A one dimensional model for ionization induced by scattering with a heavy particle.

The ionization probability for a one-dimensional model atom perturbed by a moving repulsive scatterer is considered. The moving scattering centre is meant to mimic a second quantum particle crossing the region where a much lighter particle is initially bound in the atom. We compute the first three terms (of order t^3/2, t^2, t^5/2 respectively) in the expansion for small times of the ionization probability and we deduce that the first term showing explicit dependence on the velocity of the scatterer is of order t^5/2. A possible application of the model for the description of a quantum particle in a cloud chamber is also outlined.