Systematic Iterative Approach to the Problem of Scattering on Singular Potentials

A systematic iterative approach for the evaluation of the partial-wave scattering amplitude, which is convergent both for regular and for singular potentials, is introduced and discussed. The singular potentials are assumed to be repulsive in the singular region. The convergence is proved for real $k>\mathrm{}0\mathrm{}$ for regular and singular potentials for all partial waves, and for $k=0\mathrm{}$ for repulsive potentials for $S$ waves $k$ being the momentum in the reference frame of the potential). In the latter case the convergence is monotonic.