Scattering theory for finitely many sphere interactions supported by concentric spheres

We study stationary scattering theory for finitely many sphere interactions formally given by the Hamiltonian H=-Δ+summation j=1Nαjδ(|x|-Rj) and its generalizations to the case of interactions of the second type and interactions with nonseparated boundary conditions. In a previous publication [J. Math. Phys. 29, 660 endash 664 (1988)], it was shown that the self-adjoint Hamiltonian H{αl},{R} corresponding to H may be defined as a limit in norm resolvent convergence of a family Hvar-epsilon of local scaled short-range Hamiltonians. In this paper we also study scattering theory corresponding to Hvar-epsilon and show that the scattering quantities associated with Hvar-epsilon converge to those of H{αl},{R} as var-epsilon →0. copyright 1997 American Institute of Physics