Equation of state of nuclear and neutron matter at third-order in perturbation theory from chiral effective field theory

Abstract

We compute from chiral two-and three-nucleon interactions the energy per particle of symmetric nuclear matter and pure neutron matter at third-order in perturbation theory including self-consistent second-order single-particle energies. Particular attention is paid to the third-order particle-hole ring-diagram, which is often neglected in microscopic calculations of the equation of state. We provide semi-analytic expressions for the direct terms from central and tensor model-type interactions that are useful as theoretical benchmarks. We investigate uncertainties arising from the order-by-order convergence in both many-body perturbation theory and the chiral expansion. Including also variations in the resolution scale at which nuclear forces are resolved, we provide new error bands on the equation of state, the isospin-asymmetry energy, and its slope parameter. We find in particular that the inclusion of third-order diagrams reduces the theoretical uncertainty at low densities, while in general the largest error arises from omitted higher-order terms in the chiral expansion of the nuclear forces.

Strangeness and Δ resonance in compact stars with relativistic-mean-field models

“…Meanwhile, it is worth mentioning that the covariant density functional PKDD adopted here is phenomenological, where the nucleon-meson coupling constants are fixed according to the masses of spherical nuclei, the incompressibility, saturation density, and symmetry energy of nuclear matter [70]. In light of the recent developments of microscopic many-body calculations in describing finite nuclei and nuclear matter starting from realistic nucleonnucleon interactions [82][83][84][85][86][87][88], a more refined adjustment of parameters incorporating those results are necessary. A possible way to reach this in RMF model is to intro-duce density-dependent coupling constants derived from self-energies of Dirac-Brueckner calculations of nuclear matter [57,89], which are found decreasing with density and can be reproduced with Eqs.…”

Mirror Charge Radii and the Neutron Equation of State

“…The correlations between the neutron-skins, the mirror charge radii, and the properties of the equations of state obtained with the Skryme EDF should be compared to results obtained from ab-initio approaches based on chiral two-and three-body interactions [16], [35], [36] in order to constrain and extend the functional forms used for the EDF calculations.…”

Hadron matter in neutron stars in view of gravitational wave observations

“…Still, several reliable calculations have been performed up to twice that saturation density, beyond which uncertainties were estimated by analysing the order-by-order convergence in the chiral expansion and the many-body perturbation theory [120,121,122,123]. They were performed by extending the calculations of PNM with developed local chiral N 2 LO and N 3 LO interactions, including two-and three-body forces (see figure 14).…”

“…For the low-density end, we collected calculations of the neutron matter EoS from microscopic nuclear forces at different orders in Chiral effective field theory from several standing works [120,121,122,123,134]. Those sets extend only up to nucleon-number density n of order of 1-2 n 0 ( ∼ 250MeV/fm 3 ) (only [121] extends the computation up to n = 2.5n 0 ( < 380 MeV/fm 3 for N3LO), Figure 16: Scheme of the interpolation through intermediate densities between a chiral computation [123] and the high-density pQCD physics at µ match ∼ 2.6 GeV.…”