Nuclear matter properties with nucleon-nucleon forces up to fifth order in the chiral expansion

The properties of nuclear matter are studied using state-of-the-art nucleon-nucleon forces up to fifth order in chiral effective field theory. The equations of state of symmetric nuclear matter and pure neutron matter are calculated in the framework of the Brueckner-Hartree-Fock theory. We discuss in detail the convergence pattern of the chiral expansion and the regulator dependence of the calculated equations of state and provide an estimation of the truncation uncertainty. For all employed values of the regulator, the fifth-order chiral two-nucleon potential is found to generate nuclear saturation properties similar to the available phenomenological high precision potentials. We also extract the symmetry energy of nuclear matter, which is shown to be quite robust with respect to the chiral order and the value of the regulator.

Figure 1

Density dependence of the energy per particle of SNM ${(E/A)}_{\mathrm{SNM}}$ (upper row), of PNM ${(E/A)}_{\mathrm{PNM}}$ (middle row), and of the symmetry energy $a_{\text{symm}}$ (lower row) based on chiral $NN$ potentials of [35, 36] for all available cutoff values in the range of $R=0.8–1.2\mathrm{fm}$.

Figure 2

Predictions for the EOS of SNM (left column) and PNM (right column) based on the chiral $NN$ potentials of Refs. [35, 36] for $R=0.9\mathrm{fm}$ (upper row) and $R=1.0\mathrm{fm}$ (lower row) along with the estimated theoretical uncertainties. Open rectangles visualize the empirical saturation point of symmetric nuclear matter.

Figure 3

Chiral expansion of the symmetry energy $a_{\text{symm}}$ (left panel) and the slope parameter $L$ (right panel) at the empirical saturation density $\rho =0.16{\mathrm{fm}}^{-3}$ for the cutoff values $R=0.9\mathrm{fm}$ (upper row) and $R=1.0\mathrm{fm}$ (lower row) along with the estimated theoretical uncertainty. Solid circles (open rectangles) show the complete results at a given chiral order (incomplete results based on $NN$ interactions only). Solid triangles show the current experimental constraints on $a_{\text{symm}}$ and $L$ as described in the text.