the higher order terms L hot which are responsible for the effects of medium dependence, L hot = − 1 3 β$_{S}$ ( ¯ ψψ ) 3 − 1 4 γ$_{S}$ ( ¯ ψψ ) 4 − 1 4 γ$_{V}$ [( ¯ ψγ$_{µ}$ψ )( ¯ ψγ $^{µ}$ψ )] $^{2}$, (5) L der = − 1 2 δ$_{S}$∂$_{ν}$ ( ¯ ψψ ) ∂ $^{ν}$( ¯ ψψ ) − 1 2 δ$_{V}$ ∂$_{ν}$ ( ¯ ψγ$_{µ}$ψ ) ∂ $^{ν}$( ¯ ψγ $^{µ}$ψ ) − 1 2 δ$_{T S}$∂$_{ν}$ ( ¯ ψ⃗ τ ψ ) ∂ $^{ν}$( ¯ ψ⃗ τ ψ ) − 1 2 δ$_{T V}$ ∂$_{ν}$ ( ¯ ψ⃗ τ γ$_{µ}$ψ ) ∂ $^{ν}$( ¯ ψ⃗ τ γ$_{µ}$ψ ) , (6) L em = − 1 4 F $^{µν}$F$_{µν}$ − e 1 − τ$_{3}$ 2 ¯ ψγ $^{µ}$ψA$_{µ}$ . (7) the gradient terms L der which are included to simulate the effects of finite-range, and the electromagnetic interaction terms L $^{em}$, For the Lagrangian density in Eq. (2), m is the nucleon mass and e is the charge unit for protons. A$_{µ}$ and F$_{µν}$ are respectively the four-vector potential and field strength tensor of the electromagnetic field. There are totally 11 coupling constants, α$_{S}$ , α$_{V}$ , α$_{T S}$ , α$_{T V}$ , β$_{S}$ , γ$_{S}$ , γ$_{V}$ , δ$_{S}$ , δ$_{V}$ , δ$_{T S}$ , and δ$_{T V}$ , in which α refers to the four-fermion term, β and γ respectively the third- and fourth-order terms, and δ the derivative couplings. The subscripts S , V , and T respectively indicate the symmetries of the couplings, i.e., S stands for scalar, V for vector, and T for isovector. From former experience [11], we neglect the isovector-scalar channel in Eq. (2) since a fit including the isovector-scalar interaction does not improve the description of nuclear ground-state properties. Consequently, there are nine free parameters in the present RMF- PC model, which are comparable with those in the RMF-FR model. Furthermore, the pseudoscalar γ$_{5}$ and pseudovector γ$_{5}$γ$_{µ}$ channels are also neglected in Eq. (2) since they do not contribute at the Hartree level due to parity conservation in nuclei. Similar to the RMF-FR case, the mean-field approximation leads to the replacement of the operators ¯ ψ ( ˆ O Γ)$_{i}$ ψ in Eq. (2) by their expectation values which become bilinear forms of the nucleon Dirac spinor ψ$_{k}$ , where i indicates S , V , and T V . The sum ∑ runs over only positive energy states with the occupation probabilities v 2 $_{k}$, i.e., the “no-sea” approximation. Based on these approxima- tions, one finds the energy density functional for a nuclear system ¯ ψ ( ˆ O Γ)$_{i}$ ψ → 〈 Φ | ¯ ψ ( ˆ O Γ)$_{i}$ ψ | Φ 〉 = ∑ k v 2 k ¯ ψ$_{k}$ ( ˆ O Γ)$_{i}$ ψ$_{k}$, (8) E$_{DF}$ [ τ , ρ$_{S}$ , j µ i , A$_{µ}$ ] = ∫ d $^{3}$r E ( r ) , (9) 5