Shapes describing the fusion, fission and fragmentation phenomena and alpha molecules

The purpose of this presentation is to provide geometric shapes and to give their main characteristics in order to determine the energy and the dynamics of reactions such as the nuclear fusion, fission, fragmentation processes and alpha emission. After recalling general definitions, the following shapes will be successively studied: ellipsoids, symmetric and asymmetric elliptic and hyperbolic lemniscatoids, prolate symmetric and asymmetric compact ternary shapes, toroids and bubbles. Other planar and three-dimensional multi-body shapes such as linear chain, triangle, square, tetrahedron, pentagon, trigonal bi-pyramid, square pyramid, hexagon, octahedron, octagon and cube used to describe some light nuclei as alpha molecules will be also shown as the associated potentials. The energies of the ¹²C, ¹⁶O, ²⁰Ne, ²⁴Mg and ³²S 4n nuclei have been determined assuming different planar and three-dimensional shapes of the alpha molecules: linear chain, triangle, square, tetrahedron, pentagon, trigonal bi-pyramid, square pyramid, hexagon, octahedron, octagon and cube. These calculations suggest that an oblate equilateral triangular configuration is compatible with the ground state shape of ¹²C and a prolate almost aligned shape for the excited Hoyle state shape. The three dimensional shapes are favored for the heavier nuclei. This document is composed of an abstract and the slides of the presentation