Coulomb Energy of alpha-Aggregates on a Soap Bubble Shape

TL;DR

This paper investigates the Coulomb energy of alpha-cluster arrangements on soap bubble shapes, highlighting how geometric configurations can reduce repulsive effects compared to uniform density distributions.

Contribution

It introduces a microscopic framework considering the Pauli principle to analyze alpha-cluster configurations on exotic nuclear shapes, comparing their Coulomb energies.

Findings

Alpha-cluster configurations on polyhedra reduce Coulomb repulsion.

Different polyhedral arrangements correspond to specific nuclei.

Geometric configurations influence nuclear Coulomb energy significantly.

Abstract

We study the property of alpha-aggregates on a soap bubble shape within a microscopic framework, which takes full account of the Pauli principle. Our special attention is payed to the Coulomb energy for such an exotic shapes of nuclei, and we discuss the advantage of alpha-clusters with geometric configurations compared with the uniform density distributions in reducing the repulsive effect. We consider four kinds of configurations of alpha clusters on a soap bubble, which are dual polyhedra composed of a dodecahedron and an icosahedron, octacontahedron and two types of truncated icosahedrons, that is, two kinds of Archimedean solids. The latter two are an icosidodecahedron and a fullerene shape. When putting each alpha-cluster on the vertex of polyhedra, four $\alpha$-cluster aggregates correspond to the following four nuclei; Gd (64 protons), Po (84 protons), Nd (60 protons) and a nucleus with 120 protons, respectively.