Pseudospin symmetry in single particle resonant states

TL;DR

This paper investigates the conditions under which pseudospin symmetry is conserved or broken in single particle resonant states within atomic nuclei, using relativistic quantum mechanics and potential models.

Contribution

It demonstrates that pseudospin symmetry in resonant states is conserved when scalar and vector potentials are equal in magnitude but opposite in sign, providing a detailed analysis with model potentials.

Findings

Pseudospin symmetry is conserved when scalar and vector potentials are equal and opposite.

The symmetry can be broken depending on the potential parameters.

Resonance behaviors are analyzed using Jost functions and phase shifts.

Abstract

The pseudospin symmetry is a relativistic dynamical symmetry connected with the small component of the Dirac spinor. The origin of pseudospin symmetry in single particle bound states in atomic nuclei has been revealed and studied extensively. By examining the zeros of Jost functions corresponding to the small components of Dirac wave functions and phase shifts of continuum states, we show that the pseudospin symmetry in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. The exact conservation and the breaking of pseudospin symmetry are illustrated for single particle resonances in spherical square-well and Woods-Saxon potentials.