Transfer ionization and its sensitivity to the ground-state wave function

We present kinematically complete theoretical calculations and experiments for transfer ionization in H${}^{+}+$He collisions at 630 keV/u. Experiment and theory are compared on the most detailed level of fully differential cross sections in the momentum space. This allows us to unambiguously identify contributions from the shake-off and two-step-2 mechanisms of the reaction. It is shown that the simultaneous electron transfer and ionization is highly sensitive to the quality of a trial initial-state wave function.