Modified effective range expansion for nucleon-nucleon scattering

Abstract

The standard effective range expansion is commonly used in nucleon-nucleon scattering to encode the properties of the nuclear force model-independently in a small set of parameters. However, its applicability is limited by the longest-range part of the nuclear potential, i.e. by the one pion exchange, to the domain of momenta below half the pion mass. Therefore, it is not useful to study shorter-range parts of the interaction, e.g. two-pion exchange. To this aim a modification that explicitly takes a given long-range part of the interaction into account is required. This is known as modified effective range expansion. Here, we apply this approach to the nucleonnucleon interaction to separate the known long-range interactions from the rest. To show the effectiveness of this technique, we consider a toy model with a two-range potential. We study the scaling behaviour of the parameters of the standard and modified effective range expansion in this two-scale problem and compare their convergence behaviour.