The advanced adiabatic approach and inelastic transitions via hidden crossings

Abstract

The advanced adiabatic approach describes all inelastic processes including ionization. It is based on the time–energy Fourier transform to obtain the asymptotic solution of the non-stationary Schrödinger equation. This transformation takes into account the time delay of the outgoing wave packet related to the ionization channel which is causally connected to the Hamiltonian at the moment of ionization. Another important aspect of the adiabatic approach is the discovery of hidden crossings in 1981. They arise whenever, in the classical description of the adiabatic state, the full-dimensional classical trajectory of the electron collapses into an unstable periodic orbit. As a result, a strong coupling between adiabatic states appears. The hidden crossings provide a complete description of non-adiabatic transitions and open the way to systematic applications. The advanced adiabatic approach together with the hidden crossings can compete with direct numerical calculations in respect to precision and, particularly, in respect to the required computer facilities. But what is much more important, it also provides clear insight into the mechanisms responsible for the processes studied. The application of the theory to various inelastic processes in atomic and molecular physics, such as charge transfer in He2+ + H(1s) collision, ionization of H(1s) by an electric pulse, transitions between rotational states of the H2O molecule induced by an electric pulse etc, are discussed.