Semi-microscopic construction of multi-$\alpha$ cluster spaces

TL;DR

This paper introduces a semi-microscopic projection method for constructing multi-alpha particle spaces, bridging molecular and shell models, and applies it to several nuclei to demonstrate its effectiveness.

Contribution

It presents a new semi-microscopic construction method for multi-alpha spaces, including for 6- and 7-alpha systems, and applies it to various nuclei within an algebraic cluster model.

Findings

Constructed alpha-particle spaces for 6- and 7-alpha systems.

Applied the method to nuclei like $^{20}$Ne, $^{24}$Mg, and $^{28}$Si.

Validated the approach with previous results on $^{12}$C and $^{16}$O.

Abstract

An approximate but straight forward projection method to molecular many alpha-particle states is proposed and the overlap to the shell model space is determined. The resulting space is in accordance with the shell model, but still contains states which are not completely symmetric under permutations of the alpha-particles, which is one reason to call the construction semi-microscopic. A new contribution is the construction of the 6- and 7-$\alpha$-particle spaces. The errors of the method propagate toward larger number of alpha-particles and larger shell excitations. In order to show the effectiveness of the construction proposed, the so obtained spaces are applied, within an algebraic cluster model, to $^{20}$Ne, $^{24}$Mg and $^{28}$Si, each treated as a many-alpha-particle system. Former results on $^{12}$C and $^{16}$O are resumed.