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

TL;DR

This study examines how the off-diagonal cross-shell interaction influences the nuclear structure of carbon-14, demonstrating its significant role in configuration mixing and energy level descriptions within shell-model frameworks.

Contribution

It provides a detailed analysis of the off-diagonal cross-shell interaction's impact on $^{14}$C structure, highlighting its importance in shell-model calculations and configuration mixing.

Findings

Off-diagonal cross-shell interaction significantly affects $^{14}$C structure.

Different Hamiltonians show varying success in describing observed levels.

The interaction influences configuration mixing and occupancy patterns.

Abstract

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.