Multiple-Scattering Analysis on a Soluble Neutron-Deuteron Model

Abstract

The multiple-scattering series for elastic scattering is investigated numerically for a model of the neutrondeuteron system, at neutron laboratory energies of 14.1, 50, and 100 MeV. The model is that of Aaron, Amado, and Yam, with spin-dependent, $s$-wave, separable, two-body interactions. It is found that the doublet $L=0\mathrm{}$ series converges only slowly even at 100 MeV, and that it strongly diverges at 14.1 MeV. On the other hand, the convergence is rapid for both doublet and quartet partial waves beyond $L=2\mathrm{}$, and for these the single-scattering plus Born-pickup terms provide an accurate approximation. Differential cross sections and partial-wave amplitudes are given for various orders of multiple scattering, and for a unitary version of the first-order approximation, and are compared with the exact results.