Spin–orbit splitting of protons and neutrons

Abstract

Within the framework of Yukawa-plus-exponential macroscopic model, the binding energies of magic nuclei and nuclei which are adjacent to them, are calculated using volume energy coefficient $a_V$ and surface energy coefficient $a_S$ as fitting parameters. Single-particle energies (SPE) are deduced for both protons and neutrons using binding energies of the core and core ± nucleon. Spin–orbit splitting of protons and neutrons are computed from the single-particle energies of protons and neutrons and compared with other literature values. SPEs calculated for the nuclei show gap for the usual proton and neutron magic numbers and new magic numbers $Z, N = 14$ and 16. In superheavy region, a gap is noted in SPE for the proton numbers 92, 114 and neutron numbers 164 and 184. Further, the reduced spin–orbit splitting of protons and neutrons are found to possess a linear dependence on $A^{-2/3}$ and directly proportional to ($\ell +1/2$).