Perturbative interpretation of relativistic symmetries in nuclei

Abstract

Perturbation theory is used systematically to investigate the symmetries of the Dirac Hamiltonian and their breaking in atomic nuclei. Using the perturbation corrections to the single-particle energies and wave functions, the link between the single-particle states in realistic nuclei and their counterparts in the symmetry limits is discussed. It is shown that the limit of $S\ensuremath{-}V=\text{const}$ and relativistic harmonic oscillator (RHO) potentials can be connected to the actual Dirac Hamiltonian by the perturbation method, while the limit of $S+V=\text{const}$ cannot, where $S$ and $V$ are the scalar and vector potentials, respectively. This indicates that the realistic system can be treated as a perturbation of spin-symmetric Hamiltonians, and the energy splitting of the pseudospin doublets can be regarded as a result of small perturbation around the Hamiltonian with RHO potentials, where the pseudospin doublets are quasidegenerate.