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Recent progresses on the pseudospin symmetry in single particle resonant states

The pseudospin symmetry (PSS) is a relativistic dynamical symmetry directly connected with the small component of the nucleon Dirac wave function. Much effort has been made to study this symmetry in bound states. Recently, a rigorous justification of the PSS in single particle resonant states was achieved by examining the asymptotic behaviors of the radial Dirac wave functions: The PSS in single particle resonant states in nuclei is conserved exactly when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. Several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances were investigated by employing spherical square well potentials in which the PSS breaking part can be well isolated in the Jost function. A threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners were found when the depth of the square well potential varies from zero to a finite value.