The pion cut and the negative-energy behaviour of neutron-proton effective-range functions near threshold

We study the effect of the pion cut on the negative-energy effective-range parameters of the 3S1 - 3D1 neutron-proton interaction. Utilizing an approach involving one-pionexchange potentials truncated at large distances, we demonstrate that the mixing parameter at negative energies between zero and the deuteron energy is practically independent of presence or absence of the pion cut. At the same time, the analysis gives some interesting insight into the behaviour of the mixing parameter and other effectiverange functions at more negative energies. This work complements our earlier result that the positive-energy mixing parameter is independent of the pioncut.