Multichannel Scattering Problem with Non-trivial Asymptotic Non-adiabatic Coupling

TL;DR

This paper investigates multichannel scattering with non-trivial asymptotic non-adiabatic couplings, deriving solutions that align with re-projection methods to address electron translation issues in quantum scattering.

Contribution

It introduces asymptotic solutions for multichannel scattering with non-trivial couplings, connecting them to existing re-projection approaches for improved accuracy.

Findings

Asymptotic solutions match re-projection approach at first order.

Non-trivial asymptotic behavior affects scattering solutions.

Provides a framework for handling non-adiabatic couplings asymptotically.

Abstract

The multichannel scattering problem in an adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-trivial constant asymptotic behavior at large internuclear separations. The asymptotic solutions at large internuclear distances are constructed. It is shown that these solutions up to the first order of perturbation theory are identical to the asymptotic solutions of the re-projection approach, which was proposed earlier as a remedy for the electron translation problem in the context of the Born-Oppenheimer treatment.