NEUTRON-DEUTERON SCATTERING NEAR THRESHOLD - ON-SHELL 2-BODY APPROACH

We consider the analytic structure of the on-shell S-wave n-d amplitudes below three-body breakup. We show that to a reasonable accuracy some of their main features are dominated by single-proton exchange, and can be understood in a two-body approach through the N/D equations. The quartet scattering length is calculated in close form in terms of the deuteron binding energy and the triplet effective range, without adjustable parameters; we predict 6.3 fm compared to the measured 6.17 fm. For doublet scattering, we deduce a closed formula for k cotg δ2 at very low energies, but need one adjustable parameter fitted to the measured scattering length. Because the scattering length is small, k cotg δ2 must have a pole very close below threshold. In a model with spin 0 nucleons, we illustrate, in a physically transparent way, how the triton acquires a bound excited state as soon as the nuclear forces are strong enough to bind the deuteron. Finally, and this is our main purpose, we examine the implications as to what can be learned about the nucleon-nucleon potential from three-body n-d calculations in this energy region. © 1969.