Nuclear matter properties from local chiral interactions with $\mathrm{\Delta }$ isobar intermediate states

Using two-nucleon and three-nucleon interactions derived in the framework of chiral perturbation theory (ChPT) with and without the explicit $\mathrm{\Delta }$ isobar contributions, we calculate the energy per particle of symmetric nuclear matter and pure neutron matter in the framework of the microscopic Brueckner-Hartree-Fock approach. In particular, we present for the first time nuclear matter calculations using the new fully local in coordinate-space two-nucleon interaction at the next-to-next-to-next-to-leading-order (N3LO) of ChPT with $\mathrm{\Delta }$ isobar intermediate states ($\mathrm{N}3\mathrm{LO}\mathrm{\Delta }$) recently developed by Piarulli et al. [arXiv:1606.06335]. We find that using this $\mathrm{N}3\mathrm{LO}\mathrm{\Delta }$ potential, supplemented with a local N2LO three-nucleon interaction with explicit $\mathrm{\Delta }$ isobar degrees of freedom, it is possible to obtain a satisfactory saturation point of symmetric nuclear matter. For this combination of two- and three-nucleon interactions we also calculate the nuclear symmetry energy and we compare our results with the empirical constraints on this quantity obtained using the excitation energies to isobaric analog states in nuclei and using experimental data on the neutron skin thickness of heavy nuclei, finding a very good agreement in all the considered nucleonic density range. In addition, we find that the explicit inclusion of $\mathrm{\Delta }$ isobars diminishes the strength of the three-nucleon interactions needed to get a good saturation point of symmetric nuclear matter. We also compare the results of our calculations with those obtained by other research groups using chiral nuclear interactions with different many-body methods, finding in many cases a very satisfactory agreement.

Figure 1

Energy per particle of pure neutron (a) and symmetric nuclear matter (b) as function of the nucleonic density for the models described in the text. Continuous lines have been obtained using two- plus three-body interactions, while the dashed lines have been obtained considering only the two-body interaction. The empirical saturation point of nuclear matter ${\rho }_0=0.16\pm 0.01{\mathrm{fm}}^{-3}, {E/A|}_{{\rho }_0}=-16.0\pm 1.0\mathrm{MeV}$ is denoted by the gray box in (b).

Figure 2

Energy per particle of symmetric nuclear matter versus the nucleonic density for the two TNF models which take into account the contribution of the $\mathrm{\Delta }$ isobar.

Figure 3

Nuclear symmetry energy as a function of the nucleonic density for the four interaction models used in the present work. The triangles labeled DSS represent the results of Ref. [82]. The black-dashed band, labeled IAS, represents the constraints on the symmetry energy obtained in Ref. [85] using the excitation energies of isobaric analog states (IAS) in nuclei. The additional constraints from neutron skin thickness $\mathrm{\Delta }{r}_{np}$ of heavy nuclei give the more limited region covered by the red-dashed band labeled $\mathrm{IAS}+\mathrm{\Delta }{r}_{np}$ [82].

Figure 4

Comparison of energy per particle of pure neutron (a) and symmetric nuclear matter (b) between various many-body methods (see text for more details).