To model the alpha decay, cluster radioactivity, fusion, fission and fragmentation phenomena of microscopic or macroscopic distributions of matter or charge it is useful to simulate these deformed physical objects by geometric shapes allowing the determination of their root mean square radius, volume, surface and Coulomb energies as well as their moments of inertia and quadrupole moments. Most of the shapes used in macroscopic nuclear physics are briefly recalled. In particular, several shape sequences that we have used previously, mainly formed from generalized lemniscatoids, are more extensively detailed. They allow to describe the transitions from one compact configuration to several ones or vice versa.

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.

No abstract