Two-nucleon excitation from $p$ to $sd$ shell in $^{12,14}$C

TL;DR

This paper investigates two-nucleon excitations from the p to sd shell in carbon isotopes using the YSOX shell-model Hamiltonian, revealing state-dependent effects on excitation energies and configurations.

Contribution

It demonstrates the effectiveness of the YSOX Hamiltonian in modeling 2ħω excitations and highlights the state-dependent influence of the <pp|V|sdsd> interaction in carbon isotopes.

Findings

Excitation energies in 14C are strongly affected by the <pp|V|sdsd> interaction.

The level of 12C is nearly independent of this interaction.

The 2ħω configuration percentage varies significantly in excited states.

Abstract

The effect of the two-nucleon excitation from $p$ to $sd$ shell is discussed in $^{12}$C and $^{14}$C in the frame work of shell model. The recently suggested shell-model Hamiltonian YSOX provides an suitable tool to investigate the $2~\hbar\omega$ excitation in $psd$ region. Because the strength of the $<pp|V|sdsd>$ interaction, which represents the interaction between the $0~\hbar\omega$ and $2~\hbar\omega$ configurations, is considered in the construction of the YSOX. The level of $^{12}$C is almost independent on the $<pp|V|sdsd>$ interaction, but excitation energies of certain states in $^{14}$C are strongly affected by it. Further investigation shows that the percentage of $2~\hbar\omega$ configuration in these states is quite different from that of the ground state.