Semiclassical approach to the theory of atomic excitation processes associated with heavy-ion collisions

Abstract

Starting from a quantum-mechanical description of the total system consisting of an electron and two nuclei, the semiclassical equation for the transition amplitude between electronic adiabatic basis states is derived for the case of the Rutherford scattering. This method is then generalized to include the effect of nuclear elastic and inelastic collisions. The total transition amplitude for a reaction in which both the electron and nuclei are excited is expressed as products of three factors summed over the intermediate atomic states. Of these three factors, the first and the third are the semiclassical atomic transition amplitudes before and after the nuclear collision, respectively, and the second is the $S$-matrix element for the nuclear collision.