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 i fs/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. (authors)