One dimensional scattering of a two body interacting system by an infinite wall

TL;DR

This paper analyzes the quantum-mechanical scattering of a two-body system by an infinite wall, providing exact solutions for harmonic interactions and evaluating the validity of common approximations in such scattering processes.

Contribution

It offers an exact solution for the scattering of a two-body harmonic system by an infinite wall and assesses the accuracy of adiabatic and uncorrelated approximations.

Findings

Adiabatic approximation is inadequate for this scattering problem.

Uncorrelated scattering approximation is accurate at high energies.

Exact solutions help evaluate approximation validity.

Abstract

The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear systems. The scattering problem is solved exactly, for the case of a harmonic interaction between the fragments. The exact result is used to assess the validity of two different approximations to the scattering process. The adiabatic approximation, which considers that the relative co-ordinate is frozen during the scattering process, is found to be inadequate for this problem. The uncorrelated scattering approximation, which neglects the correlation between the fragments, gives results in accordance with the exact calculations when the scattering energy is high compared to the oscillator parameter.