yWe present selected properties of solutions to the Dirac equation with the
Woods-Saxon type, in general deformed, mean-field potentials. A comparison
of the results obtained with the Dirac form of the equation given by the R
elativistic Mean Field (RMF) method, its usual Pauli-Schrodinger reduction
and a generalized form of the latter will be discussed. A possibility of ve
ry important improvements in the description of the single-nucleon properti
es, and this while using a realistic form and values of position-dependent
effective mass as suggested by the RMF method, is illustrated.