Cluster formation in heavy nuclei and cluster radioactivity / Ahmed Mohamed Hassan Husien Abdelhady ; Supertvised Walaa Mohamed Seif , Mahmoud Yahia Ismail , Hisham Anwer Saleh

Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Physics

In this thesis work, we have performed a qualitative study for - and heavier clusterdecays in heavy nuclei region. Based on the microscopic double-folding model, the interaction potential for the cluster-core system is developed by adding a physical internal repulsive core due to the change in the intrinsic kinetic energy of the interacting nuclei. We apply Bohr-Sommerfeld quantization condition to normalize the improved total nucleus-nucleus interacting potential. Based on the normalized improved potential and the decay energy for each process of the -decay of ²¹² Po and the ²⁴ Ne cluster-decay of ²³²U, as examples of reactions involving density redistribution, we solve numerically the time-independent Schr{u00A8}odinger equation and obtain the quasi-bound state wavefunction for each decay. We utilize the obtained stationary wavefunction to describe each decay by calculating the decay parameters such as the penetration probability P, the assault frequency , the preformation probability Sc, and the decay half life T₁/₂. This investigation shows the importance of including the change of the internal kinetic energy of the interacting nuclei in the calculations of - and heavier cluster-decays of heavy nuclei. Also, we examine the applicability of the Wildermuth-Tang (WT) rule in the -cluster decay calculations for Te, Po and At isotopes. For -core system we solve the relative wave motion Schr{u00A8}odinger equation using repulsive and non-repulsive core interaction potentials. Applying the Bohr-Sommerfeld (BS) quantization condition along with the WT prescription to the non-repulsive core type potentials yields a large number of nodes in the radial wavefunction compared to the one obtained using repulsive core type potentials. The repulsive core potentials produce interior wavefunction of very little nodes or even nodeless. The latter type of the potentials efficaciously simulates the Pauli principle by considering the change in the intrinsic kinetic energy. However, it is possible to reproduce the observed half-life data using the potentials that have no automatic internal pocket with applying the BS quantization with quantum numbers which are significantly less than that obtained from the WT rule, upon renormalizing the potential

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