Classical adiabatic pertubation theory of atomic excitation

In the general classical theory of collisions of electrons and protons of charge ± e and velocity v with hydrogen atoms at rest, classical impulse and Monte Carlo methods apply to ionization and charge transfer. At the other extreme, for very weak excitations and intermediate incident particle energies, classical adiabatic perturbation theory is preferable. In this limit the differential cross section with respect to energy transfer Δ E is given. The theory on its own may be applied only to fairly highly excited quantum states. Regions of validity of the approximation and corresponding quantum cross sections are obtained.