Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions

A three-body scattering process in the presence of Coulomb interaction can be decomposed formally into two-body single channel scattering, two-body multichannel scattering, and genuine three-body scattering. The corresponding integral equations are coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve these by applying the Coulomb-Sturmian separable expansion method. We present elastic scattering and reaction cross sections of the $e^{+}+H$ system both below and above the $H(n=2\mathrm{})\mathrm{}$ threshold. We find excellent agreements with previous calculations in most cases.