Neutron-proton scattering with lattice chiral effective field theory at next-to-next-to-next-to-leading order

Abstract

We present a new lattice formulation of chiral effective field theory interactions with a simpler decomposition into spin channels. With these interactions the process of fitting to the empirical scattering phase shifts is simplified, and the resulting lattice phase shifts are more accurate than in previous studies. We present results for the neutron-proton system up to next-to-next-to-next-to-leading order for lattice spacings of 1.97, 1.64, 1.32, and 0.99 fm. Our results provide a pathway to ab initio lattice calculations of nuclear structure, reactions, and thermodynamics with accurate and systematic control over the chiral nucleon-nucleon force. *

NN interaction and the spectrum of light and medium-mass nuclei using Lattice Effective Field Theory

“…The phase shifts and mixing angles can be extracted from the radial wave function in the region where the NN force is vanishing. In this range, the wave function is a superposition of the incoming plane wave and outgoing radial wave which can be expanded as [17,10] r|k…”

“…The contact operators at orders (Q/Λ χ ) and (Q/Λ χ ) 4 can be written in a similar manner, refer to [10] for the specific expressions. We also include an SU(4)-invariant short-range operator at LO which is very important for nuclear binding [5,11],…”

“…and each lattice momentum component q S is an integer multiplied by 2π/L. The specific expressions of the two-pion-exchange potentials at NLO, N2LO, and N3LO can be found in [10].…”

Galilean invariance restoration on the lattice

“…After solving the Schödinger equation, the phase shifts and mixing angles can be extracted from the radial wave function in the region where the NN force is vanishing. In this range, the wave function is a superposition of the incoming plane wave and outgoing radial wave which can be expanded as [13,29] r|k, l = A j h (1)…”

“…The contact operators at NLO and N3LO can be written in a similar manner. Their specific expressions which are not given here for simplicity can be found in [13]. Additionally, we also include an SU(4)-invariant short-range operator at LO, which has been shown to be important for nuclear binding [12,15],…”