Pseudospin symmetry and the relativistic harmonic oscillator
By R. Lisboa, M. Malheiro, A. Castro, P. Alberto, M. Fiolhais. 2003
206 citations recorded by the source corpus.
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 $\ensuremath{\Sigma}=S+V$ and $\ensuremath{\Delta}=V\ensuremath{-}S$ 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 $\ensuremath{\Sigma}=0$, for which pseudospin symmetry is exact. We also show that the case $U=\ensuremath{\Delta}=0$ 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.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/da31744c68342448bf14bf88a50e26ddfd329417
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In Atomic and Molecular Physics, and Optics
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Hidden pseudospin and spin symmetries and their origins in atomic nuclei (2014, methodology): “rent examples for illustrating the tensor effects on the pseudospin symmetry. The first example is the relativistic harmonic oscillator with a linear tensor potential, which admits analytical solutions [89]. Self-consistently, theω-N tensor coupling is one of the widely used ways to include the tensor”