Clustering and Triaxial Deformations of $^{40}$Ca

TL;DR

This study investigates the structure of $^{40}$Ca using advanced computational methods, revealing various deformed and cluster configurations, and successfully reproducing experimental electromagnetic transition data.

Contribution

The paper introduces a comprehensive analysis of $^{40}$Ca's positive-parity states, identifying multiple cluster and deformation structures using AMD and GCM methods.

Findings

Identification of deformed-shell, $ ext{α}$-$^{36}$Ar, and $^{12}$C-$^{28}$Si cluster structures.

Reproduction of experimental $B(E2)$ values with good accuracy.

Discovery of an $ ext{α}$-$^{36}$Ar higher-nodal band above the normal-deformed band.

Abstract

We have studied the positive-parity states of $^{40}$Ca using antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM). Imposing two different kinds of constraints on the variational calculation, we have found various kinds of $^{40}{\rm Ca}$ structures such as a deformed-shell structure, as well as $\alpha$-$^{36}$Ar and $^{12}$C-$^{28}$Si cluster structures. After the GCM calculation, we obtained a normal-deformed band and a superdeformed band together with their side bands associated with triaxial deformation. The calculated $B(E2)$ values agreed well with empirical data. It was also found that the normal-deformed and superdeformed bands have a non-negligible $\alpha$-$^{36}$Ar cluster component and $^{12}$C-$^{28}$Si cluster component, respectively. This leads to the presence of an $\alpha$-$^{36}$Ar higher-nodal band occurring above the normal-deformed band.