Shell-model results in $fp$ and ${fpg_{9/2}}$ spaces for $^{61,63,65}$Co isotopes

TL;DR

This study compares shell-model calculations of low-lying and high-spin states in $^{61,63,65}$Co isotopes across two different valence spaces, revealing the adequacy of interactions and the need for higher orbitals in neutron-rich isotopes.

Contribution

It provides a comparative analysis of shell-model results in ${fp}$ and ${fpg_{9/2}}$ spaces for Co isotopes, highlighting the limitations of current interactions for neutron-rich cases.

Findings

GXPF1A and KB3G interactions are reasonable for $^{61,63}$Co.

The ${fpg}$ interaction is inadequate for $^{65}$Co.

Higher orbitals beyond $1g_{9/2}$ are needed for neutron-rich isotopes.

Abstract

Low-lying spectra and several high-spin states of odd--even $^{61,63,65}$Co isotopes are calculated in two different shell-model spaces. First set of calculations have been carried out in ${fp}$ shell valence space (full $fp$ space for $^{63,65}$Co and a truncated one for $^{61}$Co) using two recently derived ${fp}$ shell interactions, namely GXPF1A and KB3G, with $^{40}$Ca as core. Similarly, the second set of calculations have been performed in ${fpg_{9/2}}$ valence space using an ${fpg}$ effective interaction due to Sorlin {\it et al}., with $^{48}$Ca as core and imposing a truncation. It is seen that the results of GXPF1A and KB3G are reasonable for $^{61,63}$Co. For $^{65}$Co, shell-model results show that the ${fpg}$ interaction adopted in the study is inadequate and also point out that it is necessary to include orbitals higher than $1g_{9/2}$ for neutron-rich Co isotopes.