Green's function method for the spin and pseudospin symmetries in the single-particle resonant states

We investigate the spin and pseudospin symmetry in the single-particle resonant states by solving the Dirac equation containing aWoods-Saxon potential with Green's function method. Taking double-magic nucleus Pb-208 as an example, three spin doublets 3d, 2h, and 1j and three pseudospin doublets 3 (p) over tilde, 1 (i) over tilde, and 1 (j) over tilde are obtained for the single-neutron resonant states. By analyzing the energy splittings, we find that the threshold effect plays an important role in resonant pseudospin doubles. Besides, there is a reversed level structure of pseudospin doublets in the continuum. Differently, all the width splittings of either the spin doublets or the pseudospin doublets are systematically positive and the splittings are very small except 1 (j) over tilde doublet. Further studies show that the splittings of the energies and widths for the resonant (pseudo) spin doublets are independent. Besides, the similarity properties of the wave functions of the spin and pseudospin doublets still maintain well in resonant states.