On the reduction of momentum space scattering equations to Fredholm form

In a momentum representation the close-coupling equations for atomic and molecular scattering problems are coupled singular integral equations. Various methods for removing the singularities from the corresponding Lippmann-Schwinger equations in nuclear physics have been proposed by Sloan (1965), Haftel and Tabakin (1970), Kowalski (1965) and Noyes (1968), and by Partovi (1965). Some of these techniques have not previously been tested for solving atomic scattering calculations. Differences between the methods are studied numerically by considering positron scattering by hydrogen atoms.