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 S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r . Setting either or both combinations Σ=S+V and Δ=V-S 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 Σ=0 , for which pseudospin symmetry is exact. We also show that the case U=Δ=0 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.
- Publication:
-
Physical Review C
- Pub Date:
- February 2004
- DOI:
- 10.1103/PhysRevC.69.024319
- arXiv:
- arXiv:nucl-th/0310071
- Bibcode:
- 2004PhRvC..69b4319L
- Keywords:
-
- 21.10.Hw;
- 21.60.Cs;
- 03.65.Pm;
- Spin parity and isobaric spin;
- Shell model;
- Relativistic wave equations;
- Nuclear Theory
- E-Print:
- 18 pages, 24 figures, uses RevTeX4, subfigure and caption macros. Revised version according to referee's comments, with typos and some figures corrected