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Harmonic oscillator and nuclear pseudospin

Authors: Ronai Lisboa, Manuel Malheiro, Antonio S. de Castro, Pedro Alberto, Manuel Fiolhais

Ref.: AIP Conference Proceedings 739, 569-571 (2004)

Abstract: A generalized relativistic harmonic oscillator for spin 1=2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either S =S+V or D =V -S to zero, analytical solutions for bound states are found. The eingenenergies and their nonrelativistic limits are presented and particular cases are discussed, especially the case S = 0, for which pseudospin symmetry is exact.