Shapes describing the alpha decay, cluster radioactivity, fusion, fission and fragmentation phenomena

Abstract

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.

Fusion and fission barrier heights and positions within the Generalized Liquid Drop Model

“…5 for the symmetric fission path of the 228 Ra nucleus. More generally, the height of the lowest theoretical potential barrier encountered in the fission channel is compared with the experimental data [1,4,10,38,39,43] in Table 4 assuming or not the deformation and microscopic effects of the fragments. The error bar of these experimental data is often of several MeV.…”

“…It is worth mentioning the tentative to reproduce the fission barrier heights by analytical formulas [52] in the region 50 ≤ Z ≤ 130. Table 4: Comparison of the experimental [1,4,10,38,39,43] fission barrier heights E exp (in MeV) with the heights E th obtained in the prefered decay channels determined from the GLDM assuming the two-sphere approximation and the heights E th,def obtained when the deformation and microscopic effects of the fragments are taken into account. The theoretical radius R fis (in fm) is also given.…”

“…Assuming volume conservation, this GLDM takes into account the proximity forces acting between surfaces in regard, the charge and mass asymmetry and the shell and pairing effects. Its complete description is displayed, particularly, in [1,5,10,11]. The quasimolecular shape sequence (elliptic lemniscatoids) previously used to describe the path leading from two spherical nuclei to one sphere or vice-versa has been retained once again to investigate these fusion and fission reactions [10].…”

“…Its complete description is displayed, particularly, in [1,5,10,11]. The quasimolecular shape sequence (elliptic lemniscatoids) previously used to describe the path leading from two spherical nuclei to one sphere or vice-versa has been retained once again to investigate these fusion and fission reactions [10]. It allows to describe smoothly the formation of a deep neck while keeping almost spherical ends and, then, a smooth transition between the two-body and one-body shapes or vice-versa.…”

The Evaluation of Fission Barrier Height by Fission Toy Model Approach

“…There is an open opportunity for research on nuclear mass fragments, that is replacing the Coulomb interactions between two candidate nuclides [25] with direct interactions between nucleons. The location of the nucleons is determined randomly through a horizontal distribution function.…”