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Pseudospin symmetry in nuclei is investigated by solving the Dirac equationwith Woods-Saxon scalar and vector radial potentials. We relate the pseudospininteraction with a pseudospin-orbit term in a Schroedinger-like equation forthe lower component of the Dirac spinor. We show that this term gives a largecontribution to the energy splittings of pseudospin partners, so that the nearpseudospin degeneracy arises from a significant cancellation among thedifferent terms in that equation. This is a manifestation of the dynamicalcharacter of this symmetry in the nucleus. We analyze the isospin dependence ofthe pseudospin symmetry in a nuclear isotope chain by including avector-isovector potential V_rho and a Coulomb potential and conclude thatV_rho gives the main contribution to the observed pseudospin isospin asymmetry.Comment: 4 pages, 2 figures, uses World Scientific style file. Contribution  presented at the VIII International Workshop on Hadron Physics, Bento  Goncalves, RS, Brazil, April 14-19, 2002. To be published by World Scientific  in the proceedings of the "International Workshop on Hadron Physics 2002

DYNAMICAL NATURE OF THE NUCLEAR PSEUDOSPIN AND ITS ISOSPIN ASYMMETRY