Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory

Abstract

We present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. We stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing.

22 pages, 8 figures

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• Structure and rotations of the Hoyle state
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• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
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• Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
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• Chiral effective field theory on the lattice at next-to-leading order
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Cited by in corpus (12)

• Microscopic Clustering in Light Nuclei
• Neutron-proton scattering with lattice chiral effective field theory at next-to-next-to-next-to-leading order
• The Tjon Band in Nuclear Lattice Effective Field Theory
• Lattice Effective Field Theory Simulations of Nuclei
• Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice
• Sign-Problem-Free Nuclear Quantum Monte Carlo Simulation
• Lattice Improvement in Lattice Effective Field Theory
• Charge-dependent nucleon-nucleon interaction at N${}^3$LO in nuclear lattice effective field theory
• Effective Field Theories for Neutron Stars Physics
• Worldline Monte Carlo method for few body nuclear physics
• A Novel Regularization Scheme for Nucleon-Nucleon Lattice Simulations with Effective Field Theory
• Two particles interacting via a contact interaction on $S^2$