On asymptotic power corrections to differential fluxes and generalization of optical theorem for potential scattering

TL;DR

This paper derives the asymptotic behavior of differential fluxes in potential scattering at finite distances and generalizes the optical theorem to finite R, expanding the applicability of scattering relations.

Contribution

It provides exact asymptotic formulas for outgoing differential flux at finite distances and extends the optical theorem to finite R in potential scattering.

Findings

Asymptotic dependence on finite R established for differential flux.

Integration over solid angle removes R dependence for total flux.

Optical theorem generalized to finite R.

Abstract

In a wide class of potentials the exact asymptotic dependence on finite distance R from scattering center is established for outgoing differential flux. It is shown how this dependence is eliminated by integration over solid angle for total flux, unitarity relation, and optical theorem. Thus, their applicability domain extends naturally to the finite R.