Single-particle resonances in a deformed Dirac equation

Abstract

Single-particle bound and resonant states are obtained by solving the Dirac equation with quadrupole-deformed Woods-Saxon potential in coordinate space with the coupled-channel approach. Taking the ${m}^{\ensuremath{\pi}}=1/{2}^{+}$ resonant states at deformation $\ensuremath{\beta}=0.1$ as examples, the roles of their spherical components have been investigated based on the behaviors of the eigenphases and the corresponding probabilities weighted by the scalar spherical potential. It is shown that the realization of the ${m}^{\ensuremath{\pi}}=1/{2}^{+}$ resonances is supported mainly by the $l\ensuremath{\ne}0$ components, and the mixture of the ${s}_{1/2}$ component can lead to the disappearance of some resonances at finite energy. The dominance of the $l\ensuremath{\ne}0$ component (${d}_{3/2}$) in the small-energy region guarantees the continuation of a certain resonance to the corresponding bound state.