  We investigate spin- and velocity-dependent contributions to the
gravitational inter-particle potential. The methodology adopted here is based
on the expansion of the effective action in terms of form factors encoding
quantum corrections. Restricting ourselves to corrections up to the level of
the graviton propagator, we compute, in terms of general form factors, the
non-relativistic gravitational potential associated with the scattering of
spin-0 and -1/2 particles. We discuss comparative aspects concerning different
types of scattered particles and we also establish some comparisons with the
case of electromagnetic potentials. Moreover, we apply our results to explicit
examples of form factors based on non-perturbative approaches for quantum
gravity. Finally, the cancellation of Newtonian singularity is analysed in the
presence of terms beyond the monopole-monopole sector.
