Direct determination of the fully differential cross section of the ionization by the wave function in the coordinate representation

TL;DR

This paper demonstrates that the fully differential cross section of ionization in proton-antiproton collisions with hydrogen can be directly derived from the wave function in coordinate space, linking wave function analysis to ionization dynamics.

Contribution

It introduces a method to directly express the differential cross section of ionization using the wave function in coordinate representation, bridging impact parameter and momentum transfer frameworks.

Findings

Wave function in coordinate space can be used to directly determine ionization cross sections.

The method aligns with traditional ionization amplitude approaches.

Visualizes electron flow and angular distribution over time.

Abstract

This paper is focused on showing that the fully differential cross section of ionization during a collision of a proton and an antiproton with a hydrogen atom is directly expressed by the wave function in the coordinate representation. Wave function is converted from impact parameter representation to momentum transfer representation. In this case, the calculated wave function corresponds at a certain projectile angle of scattering. The square representation of this wave function module shows how the angular distribution of ionized electrons varies over time. The ionized electron's flow is directly visible from the image. In addition, the direct differentiation of the fully differential ionization cross section by the wave function is shown to be consistent with the effective time determined by the ionization amplitude, which is the traditional method.