EFFECTS OF COULOMB AND PAIRING INTERACTIONS BETWEEN NUCLEONS IN DETERMINING NUCLEAR STABILITY OF FINITE NUCLEI

Abstract

From time to time, several nuclear models have been proposed by various research groups to explain the properties of finite nuclei and large nuclear systems in nuclear physics and astrophysics. However, no single model could explain the properties of all the nuclear systems due to the concept of many body interactions of particles, which cannot be solved by Schrödinger equation. The stability of the nuclei is one of the fundamental properties of the nuclear system that is related to the average binding energy of the nuclei. However, the binding energy calculations are not accurate since they are based on the rough estimates of the large number of nucleons that are in collective motion. Therefore, the energy terms in the binding energy equation have to be modified in order to describe accurately the interaction of the nucleons. In this research, the effects of Coulomb interaction and pairing interaction between nucleons in the binding energy equation have been carried out in order to determine the stability of finite nuclei. This was achieved by formulating a modified Coulomb potential based on the assumptions of charge distribution in a spherical nucleus. In addition, the pairing energies of finite nuclei were calculated using the principles of the shell model and the binding energies obtained from atomic mass evaluation tables. The results obtained in this study revealed that, the modified Coulomb energy model defines the limits of long-range Coulomb potential as well as generating the most stable isobars for a fixed mass number. The most stable atomic numbers (ZSTABLE) obtained from the derived models include, Z=126, Z=132, Z=134, Z=141, Z=148, Z=152, Z=162, Z=164 and Z=193. Furthermore, it was found that, the absolute values of pairing energies decrease with increase in the mass numbers with occurrence of undulating peaks and troughs in the pairing energy-mass number graphs. The modified Coulomb potential model is useful in calculating the finite range Coulomb potentials, describing the decay transformations of radioactive nuclei and predicting for the existence of the stable isobars among the super heavy elements that may reside in the island of stability. Similarly, the pairing energy calculations are important in describing the stability and nuclear abundance of all the nuclei isotopewise, using the peak-trough theory. Based on the results obtained from the Coulomb potential model and pairing energy model, a unifying model that can link up the two models can be developed, such that, the stability of the nuclei and the nuclear abundance can be described simultaneously.