Three-body models of electron-hydrogen ionization

Abstract

Although the importance of electron-electron correlations in (e,2e) reactions has long been realized, untill recently only little theoretical progress had been made including these correlations. Theoretical studies using “three-body” models (models with explicit dependence on the electron-electron coordinate) are hampered by the difficult six-dimensional integral for the scattering amplitude. “Two-body” models, on the other hand, retain only electron-ion interactions and the standard techniques of partial-wave analysis greatly simplify the integral. In contrast, the wave functions used in three-body models give rise to two-center integrals, which are not efficiently evaluated using partial-wave methods. Therefore, a different method was sought for. We have found that direct six-dimensional numerical quadrature is efficient (about five minutes on a workstation to compute one scattering amplitude). As a result, we now have the capability of calculating (e,2e) triply-differential cross sections using three-body wave functions of arbitrary complexity. This allows for a severe test of three-body models. The utility of our method is demonstrated by using two recently reported analytical three-body wave functions in an (e,2e) calculation.