Exact Solution of the Schrodinger and Faddeev Equations for Few Body Systems

E. N. Maslen, Paul C Abbott, J E Gottschalk +1 more

ALI AKBAR RAJABI

Hiroshi Isozaki

Nir Barnea, M. Viviani

Cluster expansion of the many-body Schr\"odinger wave function is manifested through the projected Faddeev-Yakubovsky equations. It is shown that using these equations one can formulate a systematic expansion for the wave function of finite systems in a translational invariant manner. The solution of the N-body problem at a given order becomes equivalent to solving the few-body Faddeev-Yakubovsky equations. The first two orders in this expansion are given explicitly and then solved for the case of N bosons interacting through the nucleon-nucleon Afnan-Tang S3 and Malfliet-Tjon MT-V potentials.

A. P. Machil'skii

Leonard Rosenberg

Integral equations of the Watson-Faddeev type, developed in the context of few-body nonrelativistic scattering theory, are shown to play an important role in the structure analysis of many-body Green's functions and in variational techniques for the approximate determination of these Green's functions. Such equations sum up an infinite chain of few-body correlations. Those correlations which are not of this form, i.e., the intrinsic many-body correlations, are accounted for by the appearance of an effective (or "renormalized") interaction, as can be seen by direct transformation of the exact Martin-Schwinger equations for the Green's functions. For a given choice of effective interaction, the few-body correlation functions must be determined self-consistently. The Schwinger variational principle, originally developed for linear integral equations, is nevertheless the key element in a variational formulation of the nonlinear equations encountered here. For simplicity we confine our attention to equations which determine the two-body Green's function, although the entire procedure can be generalized to higher orders.