ABSTRACT
A theoretical framework for a system of interacting nucleons that interact in pairs is developed using the method of second quantization and many-body theory. Essential parameters such as binding energy of nucleus, binding fraction, separation energy of nucleons, energy gap and phase shift, that describe characteristics of nuclei have been related to each other. Separation energies and energy gaps are calculated for some selected medium, heavy and super heavy nuclei using the different values for the density of states, 𝐷(𝐸𝑓), at the Fermi surface. Calculations show that, the neutron separation energy (𝑆𝑛) decreases as the mass number (𝐴) increases from 𝐴=92 to 𝐴=294 indicating that the neutrons become loosely bound to the nucleus as 𝐴 increases. The energy gap (Δ), increases as the density of states decreases from 𝐴/8𝑀𝑒𝑉−1 to 𝐴/16𝑀𝑒𝑉−1. Calculations done by adding eight neutrons to some super heavy nuclei from 𝑍=110 to 𝑍=118, showed that the separation energies in each pair of isotopes decreased in a range 1.0 𝑘𝑒𝑉 to 1.2 𝑘𝑒𝑉 and energy gaps decreased in a range 1.9 𝑘𝑒𝑉−1 to 2.3 𝑘𝑒𝑉−1. Decrease in separation energy and decrease in the magnitude of energy gap implies instability of the said isotopes, and these isotopes may not become a part of the island of stability unless filling of shells by additional neutrons leads to filling of shells by magic numbers of nucleons.
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