Semiclassical S-matrix theory for atomic fragmentation

Abstract

A semiclassical scattering approach is developed which can handle long-range (Coulomb) forces without the knowledge of the asymptotic wave function for multiple charged fragments in the continuum. The classical cross section for potential and inelastic scattering including fragmentation (ionization) is derived from first principles in a form which allows for a simple extension to semiclassical scattering amplitudes as a sum over classical orbits and their associated actions. The object of primary importance is the classical deflection function which can show regular and chaotic behavior. Applications to electron impact ionization of hydrogen and electron–atom scattering in general are discussed in a reduced phase space, motivated by partial fixed points of the respective scattering systems. Special emphasis, also in connection with chaotic scattering, is put on threshold ionization. Finally, motivated by the reflection principle for molecules, a semiclassical hybrid approach is introduced for photoabsorption cross sections of atoms where the time-dependent propagator is approximated semiclassically in a short-time limit with the Baker–Hausdorff formula. Applications to one- and two-electron atoms are followed by a presentation of double photoionization of helium, treated in combination with the semiclassical S-matrix for scattering.