Light–heavy quark-type linear potential models with spin- and pseudospin-symmetric states

Abstract

Possible spin- and pseudospin-symmetric states with positive energies of the Dirac equation with linear scalar and vector potentials are investigated. Two exact relativistic spin symmetries of linear quark-type potential models are shown to exist for positive energies. It is known that positive-energy states which still exist in the non-relativistic limit are always of the spin-symmetric type, like those described in the Schrödinger framework. However, if significant relativistic corrections to the Schrödinger theory are considered and also different possible signs of vector and scalar potentials, there exist two exact spin symmetries: a spin-symmetric energy spectrum that tends to the previously known spectrum obtained by the Schrödinger theory in the non-relativistic limit, and a pseudospin-symmetric energy spectrum that does not. The exact symmetries are perturbed by modifying the strengths of the relativistic linear vector and scalar potentials and introducing a tensor coupling. These perturbations may cancel each other.