Nucleon-nucleon scattering process in Lattice Chiral Effective Field Theory approach up to next-to-next-to-next-to-leading order

Abstract

We carry out a comprehensive analysis of the neutron-proton interaction up to the third order in the scheme of chiral effective field theory on the lattice. The complete two-pion exchange potential is taken into account to allow for a variation of the lattice spacing. We analyze the perturbative as well as the non-perturbative inclusion of the higher-order corrections and present a thorough analysis of the theoretical uncertainties.<br /> In addition, a first attempt is made to include chiral contributions at the fourth order as well as the electromagnetic effects relevant for proton-proton scattering. For that, we include all fourth order local four-nucleon interactions and the dominant corrections to the two-pion exchanges. As expected, the higher order chiral corrections give an improved description for the scattering of two nucleons. This work should be extended by performing an uncertainty analysis and investigating the lattice spacing dependence in the future.<br /> We further scrutinize nuclei with even and equal numbers of protons and neutrons using nuclear lattice effective field theory, based upon a set of highly improved (smeared) leading order interactions. We present numerical evidence that reveals a first-order transition at zero temperature from a Bose-condensed gas of alpha particles to the nuclear liquid, which is regulated by the strength and locality of the nucleon-nucleon interactions.