1/2}$=27 min), and $^{212}\mathrm{Bi}^{\mathit{m}2}$ (${\mathit{T}}_{1/2}$=8 min) are considered in the spherical shell model. The wave functions and energy spectra of all even and odd states in the Kuo-Herling model space were calculated for both $^{212}\mathrm{Bi}$ and $^{212}\mathrm{Po}$. Possible candidates for the two $^{212}\mathrm{Bi}$ isomers were located from these results and the allowed and first-forbidden ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ decays rates were formed using a recently developed parametrization of first-forbidden decays in the lead region. It was concluded that $^{212}\mathrm{Bi}^{\mathit{m}1}$ is the yrast ${8}^{\mathrm{\ensuremath{-}}}$ state and $^{212}\mathrm{Bi}^{\mathit{m}2}$ the yrast ${18}^{\mathrm{\ensuremath{-}}}$ state of $^{212}\mathrm{Bi}$. The decay rates calculated for these two ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ emitters are in excellent agreement with experiment. The predictions for the decay of the ground state of $^{212}\mathrm{Bi}$ are not in good agreement with experiment, illustrating the difficulty of calculating weak first-forbidden decay modes reliably.