Cluster structures and superdeformation in $^{28}$Si

TL;DR

This study uses advanced computational methods to analyze the structure of $^{28}$Si, revealing various cluster configurations and superdeformed states, and identifying the dominant cluster components in different bands.

Contribution

It introduces a novel application of AMD and MCM with constrained variation to explore cluster structures and superdeformation in $^{28}$Si, highlighting the role of specific cluster components.

Findings

Normal-deformed and superdeformed bands contain large $^{12}$C-$^{16}$O and $eta$-$^{24}$Mg$ components.

Identification of two excited bands with developed $eta$-$^{24}$Mg$ cluster structure.

Presence of various cluster structures such as $ ext{α}$-$^{24}$Mg and $^{12}$C-$^{16}$O in the states.

Abstract

We have studied positive-parity states of $^{28}$Si using antisymmetrized molecular dynamics (AMD) and multi-configuration mixing (MCM) with constrained variation. Applying constraints to the cluster distance and the quadrupole deformation of the variational calculation, we have obtained basis wave functions that have various structures such as $\alpha$-$^{24}$Mg and $^{12}$C-$^{16}$O cluster structures as well as deformed structures. Superposing those basis wave functions, we have obtained a oblate ground state band, a $\beta$ vibration band, a normal-deformed prolate band, and a superdeformed band. It is found that the normal-deformed and superdeformed bands contain large amounts of the $^{12}$C-$^{16}$O and $\alpha$-$^{24}$Mg cluster components, respectively. The results also suggest the presence of two excited bands with the developed $\alpha$-$^{24}$Mg cluster structure, where the inter-cluster motion and the $^{24}$Mg-cluster deformation play important roles.