  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.
