Three-cluster states in reaction theory

Abstract

In recent work it was shown how a rigorous subsidiary minimum principle of the Rayleigh-Ritz type could be used as an aid in the construction of the closed-channel part of the scattering wave function, thereby making available a potentially powerful new tool in the variational approach to multiparticle scattering problems. The earlier discussion, which was restricted to scattering below the threshold for target breakup, is generalized here to the case where both two-body and three-body channels are open. The scattering problem is formally reduced to an equivalent three-body problem. Effective two-body and three-body potentials are defined explicitly (without the use of projection operators) and integral equations of the Faddeev type are derived. This analysis, which suggests a variety of cluster approximations, is used here as the basis for a decomposition of the wave function into an open-channel part, which contains the two-body and three-body outgoing scattered waves, and a decaying closed-channel part. The closed-channel part is shown to satisfy a minimum principle whose rigor can be maintained even when the target bound-state wave functions are imprecisely known. A calculational procedure which combines this minimum principle with the Kohn variational construction of the scattering amplitude is described.NUCLEAR REACTIONS Scattering theory. Effective three-body formulation. Derivation of extremum principle for the wave function.