On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V-j(x) 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(k(0)(2) +/- i0)\k'), = \k'\ = k(0), then each t(j) is also on-shell. (C) 1997 Elsevier Science B.V.