On-shell T-matrices in Multiple Scattering

TL;DR

This paper demonstrates that for multiple scattering potentials, if the overall transition operator is on-shell, then each individual potential's transition operator is also on-shell, using analytic continuation techniques.

Contribution

It provides a proof that on-shell property of the total transition operator implies the same for each individual transition operator in multiple scattering scenarios.

Findings

On-shell T implies on-shell t_j for each potential

Uses analytic continuation to establish the result

Applicable to potentials that are absolutely and square integrable

Abstract

The transition operator T for the scattering of a particle from N potentials V_j can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in < k|T(sigma^{2}+ i0)|k' >, |k|=|k'|=\sigma, then each t_j is also on-shell.