Pseudospin symmetry in the relativistic harmonic oscillator

Pseudospin symmetry in the relativistic harmonic oscillator is investigated systemically by solving the Dirac equation with vector and scalar potentials quadratic, and found to be a good approximation in realistic nuclei such as Pb208. The pseudospin breaking is shown in correlation with nuclear mean-field shaped by the harmonic oscillator frequency and the distance of well-bottom deviation from the center, which play a important role in the splittings of energy and wavefunction, especially for the doublets with fewer nodes and lower angular momentum. The energy-level crossings are found for all the pseudospin partners