Three-Body Problem with Separable Potentials. II.n−dScattering

The three-body formalism, using separable potentials in $s$ and $p$ states of nucleon pairs, is set up under the conditions of full antisymmetrization of the three-nucleon wave function. The formalism is applied to the problem of $n-d$ scattering, where the effects of "polarization" are fully taken into account. The amplitudes for quartet and doublet scattering are found to satisfy two- and four-coupled one-dimensional integral equations, respectively. The quartet scattering length is found to agree with the figure for the so-called experimental set I for this parameter. The doublet scattering length, on the other hand, is found to be much more sensitive to the details of the potentials, thus preventing a theoretical resolution of its ambiguity within the present formalism without tensor forces.