Equation of state and Fermi liquid properties of dense matter based on chiral effective field theory interactions

TL;DR

This work computes the equation of state (EOS) of symmetric nuclear matter and pure neutron matter using many-body perturbation theory (MBPT) up to third order with diverse chiral NN and 3N interactions, and it analyzes uncertainties from both MBPT truncation and chiral EFT truncation via Gaussian-process Bayesian methods. It also extends the Fermi liquid theory (FLT) framework to include all NN and 3N contributions up to second order, extracting Landau parameters and deriving the effective mass $m^*$ and speed of sound $c_s^2$. The study finds generally good MBPT convergence, with EFT truncation uncertainties typically larger than MBPT corrections, and shows that 3N forces significantly stiffen the EOS, especially near higher densities. The authors extract ranges for key EOS parameters, including $K$, $E_{ ext{sym}}$, and $L$, and discuss implications for neutron-star matter and astrophysical phenomena, while outlining future work to merge chiral EFT and many-body uncertainties and to broaden FLT analyses to additional channels and higher orders.

Abstract

We present results for the equation of state of symmetric nuclear matter and pure neutron matter obtained in many-body-perturbation theory (MBPT) up to third order, based on various chiral two- and three-nucleon interactions used in ab initio calculations of nuclei. We extract equation of state properties, such as the incompressibility and the symmetry energy, and discuss estimates of the theoretical uncertainties due to neglected higher-order contributions in the MBPT expansion as well as the chiral effective field theory expansion. In addition, we discuss the Fermi liquid approach to nuclear matter. We calculate all two- and three-nucleon contributions to the quasiparticle interaction up to second order in MBPT and present results for the Landau parameters, effective mass, and speed of sound for pure neutron matter.

Figures (12)

• Figure 1: Energy per particle $E/N$ of PNM as a function of particle density $n$ based on different NN and 3N interactions (see main text). Note that the results for the interactions 1.8/2.0 (EM) and 1.8/2.0 (EM7.5) are identical since the short-range terms $c_D$ and $c_E$ do not contribute to neutron matter for nonlocal regulators. The dotted line shows the energy per particle of the unitary Fermi gas for comparison Ku2012.
• Figure 2: Energy per particle $E/A$ of SNM as a function of particle density $n$ based on the same NN and 3N interactions as in Fig. \ref{['fig:EOS_PNM']}.
• Figure 3: Energy per particle of neutron matter (upper rows in both panels) and symmetric matter (lower rows) for different NN and 3N interactions at different orders in the MBPT expansion. Results are shown at the HF level (dotted lines), including MBPT(2) (dashed lines) and MBPT(3) (solid lines).
• Figure 4: Energy per particle of neutron matter (top panels) and symmetric nuclear matter (lower panels) at different orders of the chiral expansion for the three different interactions, for which order-by-order potentials are available. All results are based on MBPT(3) calculations. Solid lines refer to results at N$^2$LO, dashed lines to NLO, and dotted lines to LO. The corresponding $68 \%$ confidence intervals based on GP-Bayesian uncertainties from the chiral EFT truncation (following Refs. Drischler2020PRLDrischler2020) are indicated by dark bands at N$^2$LO, medium-dark bands at NLO, and light bands at LO.
• Figure 5: Hartree-Fock and second-order diagrams that contribute to the quasiparticle interaction. The left column shows the diagrams with NN and 3N vertices contributing to the energy density $\mathcal{E}$. The diagrams on the right show the resulting diagrammatic contributions to the quasiparticle interaction $\mathcal{F}$. Upward (downward) lines represent particles (holes).