  We analyze the spin-orbit coupling term in the nuclear energy density
functional in terms of a zero-range NN-contact interaction and finite-range
contributions from two-pion exchange. We show that the strength of the
spin-orbit contact interaction as extracted from high-precision nucleon-nucleon
potentials is in perfect agreement with that of phenomenological Skyrme forces
employed in non-relativistic nuclear structure calculations. Additional
long-range contributions from chiral two-pion exchange turn out to be
relatively small. These explicitly density-dependent contributions reduce the
ratio of the isovector to the isoscalar spin-orbit strength significantly below
the Skyrme value 1/3. We perform a similar analysis for the strength function
of the $(\vec \nabla \rho)^2$-term and find values not far from those of
phenomenological Skyrme parameterizations.
