The relativistic spin-orbit force and its dependence on neutron excess
are studied using the sigma - omega - rho model. By working within th
e schematic model of asymmetric semi-infinite nuclear matter we are ab
le to isolate the spin-orbit potential and to investigate the followin
g aspects: (i) the influence of the spin-orbit force on nuclear surfac
e properties as a function of neutron excess, (ii) the local variation
of the spin-orbit strength at various asymmetries, and (iii) the depe
ndence of the spin-orbit force on the nucleonic isospin. Calculations
have been performed for the currently used parameter sets NL1 and NL-S
H up to the corresponding neutron-drip line. We conclude that with inc
reasing neutron excess the spin-orbit strength drastically decreases w
hile its impact on nuclear surface properties depends only slightly on
asymmetry. The isospin dependence of the relativistic spin-orbit forc
e is negligible.