Calculation of the two-body scattering T-matrix in Configuration Space

Three-body Faddeev calculations require as input two-body T-matrices. For atomic physics applications configuration space is preferable over momentum space, since the potentials are given in the former. A recently developed solution of the Lippmann-Schwinger integral equation for the one-variable scattering wave function in configuration space [1] has now been extended to obtain the two variable scattering T-matrix, as will be shown. The method is based on spectral expansions into Chebyshev Polynomials of two auxiliary functions in each radial partition, in terms of which the T-matrix is obtained. The result is an important ingredient for the solution of the Faddeev integral equations in configuration space [2]. \newline \newline [1] G. Rawitscher and I. Koltracht, Computing in. Sc. and Eng., 7, 58 (2005); \newline [2] W. Gl\"{o}ckle, and G. Rawitscher; ``Three-atom scattering via the Faddeev scheme in configuration space,'' submitted for publication, and physics/0512010 at arxiv.com;.