PERTURBATIVE BREAKING OF THE PSEUDOSPIN SYMMETRY IN THE RELATIVISTIC HARMONIC OSCILLATOR
2004
We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S=-V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.
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