The Role of Shell Model in Determining Pairing Interaction in Nuclei

Abstract

The role of the shell model in pairing interaction in nuclei is investigated by calculating the pairing energies of O–O (odd–odd), O–E (odd–even), E–E (even–even) and E–O (even–odd) isotopes of four elements namely; 15P, 25Mn, 40Zr and 60Nd. The pairing energies were computed using the values of binding energy (B) obtained from AME2016 atomic mass evaluation. The graphs of the pairing energies against the mass numbers revealed an increase of the pairing energies with the occurrence of periodic humps adjacent to the neutron magic numbers. The rise in the pairing energies is attributed to the bound states of heavy nuclei arising from the neutron-neutron pairs in the shell structures beyond the Fermi-surface, while in the light and intermediate nuclei, the rise in the pairing energies is due to the increase in the number of nucleons occupying the surface region. These neutron-neutron pairs formed beyond the Fermi-surface of nuclei of heavy elements have greater pairing energies, which contribute to greater binding energies associated with the heavy elements found in the neutron stars. It is concluded that the shell model can predict the existence of isotopes of heavy elements in the neutron stars and the criterion to ascertain their existence lies on the pairing energies. Calculations show that the isotopes with highest peaks among the heavy elements can predict the most abundant isotopes of the heavy elements in the neutron stars, for instance, 90Zr, 91Zr, 142Nd, 145Nd, 146Nd, 148Nd and 150Nd nuclei.