Disappearance of the spin-orbit splitting between single particle states near threshold

Abstract

A mechanism of the disappearance or the reduction of the spin-orbit splitting for the single particle state near a core+N threshold is given. The single particle resonance energies and widths for a schematic potential are calculated by using the Complex Scaling Method (CSM). Furthermore, we calculate the complex expectation values of a spin-orbit potential by using a recently developed new method of the CSM. We choose the strength of the central potential and the spin-orbit potential as that the resonance energy E_r of a p_<3/2> state is near the core+N threshold energy. The situation often occurs in the loosely bound (unbound) systems such as unstable nuclei and hyper nuclei. We show that the calculated expectation value of the spin-orbit potential energy for p<1/2> states is small even in the case of very strong spin-orbit potential.