Slide 14 of 48
Notes:
See Longair, HEA, 2nd Edition, Volume 1, p92-96
The full derivation of the cross-section presented by an electron to an incoming photon in the case of Thomson scattering is given in Longair.
For this course, you will only need to know that the cross-section, sigma_e, is given by the above expressions (r_e is the classical electron radius).