Invariant Time-Dependent Exchange Perturbation Theory and its Application to the Particles Collision Problem

TL;DR

This paper develops a comprehensive time-dependent exchange perturbation theory that accounts for electron rearrangements in collision processes and applies it to proton-Lithium scattering to compute cross-sections.

Contribution

It introduces a novel formalism of invariant time-dependent exchange perturbation theory that includes electron rearrangements and demonstrates its application to particle collision problems.

Findings

Derived expressions for scattering S-matrix and T-matrix.

Calculated differential and total cross-sections for proton-Lithium collisions.

Validated the theory with specific collision examples.

Abstract

We present the formalism of Time-dependent Exchange Perturbation Theory (TDEPT) built to all orders of perturbation, for the arbitrary time dependency of perturbation. The theory takes into account the rearrangement of electrons among centres. We show how the formalism can be reduced to the standard form of invariant perturbation theory by 'switching off' the re-arrangement of electrons among centres. The elements of the scattering S-matrix and transitions T-matrix and the formula for the electron scattering differential cross section are derived. The application of the theory to scattering and collision problems is discussed. As an example, we apply the theory to proton scattering on a Lithium atom, calculating the differential and total cross-sections.