Interpreting scattering wave functions in the presence of energy-dependent interactions

TL;DR

This paper investigates how energy-dependent interactions modify the interpretation of scattering wave functions, deriving a correction factor to accurately describe emission enhancements in final-state interactions, with examples including relativistic vector interactions.

Contribution

It derives a modified equivalence relation for squared wave functions in the presence of energy-dependent potentials, clarifying their interpretation in scattering theory.

Findings

The standard relation is altered by an additional factor for energy-dependent potentials.

The correction factor is derived explicitly for relativistic vector interactions.

Examples with Coulomb interactions illustrate the modified interpretation.

Abstract

In scattering theory, the squared relative wave function $|\phi({\bf q},{\bf r})|^2$ is often interpreted as a weight, due to final-state interactions, describing the probability enhancement for emission with asymptotic relative momentum $q$. An equivalence relation also links the integral of the squared wave function over all coordinate space to the density of states. This relation, which plays an important role in understanding two-particle correlation phenomenology, is altered for the case where the potential is energy dependent, as is assumed in various forms of reaction theory. Here, the modification to the equivalence relation is derived, and it is shown that the squared wave function should be augmented by a additional factor if it is to represent the emission enhancement for final-state interactions. Examples with relativistic vector interactions, e.g., the Coulomb interaction, are presented.