Coulomb Energy of alpha-Aggregates on a Soap Bubble Shape

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.