On the Scattering Length Spectrum for Real Analytic Obstacles

It follows trivially from old results of Majda and Lax–Phillips that connected obstacles K with real analytic boundary in Rn are uniquely determined by their scattering length spectrum. In this paper we prove a similar result in the general case (i.e. K may be disconnected) imposing some non-degeneracy conditions on K and assuming that its trapping set does not topologically divide S*(C), where C is a sphere containing K. It is shown that the conditions imposed on K are fulfilled, for instance, when K is a finite disjoint union of strictly convex bodies.