  An emissivity formula is derived using the generalised
Fermi-Weizacker-Williams method of virtual photons which accounts for the
recoil the charged particle experiences as it emits radiation. It is found that
through this derivation the formula obtained by Sokolov et al using QED
perturbation theory is recovered. The corrected emissivity formula is applied
to nonlinear Thomson scattering scenarios in the transition from the classical
to the quantum regime, for small values of the nonlinear quantum parameter
\chi. Good agreement is found between this method and a QED probabilistic
approach for scenarios where both are valid. In addition, signatures of the
quantum corrections are identified and explored.
