The three-body problem with short-range interactions

The quantum mechanical three-body problem is studied for general short-rang e interactions. We work in coordinate space to facilitate accurate computat ions of weakly bound and spatially extended systems. Hyperspherical coordin ates are used in both the interpretation and as an integral part of the num erical method. Universal properties and model independence are discussed th roughout the report. We present an overview of the hyperspherical adiabatic Faddeev equations. The wave function is expanded on hyperspherical angular eigenfunctions which in turn are found numerically using the Faddeev equat ions. We generalize the formalism to any dimension of space d greater or eq ual to two. We present two numerical techniques for solving the Faddeev equ ations on the hypersphere, These techniques are effective for short and int ermediate/large distances including use for hard core repulsive potentials. We study the asymptotic limit of large hyperradius and derive the analytic behaviour of the angular eigenvalues and eigenfunctions. We discuss four a pplications of the general method. We first analyze the Efimov and Thomas e ffects for arbitrary angular momenta and for arbitrary dimensions d. Second we apply the method to extract the general behaviour of weakly bound three -body systems in two dimensions. Third we illustrate the method in three di mensions by structure computations of Borromean halo nuclei, the hypertrito n and helium molecules. Fourth we investigate in three dimensions three-bod y continuum properties of Borromean halo nuclei and recombination reactions of helium atoms as an example of direct relevance for the stability of Bos e-Einstein condensates. (C) 2001 Elsevier Science B.V. All rights reserved.