Green’s functions and the adiabatic hyperspherical method

Abstract

We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green's function in $d$ dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of three particles with $s$-wave zero-range interactions. Identical particle symmetry is incorporated in a general and intuitive way. Complete semianalytic expressions for the nonadiabatic channel couplings are derived. Finally, a model to describe the atom loss due to three-body recombination for a three-component Fermi gas of $^{6}\mathrm{Li}$ atoms is presented.