Single differential cross sections for electron-hydrogen ionization: the quantum mechanical flux formula revisited

One way of extracting single differential cross sections (SDCS) for the electron-hydrogen ionization process is based on using the quantum mechanical flux operator evaluated at asymptotic distances. This procedure is formally correct; however, numerical evaluations are necessarily performed at finite distances. As a consequence, unphysical oscillations appear at very unequal energy sharing [1] and, for this reason, the flux formula was somehow discarded by the community. In this contribution we propose two corrections based on alternative ways of defining the energy fraction. The first one uses the components of the probability flux instead of the usual asymptotic kinematical (or geometrical) approximation. The second comes from a finite distance energy reinterpretation related to a simple, classical, energy conservation analysis. Results of calculations for the s-wave approximation of the e-H processes, performed at various impact energies and for both singlet and triplet symmetry, are presented. Once our flux formula corrections are applied, the unphysical behavior previously observed is removed, and our SDCS results compare favorably with benchmark theoretical data.\\[4pt] [1] M. Baertschy et al,~Phys. Rev. A, 60 (1999) R13.