Perturbative pseudospin symmetry limit with linear spin-orbit potential

The pseudospin symmetry(PSS) limits which conserve substantial spin-orbit splitting are investigated.It is found that while the strength of the spin-orbit potential as well as the spin-orbit splitting increase,the pseudospin doublets,e.g.,2p3/2 and 1f5/2 states,are always degenerate.Furthermore,by examining the perturbation corrections to the single-particle energies,the perturbative nature of the proposed PSS limits is also discussed.