The Description of Spatial Characteristics of Elastic Processes in the Wigner Function Formalism

TL;DR

This paper applies the Wigner function formalism to elastic scattering, introducing a novel phase space choice and deriving an exact expression for the mean radius of particle production area.

Contribution

It presents a new phase space for the Wigner function in elastic scattering and derives an exact formula for the mean production area radius.

Findings

New phase space for Wigner function in scattering

Exact expression for mean production area radius

Enhanced understanding of spatial characteristics in elastic processes

Abstract

The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional space of canonically conjugate variables - the transverse momentum of scattered particle and the projection of the vector of the closest approach of particles in the plane which is perpendicular to the momentum of initial particle. The exact expression for the mean value of the scattered particles production area radius through a scattering amplitude has been obtained.