Interaction Hamiltonian

The Hamiltonian, describing the electron-photon interaction in a scattering process, is composed, in the weak relativistic limit, of four terms⁶. Neglecting resonance phenomena close to X-ray absorption thresholds and the much weaker magnetic couplings, only the term arising from the Thomson interaction Hamiltonian has to be retained:

where r_o = e²/m_ec² is the classical electron radius, and A(r_j,t) is the electromagnetic field vector potential in the r_j, coordinate of the j^th electron. The sum extends over all the electrons in the system.

6. W. Schülke, “Inelastic scattering by electronic excitations”, in “Handbook on Synchrotron Radiation”, Vol. 3, ed. G. Brown and D.E. Moncton, Elsevier Science Publ., (1991).