Steps for the Solution of Faddeev Integral Equations in Configuration Space

¹ Physics Department, University of Connecticut, Storrs, CT 06268 USA
² Institut fur Theoretische Physik II. Ruhr Universität Bochum, D-44780, Bochum, Germany

Abstract

Faddeev equations in configuration space for three-atom scattering processes that have previously b een formulated in integral form allowing for additive and nonadditive forces, are now examined in terms of their numerical prop erties for a “toy-model” case. The numerical implementation is based on a sp ectral decomp osition in terms of Chebyshev p olynomials. The potential for high accuracy of this method, of the order of 6 to 8 significant figures is one of the main motivations for the present investigation.The ob ject of the equations are T-functions, that are the product of wave functions times potentials, that decay to zero in all directions. The driving and coupling terms are based on the two-body t-matrices, which describe the two-body correlations in each arrangement. The preferred form for b oth the driving term and the integral kernel terms is of a hybrid nature, the x-dependence is expanded into Chebyshev p olynomials, and the y-dependence is given in terms of a Fourier series. The numerical prop erties of the driving term are examined in detail, and the integral kernel is left for a subsequent analysis.