Examination of the pseudospin symmetry for the relativistic harmonic oscillator with the similarity renormalization group

Abstract

The similarity renormalization group is used to explore the origin and breaking mechanism of the pseudospin symmetry for the relativistic harmonic oscillator. The calculated energies from the diagonal Dirac operator ${H}_{P}$ are shown to be in agreement with the exact results. In comparison with the contribution of every term to the pseudospin splitting, the quality of the pseudospin symmetry is revealed from the competition of the dynamical effect and the spin-orbit interaction. The shape of the potentials also has an important influence on the pseudospin symmetry. The dependence of the pseudospin symmetry on the shape of $\ensuremath{\Sigma}(r)$ is dominated by the nonrelativistic term, while that of $\ensuremath{\Delta}(r)$ is governed by the dynamical term and the spin-orbit interaction.