Abstract
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 Pb 208 . 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.
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