Formulation of $s$-wave zero-energy Faddeev-type scattering equations including a Coulomb interaction is discussed. Numerical solutions of these equations for the $s$-wave NN potential models of Malfliet and Tjon are obtained using spline techniques. Kohn variational estimates are presented and comparison is made to previously published results. Our quartet pd scattering lengths are larger than others previously obtained, and our pd doublet results are smaller than the corresponding nd results, and thus in contrast to the experimental values. An explication of this feature is presented in terms of a model two-body problem. Perturbation theory for the Coulomb corrections to the scattering length is developed and confirms the Kohn estimates.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(p,p)${}_{}{}^2{}_{}{}^{}\mathrm{H}$, $E=0\mathrm{}$ MeV, p-d $s$-wave scattering lengths, configuration space Faddeev calculations.

• Received 31 May 1983

DOI:https://doi.org/10.1103/PhysRevC.28.983