Electron Collisions with Atoms and Ions — A Solved Problem?

Electron collisions with atoms and ions have been an essential part of Quantum Mechanics since its very beginning about a century ago. In principle, the description of these processes for any target and any collision energy "only" requires the solution of the (many-electron) Schrödinger equation, with possible further improvements through semi-relativistic or even full-relativistic formulations with the Breit-Pauli or Dirac-Breit hamiltonians. The boundary conditions are well known, and hence it appears as if little "new physics" is left to discover in this field.

(Un?)fortunately, the solution of the underlying equations is by no means trivial and remains a serious challenges. While some targets such as atomic hydrogen, hydrogen-like ions, and alkali-like configurations (if one is only interested in the outermost valence electron) and even light (quasi-)two-electron systems have become treatable to the extent that the accuracy of theoretical predictions in some cases even exceeds that of experiment (especially when absolute cross sections are required), there is no general recipe available that works in all cases. Special methods tend to be employed to treat low or high collision energies, only to find out that the cross sections often peak in the intermediate energy range. While elastic scattering from closed-shell targets such as the noble gases can be treated very well, this is by no means guaranteed when excitation or ionization processes are of interest and the closed shell is broken up, or one has to deal with a complex open-shell target (e.g., transitions metals) already from the start. Furthermore, resonances can be of utmost importance, and their accurate theoretical description requires a well-tuned balance of handling the N-electron target structure and the (N+1)-electron collision problems. Finally, the more detailed the information of interest is (e.g., angle-differential, spin-resolved), the more challenging the problem becomes.

In this talk, I will attempt to give an overview of the current state of the art in this field as an update to [1]. I will also mention where the data of interest to the plasma community might be found.