SCATTERING-THEORY FOR FINITELY MANY SPHERE INTERACTIONS SUPPORTED BY CONCENTRIC SPHERES

We study stationary scattering theory for finitely many sphere interac tions formally given by the Hamiltonian H=-Delta+Sigma(j=1)(N) alpha(j ) delta(\x\-R-j) and its generalizations to the case of interactions o f the second type and interactions with nonseparated boundary conditio ns. In a previous publication [J. Math. Phys. 29, 660-664 (1988)], it was shown that the self-adjoint Hamiltonian H-{alpha l},H-{R} correspo nding to H may be defined as a limit in norm resolvent convergence of a family H-epsilon of local scaled short-range Hamiltonians. In this p aper we also study scattering theory corresponding to H-epsilon and sh ow that the scattering quantities associated with H-epsilon converge t o those of H-{alpha l},H-{R} as epsilon-->0. (C) 1997 American Institu te of Physics.