Effective range function below threshold

Abstract

We demonstrate that the kernel of the Lippmann-Schwinger equation, associated with interactions consisting of a sum of the Coulomb plus a short range nuclear potential, below threshold becomes degenerate. Taking advantage of this fact, we present a simple method of calculating the effective range function for negative energies. This may be useful in practice since the effective range expansion extrapolated to threshold allows to extract low-energy scattering parameters: the Coulomb-modified scattering length and the effective range.