Time-dependent calculations of transfer ionization by fast proton-helium collision in one-dimensional kinematics

TL;DR

This paper investigates transfer ionization in fast proton-helium collisions using time-dependent Schrödinger equation calculations and compares them with Born series models, highlighting the importance of including momentum space overlap for accurate results.

Contribution

The study introduces a detailed time-dependent approach and refines the Born series model, addressing discrepancies between experimental data and theoretical predictions in transfer ionization.

Findings

TDSE calculations provide accurate transfer ionization descriptions.

Standard Born models lack the momentum space overlap component.

Including the overlap improves agreement with experimental data.

Abstract

We analyze a transfer ionization (TI) reaction in the fast proton-helium collision $\rm H^+ + He \to H^0 + He^{2+} + e^-$ by solving a time-dependent Schr\"odinger equation (TDSE) under the classical projectile motion approximation in one-dimensional kinematics. In addition, we construct various time independent analogues of our model using lowest order perturbation theory in the form of the Born series. By comparing various aspects of the TDSE and the 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.