The Tjon Band in Nuclear Lattice Effective Field Theory

TL;DR

This paper investigates how lattice spacing affects nuclear calculations in lattice effective field theory, demonstrating that decreasing lattice spacing reproduces the Tjon band and confirms no four-body force is needed for light nuclei.

Contribution

It provides a comprehensive next-to-next-to-leading order analysis of few-body nuclear systems including all relevant effects and clarifies the role of lattice spacing in reproducing nuclear correlations.

Findings

Decreasing lattice spacing approaches the Tjon band.

Four-body force is not required for light nuclei.

Accurate phase shifts and binding energies are obtained.

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.