The impact of the off-diagonal cross-shell interaction on $^{14}$C

The shell-model investigation is performed to show the impact on the structure of $^{14}$C contributed by the off-diagonal cross-shell interaction, $\langle pp \mid$V$\mid sdsd\rangle$, which represents the mixing between the $0$ and $2\hbar\omega$ configurations in the $psd$ model space. Observed levels of the positive states in $^{14}$C can be nicely described in $0-4\hbar\omega$ or a larger model space through the well defined Hamiltonians, YSOX and WBP, with a reduction on the strength of the $\langle pp \mid$V$\mid sdsd\rangle$ interaction in the latter. The observed B(GT) values for $^{14}$C can be generally described by YSOX, while WBP and their modifications on the $\langle pp \mid$V$\mid sdsd\rangle$ interaction fail for some values. Further investigation shows the effect of such interaction on the configuration mixing and occupancy. The present work shows examples on how the off-diagonal cross-shell interaction strongly drives the nuclear structure.