Scatter from an Electron

In 1906 J. J. Thompson showed that the scattered amplitude, y, from the interaction of unpolarized radiation of amplitude A and wavelength l with a free classical electron of charge e and mass m viewed at a distance R (R>>l) from the electron is

Here c is the velocity of light and the term in brackets arises from a loss in amplitude due to the partial polarization of the scattered beam.  Though we are interested in amplitude, note that the scattered intensity would be represented by the square of this quantity, thus giving rise to the well recognized  1/R2 relationship between intensity and distance.

This relation shows that for a point electron there is no change in scattered amplitude (other than the polarization term) for changes in either wavelength or observation angle (q).