Spin-orbit splitting for single-particle and single-hole energies: Interplay of relativity and core polarization

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Abstract
The effects of core polarization on the single-particle energies and single-hole energies relative to a closed major shell core are considered. Not only the familiar two-particle–one-hole and three-particle– two-hole diagrams but also Hartree-Fock insertions are included. We further consider the effects of the Dirac spinor approach for nucleons inside the nucleus with a Dirac effective mass less than the bare mass and also for nucleons at the surface with an effective mass essentially equal to the bare mass. This relativistic effect tends to reduce the spin-orbit splitting of particle states as compared to that for hole states, which corresponds to the empirical data. The calculations are performed employing modern versions of the Bonn one-boson-exchange potentials with various strengths for the tensor component.