Novel and simple description for a smooth transition from $\alpha$-cluster wave functions to $jj$-coupling shell model wave functions

TL;DR

This paper introduces an improved Antisymmetrized Quasi-Cluster Model (AQCM) that smoothly transitions between alpha-cluster and shell model descriptions, successfully applied to the ground state of carbon-12 with fewer parameters.

Contribution

An enhanced AQCM method is proposed to efficiently model the cluster-shell transition in nuclei, reducing degrees of freedom while maintaining accuracy.

Findings

Optimal wave function is an intermediate between cluster and shell states.

AQCM results agree with AMD calculations.

Fewer parameters are needed compared to AMD.

Abstract

We propose an improved version of Antisymmetrized Quasi-Cluster Model (AQCM) to describe a smooth transition from the $\alpha$-cluster wave function to the $jj$-coupling shell model wave function and apply it to the ground state of $^{12}$C. The cluster-shell transition in $^{12}$C is characterized in AQCM by only two parameters: $R$ representing the distance between $\alpha$ clusters and the center of mass, and $\Lambda$ describing the break of $\alpha$ clusters. The optimal AQCM wave function for the ground state of $^{12}$C is an intermediate state between the three-$\alpha$ cluster state and the shell model state with the $p_{3/2}$ subshell closure configuration. The result is consistent with that of the Antisymmetrized Molecular Dynamics (AMD), and the optimal AQCM wave function quantitatively agrees with the AMD one, although the number of degrees of freedom in AQCM is significantly fewer.