Pseudospin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line

TLDR: In this paper, the pseudo-spin orbital potential (PSOP) was investigated in Zr and Sn isotopes from the proton drip line to the neutron drip line, and the PSOP depends on the derivative of the difference between the scalar and vector potentials dV/dr.

Abstract: Based on the Relativistic continuum Hartree-Bogoliubov (RCHB) theory, the pseudo-spin approximation in exotic nuclei is investigated in Zr and Sn isotopes from the proton drip line to the neutron drip line. The quality of the pseudo-spin approximation is shown to be connected with the competition between the centrifugal barrier (CB) and the pseudo-spin orbital potential ( PSOP ). The PSOP depends on the derivative of the difference between the scalar and vector potentials dV/dr. If dV/dr = 0, the pseudo-spin symmetry is exact. The pseudo-spin symmetry is found to be a good approximation for normal nuclei and to become much better for exotic nuclei with highly diffuse potential, which have dV/dr ∼ 0. The energy splitting of the pseudo-spin partners is smaller for orbitals near the Fermi surface ( even in the continuum ) than the deeply bound orbitals. The lower components of the Dirac wave functions for the pseudo-spin partners are very similar and almost equal in