  Generalizing Dollard's strategy, we investigate the structure of the
scattering theory associated to any large time reference dynamics $U_D(t)$
allowing for the existence of M{\o}ller operators. We show that (for each
scattering channel) $U_D(t)$ uniquely identifies, for $t \to \pm \infty$, {\em
asymptotic dynamics} $U_\pm(t)$; they are unitary {\em groups} acting on the
scattering spaces, satisfy the M{\o}ller interpolation formulas and are
interpolated by the $S$-matrix. In view of the application to field theory
models, we extend the result to the adiabatic procedure. In the Heisenberg
picture, asymptotic variables are obtained as LSZ-like limits of Heisenberg
variables; their time evolution is induced by $U_\pm(t)$, which replace the
usual free asymptotic dynamics. On the asymptotic states, (for each channel)
the Hamiltonian can by written in terms of the asymptotic variables as $H =
H_\pm (q_{out/in}, p_{out/in})$, $ H_\pm (q,p) $ the generator of the
asymptotic dynamics. As an application, we obtain the asymptotic fields
$\psi_{out/in}$ in repulsive Coulomb scattering by an LSZ modified formula; in
this case, $U_\pm(t)= U_0(t)$, so that $\psi_{out/in}$ are \emph{free}
canonical fields and $H = H_0(\psi_{out/in})$.
