Calculations of three-nucleon reactions with N3LO chiral forces: achievements and challenges
We discuss the application of the chiral N3LO forces to three-nucleon reactions and point to the challenges which will have to be addressed. Present approaches to solve three-nucleon Faddeev equations are based on a partial-wave decomposition. A rapid increase of the number of terms contributing to the chiral three-nucleon force when increasing the order of the chiral expansion from N2LO to N3LO forced us to develop a fast and effective method of automatized partial-wave decomposition. At low energies of the incoming nucleon below ≈20 MeV, where only a limited number of partial waves is required, this method allowed us to perform calculations of reactions in the three-nucleon continuum using N3LO two- and three-nucleon forces. It turns out that inclusion of consistent chiral interactions, with relativistic 1/m corrections and short-range 2π-contact term omitted in the N3LO three-nucleon force, does not explain the long standing low energy Ay-puzzle. We discuss problems arising when chiral forces are applied at higher energies, where large three-nucleon force effects are expected. It seems plausible that at higher energies, due to a rapid increase of a number of partial waves required to reach convergent results, a three-dimensional formulation of the Faddeev equations which avoids partial-wave decomposition is desirable.