Consistent description for cluster dynamics and single-particle correlation

TL;DR

This paper develops an extended antisymmetrized quasi cluster model (AQCM) to simultaneously describe cluster dynamics and single-particle correlations in the ground state of carbon-12, including two-particle-two-hole excitations.

Contribution

It introduces an extension of AQCM that incorporates single-particle excitations and superposes basis states using GCM, providing a more comprehensive description of nuclear structure.

Findings

Two-particle-two-hole states significantly lower the ground state energy.

The extended model captures pairing-like correlations in ${}^{12} ext{C}$.

The approach unifies cluster and shell-model descriptions.

Abstract

Cluster dynamics and single-particle correlation are simultaneously treated for the description of the ground state of ${}^{12} \mathrm{C} $. The recent development of the antisymmetrized quasi cluster model (AQCM) makes it possible to generate $jj$-coupling shell-model wave functions from $\alpha$ clusters models. The cluster dynamics and the competition with the $jj$-coupling shell-model structure can be estimated rather easily. In the present study, we further include the effect of single-particle excitation; the mixing of the two-particle-two-hole excited states is considered. The single-particle excitation is not always taken into account in the standard cluster model analyses, and the two-particle-two-hole states are found to strongly contribute to the lowering of the ground state owing to the pairing-like correlations. By extending AQCM, all of the basis states are prepared on the same footing, and they are superposed based on the framework of the generator coordinate method (GCM).