A time-dependent analysis of transfer ionization in one-dimensional kinematics

We analyze a transfer ionization (TI) reaction in the fast proton-helium collision H⁺ + He → H⁰ + He²⁺ + e^- by solving a time-dependent Schrödinger equation (TDSE) under the classical projectile motion approximation in one-dimensional kinematics. By comparing results of the TDSE and various perturbative Born series calculations, we conclude that the recent discrepancies of experimental and theoretical data may be attributed to deficiency of the Born models used by other authors. We demonstrate that the correct Born series for TI should include the momentum space overlap between the double ionization amplitude and the wave function of the transferred electron.