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., 2p 3/2 and 1f 5/2 states, are always degenerate. Furthermore, by examining the perturbation corrections to the single-particle energies, the perturbative
... [Show full abstract] nature of the proposed PSS limits is also discussed. © 2011 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.