Bare and dressed particles in collision theory

TL;DR

This paper introduces the novel application of the bare-dressed particle technique to classical and quantum collision theory, providing a unified formalism for elastic and inelastic collisions in the non-relativistic regime.

Contribution

It is the first to apply the bare-dressed approach to collision theory, simplifying kinematic calculations and extending to inelastic processes with a matrix transformation formalism.

Findings

Unified formalism for elastic and inelastic collisions

Simplified kinematic results via matrix transformation

Application to both classical and quantum collision regimes

Abstract

The bare-dressed technique is, for the first time, used in collision theory. The approach is valid for classical as well for quantum binary elastic collisions in the non relativistic regime. The same formalism can be used for inelastic collisions, when the particles undergo only a change of their internal quantum states during the collision process. All kinematic results can be obtained by a simple matrix transformation. Moreover, to make also simple and clear the results, for the inelastic collisions, the restitution coefficient formulation of inelastic processes has been used.