N-BODY QUANTUM SCATTERING-THEORY IN 2 HILBERT-SPACES - N-BODY INTEGRAL-EQUATIONS

Scattering for a nonrelativistic system of N distinguishable and spinl ess particles interacting via short-range pair potentials is considere d. Half-on-shell integral equations (the CG equations) are proposed, t he solutions of which determine approximate scattering amplitudes that converge to the exact scattering amplitude. It is proved, under mild Holder integrability assumptions, that these apparently singular equat ions actually have a compact kernel for real energies and, consequentl y, a unique solution. The CG equations have a structure that is much s impler than the Yakubovskii equations and similar to that of coupled-r eaction-channel equations. The driving terms look like distorted-wave Born integrals and nonorthogonality integrals. However, there is no re striction to channels with only two asymptotic bound clusters and for all channels, no matter how many bound clusters, appropriate boundary conditions are exactly satisfied. This work completes the establishmen t of a rigorous mathematical link between the solutions of the half-on -shell CG equations and the on-shell transition operators defined in t ime-dependent multichannel scattering theory, and it provides for the first time a rigorous theoretical basis for practical calculations of scattering amplitudes for certain problems with N greater than or equa l to 4.