Modiﬁed effective range expansion for nucleon-nucleon scattering
Institut für Kernphysik and Jülich Center for Hadron Physics,
Forschungszentrum Jülich, D-52425, Jülich, Germany
2 Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universitat Bonn, D-53115 Bonn, Germany
3 Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425, Jülich, Germany
a e-mail: firstname.lastname@example.org
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.
© Owned by the authors, published by EDP Sciences, 2010