Stationary scattering theory for a charged particles transport problem

We consider a nonautonomous transport problem, the modelization of the char ge exchange dynamics in a monoatomic ionized gas, and apply scattering theo ry to its dynamics. The free dynamics corresponds to the evolution of the t otal distribution of particles (neutral plus ionized particles) and the per turbed dynamics corresponds to the evolution of the neutral particles, whic h is the solution of a nonautonomous transport problem. The existence of th e time-dependent wave operators was proved by the first author. In the pres ent paper we follow Howland's formalism in constructing a stationary scatte ring theory for this nonautonomous transport problem by studying the evolut ion equation. We prove the existence of the wave operators and by using the smooth perturbation technique we obtain the similarity between perturbed a nd unperturbed operators.