Compton Scattering

[sanctus]

I always thought I had quite well understood the compton scattering but today at university I heard that this scattering is possible only if the photon and the electron have opposite spin directions (or the same, don't remember). As it was a prof saying it I guess it must be right. But why is there a condition on the spins?

[Qfwfq]

I think it's an exageration to say "onlf if" but the cross section certainly depends on the spin states. I vaguely remember the exercise of working out the Feynman diagram in Dirac algebra, the result has a lot of those gamma matrices in it...