Geometric shapes and relationships of some one-body and multi-body leptodermous distributions

Different families of geometric shapes, derived mainly from lemniscatoids, are proposed to describe ground and excited states of leptodermous distributions of nuclear matter. The transition from one spherical or ellipsoidal nucleus to several spherical or ellipsoidal nuclei or vice versa (in the decay and entrance channels of nuclear reactions: fission, fusion and fragmentation) is particularly investigated. The geometric characteristics of these configurations are given, allowing the calculations of the system energy, of the dynamics of the reactions and of the angular distribution of the fragments.