Origin of the spin-orbit splitting in nuclear Hartree-Fock calculations

Abstract

Hartree-Fock calculations have been carried out for 16O and 40Ca with the nucleon-nucleon potentials of Hamada-Johnston and Tabakin. The resulting spin-orbit splittings are strongly volume-dependent, being too large at the saturating radius and somewhat too small at the empirical radius. It is shown how a result from the first-order shell model theory for spherical, spin-saturated nuclei may be extended to HF theory; namely, that only a two-body spin-orbit term in the two-nucleon potential can give rise to a single-particle spin-orbit splitting. The contributions from the various first- and second-order terms in the reaction matrix elements of the Hamada-Johnston potential are isolated by use of the eigenstates of a HF Hamiltonian that has been suitably averaged to remove the spin dependence introduced by the spin-orbit term in the HJ potential. The splitting is seen to originate almost entirely in the 3P states of the long-range part of the spin-orbit term in the HJ potential, with a reduction of about 20 % due to the second-order discontinuity term in the reference spectrum method used for evaluating the odd-state reaction matrix elements.