IV. NUCLEAR MATTER PROPERTIES A. Saturation properties In this section, we will present the saturation properties and the equation of state (EOS) for nuclear matter in the covariant EDF with PC-PK1. The results will be compared with the corresponding empirical values as well as the predictions with PC-LA, PC-F1, DD-PC1, NL3*, and PK1 [19]. The saturation properties, including the binding energy per nucleon E/A , saturation density ρ$_{0}$ , incompressibility K$_{0}$ , nucleon effective mass M ∗ D and M ∗ $_{L}$, symmetry energy E$_{sym}$ , as well as the characteristics L and K$_{asy}$ for the density dependence of E$_{sym}$ will be investigated. There are several kinds of nucleon effective mass [29, 30]. Here we mainly focus on the Dirac mass and Landau mass. The Dirac mass M ∗ D is defined through the nucleon scalar self-energy in the Dirac equation, i.e., M ∗ D = M + Σ$_{S}$. It is directly related to the spin-orbit potential in finite nuclei and is thus a genuine relativistic quantity without nonrelativistic correspondence. While the Landau mass M ∗ L = pdp/dE is related to the density of state both in relativistic and non-relativistic models. In relativistic models, the relation between the Dirac mass and the Landau mass is M ∗ L = √ p 2 F + M ∗ 2 D , where p$_{F}$ is the Fermi momentum. The density dependence of the nuclear symmetry energy is very important to understand the properties of exotic nuclei with extreme isospin values, in particular the slope L ≡ 3 ρ$_{0}$ ( dE$_{sym}$/dρ )$_{ρ}$$_{=}$$_{ρ}$$_{0}$ and curvature K$_{sym}$ ≡ 9 ρ 2 $_{0}$( d $^{2}$E$_{sym}$ /d $^{2}$ρ )$_{ρ}$$_{=}$$_{ρ}$$_{0}$ of the symmetry energy at the saturation density ρ$_{0}$ . In Refs. [31, 32], the isospin-dependent part, K$_{asy}$ ≈ K$_{sym}$ − 6 L , in the isobaric incompressibility K ( δ ) = K$_{0}$ + K$_{asy}$δ 2 (with δ ≡ ( ρ$_{n}$ − ρ$_{p}$ ) /ρ ), is often used to characterize the density dependence of the symmetry energy as both L and K$_{asy}$ can be extracted from the experiment empirically (see Ref. [33] and references therein). In Table IV, the saturation properties for nuclear matter, including the binding energy per nucleon E/A , saturation density ρ$_{0}$ , incompressibility K$_{0}$ , nucleon effective mass M ∗ D and M ∗ $_{L}$, symmetry energy E$_{sym}$ , as well as the characteristics L and K$_{asy}$ for the density dependence of E$_{sym}$ , predicted by PC-PK1 are listed in comparison with those by both point-coupling DD-PC1, PC-F1, PC-LA and meson exchange NL3*, PK1 sets. In general, 10