Quark-model Baryon-Baryon Interaction Applied to the Neutron-Deuteron Scattering. I Noyes-Kowalski Approach to the AGS Equations

We solve the neutron-deuteron (nd) scattering in the Faddeev formalism, employing the NN sector of the quark-model baryon-baryon interaction fss2. The energy-dependence of the NN interaction, inherent to the resonating-group formulation of the quark-model baryon-baryon interaction, is eliminated by the standard off-shell transformation utilizing the normalization kernel of two-cluster systems. An extra nonlocality originating from this procedure is very important to reproduce all the nd scattering observables below E_n < 65 MeV. A new algorithm to solve the Alt-Glassberger-Sandhas (AGS) equations is presented in the Noyes-Kowalski method. The treatment of the moving singularity from the three-body Green function is shown in detail, which is based on the spline function method originally developed by the Bochum-Krakow group. The predicted elastic differnetial cross sections reproduce the observed deep cross section minima at E_n=35-65 MeV and $\theta_{c.m}=130^{\circ}-135^{\circ}$, which is consitent with the nearly correct triton binding energy predicted by fss2 without the three-body force.