  In the semiclassical approximation of Grassmann-valued electric charges for
regularizing Coulomb self-energies, we extract the unique
acceleration-independent interaction hidden in any Lienard-Wiechert solution
for the system of N positive-energy spinning particles plus the electromagnetic
field in the radiation gauge of the rest-frame instant form. With the help of a
semiclassical Foldy-Wouthuysen transformation, this allows us to find the
relativistic semiclassical Darwin potential. In the 2-body case the
quantization of the lowest order reproduces exactly the results from the
reduction of the Bethe-Salpeter equation.
