Deficiency of Spin Orbit Interaction in Relativistic Mean Field Theory

The spin-orbit interaction, emerging naturally from the Relativistic Mean Field (RMF) theory is examined critically in the light of the recently measured excitation energy differences between the terminating states built on two different configurations for the nuclei belonging to the lower pf shell. The calculations are carried out using the cranked RMF framework. To further probe the iso vector dependence of the spin-orbit potential, the splitting between the $h_{11/2}$ and $g_{7/2}$ in the Sb-chain is compared to experiment. It is found that the calculation at the quantitative level do deviate considerably from the experiment. In particular the balance of iso-scalar and iso-vector strength of the spin-orbit interaction indicates that additional terms are needed to account for the experimental data