Nucleon-nucleon potentials with and without<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mn/><mml:mo>(</mml:mo><mml:mn>1232</mml:mn><mml:mo>)</mml:mo><mml:mn/></mml:math>degrees of freedom

Abstract

We present two new nucleon-nucleon (NN) potentials: a ${v}_{14}$ model that is a conventional NN potential and a ${v}_{28}$ model with explicit $\ensuremath{\Delta}(1232)$ degrees of freedom. The ${v}_{14}$ model has 14 operator components describing NN channels, while the ${v}_{28}$ model has 14 additional operators, including 12 transition operators for all possible $\ensuremath{\pi}\mathrm{N}\ensuremath{\Delta}$ and $\ensuremath{\pi}\ensuremath{\Delta}\ensuremath{\Delta}$ couplings and two central operators for $\mathrm{N}\ensuremath{\Delta}$ and $\ensuremath{\Delta}\ensuremath{\Delta}$ channels; the latter are constrained so that the ${v}_{28}$ model has no additional free parameters for data fitting. The two models give excellent and almost identical fits to deuteron properties and np scattering below 330 MeV. The ${v}_{14}$ and ${v}_{28}$ forms are convenient for nuclear structure calculations; when many-body cluster contributions are evaluated the ${v}_{28}$ model will automatically include much of the effect attributed to many-body forces in conventional models, while the ${v}_{14}$ model will provide a standard of comparison.