Soft-photon approximation for bound-state Compton scattering

The transition amplitude for the inelastic scattering of a photon from a system of bound charged particles, with a single charge ejected, behaves at low-energy end of the scattered-photon spectrum as the inverse of the energy and is proportional to the on-shell matrix element corresponding to the process in which the soft photon is absent. The next term in the expansion in powers of the energy of the soft photon is derived here, and is expressed...