Nucleon-deuteron doublet scattering lengths with three-nucleon potentials

The n-d and p-d s-wave scattering lengths are calculated for the spin-doublet configuration, including a three-nucleon potential in the Hamiltonian. Numerical results for the Reid-soft-core two-body potential plus the Tucson-Melbourne or Brazil three-body forces are presented. Comparison is made with Kohn variational estimates computed using the wave functions obtained by solving the Faddeev equations. Inclusion of the three-nucleon potentials does not alter our previous conclusions about the scattering lengths; all calculated ${}_{}{}^2{}_{}{}^{}\mathrm{a}_{\mathrm{nd}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{a}_{\mathrm{pd}}^{}{}_{}{}^{}$ values lie on separate Phillips curves. The experimental value of ${}_{}{}^2{}_{}{}^{}\mathrm{a}_{\mathrm{nd}}^{}{}_{}{}^{}$ lies on the n-d Phillips curve, while a considerable discrepancy remains for the p-d case.