We extend the ab initio no-core shell model/resonating-group method to include three-nucleon ($3N$) interactions for the description of nucleon-nucleus collisions. We outline the formalism, give algebraic expressions for the $3N$-force integration kernels, and discuss computational aspects of two alternative implementations. The extended theoretical framework is then applied to nucleon-${}^4$He elastic scattering using similarity-renormalization-group (SRG)-evolved nucleon-nucleon plus $3N$ potentials derived from chiral effective field theory. We analyze the convergence properties of the calculated phase shifts and explore their dependence upon the SRG evolution parameter. We include up to six excited states of the ${}^4\text{He}$ target and find significant effects from the inclusion of the chiral $3N$ force, e.g., it enhances the spin-orbit splitting between the $3/2^{-}$and $1/2^{-}$ resonances and leads to an improved agreement with the phase shifts obtained from an accurate $R$-matrix analysis of the five-nucleon experimental data. We find remarkably good agreement with measured differential cross sections at various energies below the $d$-${}^3$H threshold, while analyzing powers manifest larger deviations from experiment for certain energies and angles.

• Received 13 August 2013

DOI:https://doi.org/10.1103/PhysRevC.88.054622