THREE-AND FOUR-BODY EQUATIONS WITH HALF-OFF-SHELL INPUT

Abstract

Publisher Summary This chapter focuses on three- and four-body equations with half-offs-shell input. The Faddeev reformulation of the three-body Schrodinger equation amounts to converting this equation into a set of multiple-scattering equations in which the basic (pair) interaction is represented by full subsystem transition amplitudes. In general, these amplitudes have to describe a two-body scattering in the presence of a third particle. Therefore, they necessarily enter the Faddeev equations off-the-energy-shell, in the conventional formulation even completely-off-shell. The Faddeev equations can naturally be converted to a form where only half-off-shell two-body transition amplitudes (and vertex functions) appear. The four-body Faddeev–Yakubovski (FY) equations can also be turned into a set of equations that only require half-off-shell input. The chapter highlights pair interactions without two-body bound states but with one three-body bound state in each channel or of the type. The chapter demonstrates converting the four-body Faddeev–Yakubovski equations into a set of equations that only require half-off-shell two-and three-body inputs.