Origin of the pseudospin symmetry in the relativistic formalism

Abstract

The grounds on which the nuclear pseudospin symmetry (PSS) is supposed to be based are analysed within the relativistic mean-field framework. A connection between the mechanisms responsible for the spin-orbit and pseudospin-orbit splittings is shown. The nature of the PSS is investigated through an extended Dirac equation which allows a generalization of the PSS breaking term. It is shown that the PSS breaking in real nuclei can be explained as a result of a non-perturbative transformation from non-physical solutions of the Dirac equation, which satisfy exactly the PSS, to the physical ones. The PSS breaking term produces important, though qualitatively similar, effects on both states of a pseudospin-orbit doublet. The similarity of these effects increases with the number of nodes of the small component of the Dirac spinor of these states.