Nonadiabatic transitions and spectra induced by atomic collisions in the weak coupling limit. Uniform formula for superbarrier and sub-barrier transitions

A formula is derived for the transition probability or shape of the electron or photon spectrum arising on the motion of atoms in potentials without coupled states. The wave functions are asymptotic involving Bessel functions, and the interaction is exponential. The formula is a generalization of the various results for intersecting and parallel terms. The dynamics of the position of the transition region is considered as well as the dependence of the probability and shape of the spectrum on the impact parameter. The Landau method for calculating the integrals of rapidly oscillating functions is discussed