SDCS Quantum Mechanical Flux Formula Revisited for Electron-Hydrogen Ionization (Journal of Atomic and Molecular Sciences, 2013)
Through a simple, classical, energy conservation analysis, wepropose a finite distance reinterpretation of the standard energy fraction definition used for the single differential cross section (SDCS) for the electron-hydrogen $S$ waveionization process. The energy modification is due to the factthat, at finite distances from the nucleus, the continuumelectrons have to overcome the remaining potential energy to becompletely free. As a consequence, the flux formula for extracting- at finite distances - SDCSis also modified. Different from the usual observations, theproposed corrections yield finite and well behaved SDCS valuesalso at the asymmetrical situation where one of the continuumelectrons carries all the energy while the other has zero energy.Results of calculations performed at various impact energies, forboth singlet and triplet symmetry, are presented and comparedfavorably with benchmark theoretical data. Although we do not knowhow, we believe that finite distance effects should stronglyaffect the evaluation of the flux and consequently the SDCS, alsoin the full electron-hydrogen case.
Keywords: ionization; flux formula; differential cross section.