Benchmark calculations of infinite neutron matter with realistic two- and three-nucleon potentials

TL;DR

This paper benchmarks three many-body methods to calculate the equation of state of infinite neutron matter using realistic nuclear potentials, revealing their agreement and limitations at high densities and with different potential models.

Contribution

It provides a comparative analysis of BBG, FHNC/SOC, and AFDMC methods for neutron matter with realistic two- and three-nucleon potentials, highlighting their consistency and discrepancies.

Findings

All three methods agree at densities below 1.5ρ₀.

AFDMC with Norfolk potentials predicts unphysical neutron droplet formation.

Including tritium β-decay data affects the potential fit and results.

Abstract

We present the equation of state of infinite neutron matter as obtained from highly-realistic Hamiltonians that include nucleon-nucleon and three-nucleon coordinate-space potentials. We benchmark three independent many-body methods: Brueckner-Bethe-Goldstone (BBG), Fermi hypernetted chain/single-operator chain (FHNC/SOC), and auxiliary-field diffusion Monte Carlo (AFDMC). We find them to provide similar equations of state when the Argonne $v_{18}$ and the Argonne $v_{6}^\prime$ nucleon-nucleon potentials are used in combination with the Urbana IX three-body force. Only at densities larger than about 1.5 the nuclear saturation density ($\rho_0 = 0.16\,\rm{fm}^{-3}$) the FHNC/SOC energies are appreciably lower than the other two approaches. The AFDMC calculations carried out with all of the Norfolk potentials fitted to reproduce the experimental trinucleon ground-state energies and $nd$ doublet scattering length yield unphysically bound neutron matter, associated with the formation of neutron droplets. Including tritium $\beta$-decay in the fitting procedure, as in the second family of Norfolk potentials, mitigates but does not completely resolve this problem. An excellent agreement between the BBG and AFDMC results is found for the subset of Norfolk interactions that do not make neutron-matter collapse, while the FHNC/SOC equations of state are moderately softer.