  Pseudospin symmetry in nuclei is investigated by solving the Dirac equation
with Woods-Saxon scalar and vector radial potentials. We relate the pseudospin
interaction with a pseudospin-orbit term in a Schroedinger-like equation for
the lower component of the Dirac spinor. We show that this term gives a large
contribution to the energy splittings of pseudospin partners, so that the near
pseudospin degeneracy arises from a significant cancellation among the
different terms in that equation. This is a manifestation of the dynamical
character of this symmetry in the nucleus. We analyze the isospin dependence of
the pseudospin symmetry in a nuclear isotope chain by including a
vector-isovector potential V_rho and a Coulomb potential and conclude that
V_rho gives the main contribution to the observed pseudospin isospin asymmetry.
