On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials Vj(x) can be expanded into a series featuring the transition operators tj associated with the individual potentials. For Vj(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 (σ2 ± i0)|k′ >, |k| = |k′| = σ, then each tj is also on-shell. (Phys. Lett. A 235, 195-199 (1997)) ∗electronic-mail: [email protected] †electronic-mail: [email protected] 1