The three-body Coulomb scattering problem in a discrete Hilbert-space basis representation

We propose modified Faddeev–Merkuriev integral equations for solving the $2\to2,3$ quantum three-body Coulomb scattering problem. We show that the solution of these equations can be obtained using a discrete Hilbert-space basis and that the error in the scattering amplitudes due to truncating the basis can be made arbitrarily small. The Coulomb Green's function is also confined to the two-body sector of the three-body configuration space by this truncation and can be constructed in the leading order using convolution integrals of two-body Green's functions. To evaluate the convolution integral, we propose an integration contour that is applicable for all energies including bound-state energies and scattering energies below and above the three-body breakup threshold.