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

Based on the relativistic continuum Hartree-Bogoliubov theory, the pseudospin 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 pseudospin approximation is shown to be connected to the competition between the pseudocentrifugal barrier and the pseudospin 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 pseudospin symmetry is exact. The pseudospin symmetry is found to be a good approximation for normal nuclei and to become much better for exotic nuclei with a highly diffuse potential, which have $dV/dr\ensuremath{\sim}0.$ The energy splitting of the pseudospin 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 pseudospin partners are very similar and almost equal in magnitude.