Single particle spectrum and spin-orbit splittings in relativistic mean field theory

The calculated single particle spectrum for odd mass systems using relativistic mean field (RMF) theory are analyzed. Assuming these states for nuclei having one particle (hole) in addition to the conventional doubly magic core, of pure single particle (hole) character, the spin-orbit splittings are calculated. The effect of time reversal breaking which exists for these odd A systems seems to cancel while taking the difference between the single particle energies. Therefore one can solve the RMF equations with time reversal invariance and obtain a reasonable estimate of the spin-orbit splittings. The RMF reproduces the spin-orbit splittings quite well. The agreement between the theory and the experiment is impressive in view of the fact that the RMF incorporates leftover correlations only phenomenologically through the choice of effective Lagrangian parameters rather than incorporating them explicitly.