On the cross sections for electron transfer, ejection and excitation in coincidence with a hole in a specific shell

Abstract

A singles (or doubles) measurement of, say, direct ionization has contributions from all events in which one (or two) electrons are ejected, including events in which additional electrons are excited, ejected, or captured. In such inclusive measurements the contributions from events in which more than the minimum required number of electrons are active can become quite significant for reactions induced by multiply charged ions. The sum of the projectile-ion induced “singles” cross sections for direct ionization, electron transfer, and excitation equals that for vacancy production in the target. We show, however, that the analogous sum of “doubles” cross sections for these processes in coincidence with a hole in a particular shell of the target (i.e. with an Auger electron or X-ray) is greater than the “singles” cross section for production of a vacancy in that shell, except in the limit of very weak interactions (exclusively single-electron transitions). The derivation is given in the independent Fermi particle representation, but the result appears to be general. Singles cross sections can be expressed entirely by terms in which only single electron transitions explicitly appear. Doubles (2-fold coincidence) cross sections require also “DET” terms in which double electron transitions appear. The DET terms are responsible for the excess in the coincidence sum mentioned above. Illustrative calculations for He2+ and C6+ on Ne show the quantitative importance of the DET terms for direct ionization as well as electron transfer. No direct ionization-hole coincidence experiment has been done yet, to our knowledge; it would provide a valuable test of the theory.