  The scattering of photons and heavy classical Coulomb interacting particles,
with realistic particle-photon interaction (without particle recoil) is studied
adopting the Koopman formulation for the particles. The model is translation
invariant and allows for a complete control of the Dollard strategy devised by
Kulish-Faddeev and Rohrlich (KFR) for QED: in the adiabatic formulation, the
M{\o}ller operators exist as strong limits and interpolate between the dynamics
and a non-free asymptotic dynamics, which is a unitary group; the $S$-matrix is
non-trivial and exhibits the factorization of all the infrared divergences. The
implications of the KFR strategy on the open questions of the LSZ asymptotic
limits in QED are derived in the field theory version of the model, with the
charged particles described by second quantized fields:
  i) asymptotic limits of the charged fields, $\Psi_{out/in}(x)$, are obtained
as strong limits of modified LSZ formulas, with corrections given by a Coulomb
phase operator and an exponential of the photon field;
  ii) free asymptotic electromagnetic fields, $B_{out/in}(x)$, are given by the
massless LSZ formula, as in Buchholz approach;
  iii) the asymptotic field algebras are a semidirect product of the canonical
algebras generated by $B_{out/in}$, $\Psi_{out/in}$;
  iv) on the asymptotic spaces, the Hamiltonian is the sum of the free
(commuting) Hamiltonians of $B_{out/in}$, $\Psi_{out/in}$ and the same holds
for the generators of the space translations.
