Pseudospin symmetry as an accidental symmetry in the relativistic framework

We analyse the arguments used in the relativistic context to base the quasi-degeneracy of pseudospin doublets (PSDs) observed in atomic nuclei on the smallness of the single-particle central potential (Sigma(S) + Sigma(0)), discussing, especially, the implications of the results obtained in the limit Sigma(S) + Sigma(0) = 0. We study also the transition from a relativistic model, where Sigma(S) + Sigma(0) is a harmonic-oscillator potential and exhibits degenerate PSDs, to a more realistic one with broken pseudospin symmetry. We examine, in particular, the effect of the corresponding pseudospin symmetry-breaking term on the Dirac spinors of the PSDs. An extension of the Nilsson model to the relativistic case is also considered.