Alpha Clustering with a Hollow Structure --- Geometrical Structure of Alpha Clusters from Platonic Solids to Fullerene Shape

摘要

We study $\alpha$-cluster structure based on the geometric configurationswith a microscopic framework, which takes full account of the Pauli principle,and which also employs an effective inter-nucleon force including finite-rangethree-body terms suitable for microscopic alpha-cluster models. Here, specialattention is focused upon the $\alpha$ clustering with a hollow structure; allthe $\alpha$ clusters are put on the surface of a sphere. All the Platonicsolids (five regular polyhedra) and the fullerene-shaped polyhedron coming fromicosahedral structure are considered. Furthermore, two configurations with dualpolyhedra, hexahedron-octahedron and dodecahedron-icosahedron, are alsoscrutinized. As a consequence, we insist on the possible existence of stable$\alpha$-clustering with a hollow structure for all the configurations.Especially, two configurations, that is, dual polyhedra ofdodecahedron-icosahedron and fullerene, have a prominent hollow structurecompared with other six configurations.