Asymptotic Electromagnetic Fields in Non-relativistic QED: the Problem   of Existence Revisited
  This paper is devoted to the scattering of photons at electrons in models of non-relativistic quantum mechanical particles coupled minimally to the soft modes of the quantized electromagnetic field. We prove existence of scattering states involving an arbitrary number of asymptotic photons of arbitrarily high energy. Previously, upper bounds on the photon energies seemed necessary in the case of $n>1$ asymptotic photons and non-confined, non-relativistic charged particles. 
Marcel Griesemer, Heribert Zenk