Deformed shell model calculations of half lives for ${\ensuremath{\beta}}^{+}$/EC decay and $2\ensuremath{\nu}$ ${\ensuremath{\beta}}^{+}{\ensuremath{\beta}}^{+}/{\ensuremath{\beta}}^{+}$EC/ECEC decay in medium-heavy $N~Z$ nuclei

Deformed shell model calculations of half lives for $β^{+}$ /EC decay and $2 ν$ $β^{+} β^{+} / β^{+}$ EC/ECEC decay in medium-heavy $N ~ Z$ nuclei

S. Mishra, A. Shukla, R. Sahu, and V. K. B. Kota

Phys. Rev. C 78, 024307 – Published 14 August 2008

Abstract

The $β^{+}$ /EC half-lives of medium heavy $N ~ Z$ nuclei with mass number $A ~ 64 − 80$ are calculated within the deformed shell model (DSM) based on Hartree-Fock states by employing a modified Kuo interaction in ( $^{2} p_{3 / 2},^{1} f_{5 / 2},^{2} p_{1 / 2},^{1} g_{9 / 2}$ ) space. The DSM model has been quite successful in predicting many spectroscopic properties of $N ~ Z$ medium heavy nuclei with $A ~ 64 − 80$ . The calculated $β^{+}$ /EC half-lives, for prolate and oblate shapes, compare well with the predictions of the calculations with Skyrme force by Sarriguren et al. Going further, following recent searches, half-lives for $2 ν$ $β^{+} β^{+} / β^{+}$ EC/ECEC decay for the nucleus ${}^{78}{Kr}$ are calculated using DSM and the results compare well with QRPA predictions.