Second Order Processes
We have shown in Chap. 11 how one can describe the quantum interaction between the radiation field and material systems. We used an appropriate theoretical framework, known as quantum electrodynamics, to obtain, with an expansion at the lowest perturbative order, a number of results about the more elementary processes that occur in the interaction between radiation and atomic systems, namely the processes of absorption and emission (spontaneous and stimulated) of photons. Quantum electrodynamics has however a much wider scope. The purpose of this chapter is to deduce further consequences, obtained by extending the perturbation theory to the second order. These consequences affect the interaction of radiation with electrons, free or bound, either non-relativistic or relativistic. In particular, we will analyse the scattering processes of free non-relativistic electrons (Thomson scattering), of bound non-relativistic electrons (Rayleigh and Raman scattering) and of relativistic electrons (Compton effect). The study of this latter effect will lead us to obtain the properties of the cross section (equation of Klein-Nishina) and of the polarisation of the emitted radiation. We will also develop some considerations with respect to the exchange of energy between photons and relativistic electrons, which are the basis of the inverse Compton effect. The topics covered in this chapter are a valuable complement to the ones we already developed in Chap. 3 using exclusively classical (non-quantum) electrodynamics.