Pseudospin symmetry and the relativistic harmonic oscillator

Abstract

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar [Formula Presented] and a vector [Formula Presented] quadratic potentials in the radial coordinate, as well as a tensor potential [Formula Presented] linear in [Formula Presented]. Setting either or both combinations [Formula Presented] and [Formula Presented] to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case [Formula Presented], for which pseudospin symmetry is exact. We also show that the case [Formula Presented] is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit. © 2004 The American Physical Society.