One-dimensional Migdal effect

Abstract The problem of atomic ionization by the sudden absorption of momentum by its nucleus is studied. By means of a simple one dimensional model we obtain analytical expressions for the re-capture and ionization probabilities. Simple integral formulas for the evaluation of the time evolution of the electronic state are given. Analytical expressions for the ionization probabilities show structures found in realistic three dimensional collisional problems, such as capture probability (by the recoil nucleus) and the binary ionization peak.