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 leadingorder (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.PACS numbers:

The Tjon band in Nuclear Lattice Effective Field Theory

“…For the neutron-proton fit procedure we follow Ref. [6]. In general, we do a χ 2 fit to partial wave analysis data PWA, NijmI, NijmII and Reid93 of [36] according to [27],…”

“…Using this method it was possible to calculate the binding energies of medium mass nuclei with good accuracy [1,2] and postdict the Hoyle state [3,4], which is an excited state in carbon-12 indispensable for nucleosynthesis in stars. Besides binding energies, also scattering processes like nucleon-nucleon [5,6] or alpha-alphascattering [7] were investigated. NLEFT combines two powerful concepts.…”

“…A detailed analysis of the lattice space dependence of the two-body sector can be found in Ref. [6], where higherorder corrections were included both perturbatively and non-perturbatively. In the following we will include and extend the two-body analysis, but we will focus on the perturbative approach as we want to be in agreement three-and four-body calculations in which all corrections beyond LO have been included perturbatively.…”

Lattice improvement in lattice effective field theory

“…Lattice simulations based on the framework of effective field theory (EFT) have been used in the study of nuclear forces [1,2], nuclear structure [3][4][5][6][7][8], as well as scattering and reactions [9][10][11]. It has also been applied to few-body [12,13] and many-body [14][15][16][17][18][19][20] problems in ultracold atomic systems.…”

“…This general technique is called lattice improvement and was first introduced by Symanzik [27,28]. The key idea is to write the lattice action as S(a) = S 0 + f 1 (a) · S 1 + f 2 (a) · S 2 + · · · (1) where the coefficient functions f i (a) vanish in the continuum limit a → ∞ and are tuned to cancel the dependence of the lattice Green's functions on the lattice spacing, a, at momentum scales well below the lattice cutoff momentum, π/a. The coefficient functions are ordered so that f i (a) vanishes more rapidly in the limit a → 0 with increasing i. Symanzik's improvement program has been widely used in lattice quantum chromodynamics [29][30][31][32].…”