Accurate direct determination of effective-range expansion parameters for several central potentials

Abstract

Instead of calculating phase shifts at small scattering energies for a given two-body central potential and from these deduce by extrapolation to zero energy the associated scattering length and effective range, we write those parameters as integrals which are evaluated numerically to high accuracy for the Lennard-Jones and Aziz et al. interatomic potentials for both $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$, as well as for the Kolos-Wolniewicz potential between hydrogen isotopes.