β-decay half-life ofV50calculated by the shell model

Abstract

In this work we survey the detectability of the ${\ensuremath{\beta}}^{\ensuremath{-}}$ channel of ${}_{23}^{50}\mathrm{V}$ leading to the first excited ${2}^{+}$ state in ${}_{24}^{50}\mathrm{Cr}$. The electron-capture (EC) half-life corresponding to the transition of ${}_{23}^{50}V$ to the first excited ${2}^{+}$ state in ${}_{22}^{50}\mathrm{Ti}$ had been measured earlier. Both of the mentioned transitions are 4th-forbidden non-unique. We have performed calculations of all the involved wave functions by using the nuclear shell model with the GXPF1A interaction in the full f-p shell. The computed half-life of the EC branch is in good agreement with the measured one. The predicted half-life for the ${\ensuremath{\beta}}^{\ensuremath{-}}$ branch is in the range $\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{19}$ yr whereas the present experimental lower limit is $1.5\ifmmode\times\else\texttimes\fi{}{10}^{18}$ yr. We discuss also the experimental lay-out needed to detect the ${\ensuremath{\beta}}^{\ensuremath{-}}$-branch decay.