An attempt has been made to select the core radius and coupling constant of the Lévy potential for the interaction of two nucleons in order to fit the binding energy of the deuteron and the singlet state neutron–proton scattering length. It was found that these two quantities cannot be fitted simultaneously. For any given choice of coupling constant, a somewhat larger core radius is required to fit the deuteron binding energy than is required for the scattering length. This spin dependence of the core radius does not preclude the possibility of a fit to the low energy data with the Lévy potential.
We apply our quark-model NN interaction fss2 to the nd scattering in the Faddeev formalism. A consistent description of the triton binding energy, the nd scattering length, the differential cross sections, and spin observables of the elastic scattering up to 65 MeV is achieved without introducing three-body forces.
The triton ground state energy and the neutron–deuteron doublet scattering length have been calculated with two families of phase equivalent separable interactions in the 1S0 and 3S1–3D1 states of the nucleon–nucleon interaction. Generating the interactions from a solution of the inverse scattering problem, a separable representation of the nucleon–nucleon interaction is fully exploited to fit the scattering and bound state data as well as possible. Off shell constraints on the interactions are then discussed. Results for the three nucleon quantities are compared to those obtained with realistic local and one boson exchange potentials. It is shown that all results for potentials obeying the known off shell constraints lie on the Phillips band, which appears to be independent of the potential model employed. This is a consequence of the fact that the triton binding energy and doublet scattering length are only sensitive to the broad detail of the nucleon–nucleon S matrix in the 1S0 and 3S1–3D1 states and to certain global features of the residues at the singlet deuteron and deuteron poles. Relatively large off shell variations in the triton binding energy and doublet scattering length along this Phillips band are possible and the plausibility that the experimental values could be fitted is discussed.
Transformation Between Complex Scattering Length and Binding Energy