The Tjon band in Nuclear Lattice Effective Field Theory

Abstract

We explore the lattice spacing dependence in Nuclear Lattice Effective Field Theory for few-body systems up to next-to-next-to leading order in chiral effective field theory including all isospin breaking and electromagnetic effects, the complete two-pion-exchange potential, and the three-nucleon forces. We calculate phase shifts in the neutron-proton system and proton-proton systems as well as the scattering length in the neutron-neutron system. We then perform a full next-to-next-to-leading order calculation with two-nucleon and three-nucleon forces for the triton and helium-4, and analyse their binding energy correlation. We show how the Tjon band is reached by decreasing the lattice spacing, and confirm the continuum observation that a four-body force is not necessary to describe light nuclei.