Coulomb energy of α -particle aggregates distributed on Archimedean solids

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