Use of the multiple-scattering expansion of the three-body amplitude f
or atomic direct and exchange reactions requires the evaluation of mul
tidimensional integrals involving the two-body Coulomb T-operator. We
present here numerical results for the first-order terms, both for the
attractive and repulsive case. Furthermore, easy-to-calculate approxi
mations are described which in their domain of validity (i) reproduce
the exact amplitudes to high accuracy, and (ii) also serve to derive i
nteresting theoretical results.