Scattering length and effective range for the Coulomb plus separable potential

A simple prescription is given for evaluating the scattering length and effective range, to first order in the fine structure constant, for the Coulomb plus separable potential. It can handle a separable potential of an arbitrary form, in contrast to earlier calculations for separable potentials with form factors that are rational functions in the momentum space. The method can easily be extended to higher partial waves.