Pseudospin and spin symmetries in single particle resonant states in Pb isotopes

Abstract

Based on the newly developed RMF-CMR theory by combining relativistic mean field (RMF) with complex momentum representation (CMR), we have explored the single particle resonant states, and their pseudospin and spin symmetries for Pb isotopes. The available energies and widths decrease monotonously with the increasing mass number in accompany with clear shell structure including the appearance of magic number N=184. The extracted pseudospin and spin splittings become smaller for the neutron-richer nuclei. The extent of the splittings depends on the quantum numbers and position of the states lying in mean field. Good pseudospin and spin symmetries are expected in the neutron-rich nuclei and the states with lower orbital momentum and lying near the continuum threshold. Especially, it is found that both lower (upper) components of the every pseudospin (spin) doublet look similar for not only bound states but also resonant states, which confirms the presence of the pseudospin (spin) symmetry although the corresponding energy splitting is slightly large.