with the energy density which is composed of a kinetic part an interaction part with the local densities and currents and an electromagnetic part Minimizing the energy density functional Eq. (9) with respect to ¯ ψ$_{k}$ , one obtains the Dirac equation for the single nucleons The single-particle effective Hamiltonian contains local scalar S ( r ) and vector V $^{µ}$( r ) poten- tials, where the nucleon scalar-isoscalar Σ$_{S}$, vector-isoscalar Σ $^{µ}$, and vector-isovector ⃗ Σ µ T V self- energies are given in terms of the various densities, E ( r ) = E $^{kin}$( r ) + E $^{int}$( r ) + E $^{em}$( r ) , (10) E $^{kin}$( r ) = ∑ k v 2 k ψ † $_{k}$( r ) ( α · p + βm ) ψ$_{k}$ ( r ) , (11) E $^{int}$( r ) = α$_{S}$ 2 ρ 2 S + β$_{S}$ 3 ρ 3 S + γ$_{S}$ 4 ρ 4 S + δ$_{S}$ 2 ρ$_{S}$ △ ρ$_{S}$ + α$_{V}$ 2 j$_{µ}$j µ + γ$_{V}$ 4 ( j$_{µ}$j $^{µ}$) 2 + δ$_{V}$ 2 j$_{µ}$ △ j µ (12) + α$_{T V}$ 2 ⃗ j µ T V · ( ⃗ j$_{T V}$ )$_{µ}$ + δ$_{T V}$ 2 ⃗ j µ T V · △ ( ⃗ j$_{T V}$ )$_{µ}$ , ρ$_{S}$ ( r ) = ∑ k v 2 k ¯ ψ$_{k}$ ( r ) ψ$_{k}$ ( r ) , (13a) ⃗ j µ $_{T V}$( r ) = ∑ k v 2 k ¯ ψ$_{k}$ ( r ) ⃗ τ γ $^{µ}$ψ$_{k}$ ( r ) , (13c) E $^{em}$( r ) = 1 4 F$_{µν}$ F µν − F 0 $^{µ}$∂$_{0}$ A$_{µ}$ + eA$_{µ}$j µ p . (14) j µ $_{V}$( r ) = k v 2 k ¯ ψ$_{k}$ ( r ) γ $^{µ}$ψ$_{k}$ ( r ) , (13b) [ γ$_{µ}$ ( i∂ µ − V $^{µ}$) − ( m + S )] ψ$_{k}$ = 0 . (15) S ( r ) = Σ$_{S}$ , V $^{µ}$( r ) = Σ µ + ⃗ τ · ⃗ Σ µ T V , (16) Σ$_{S}$ = α$_{S}$ρ$_{S}$ + β$_{S}$ρ 2 S + γ$_{S}$ρ 3 S + δ$_{S}$ △ ρ$_{S}$, (17a) Σ µ = α$_{V}$ j µ V + γ$_{V}$ ( j µ $_{V}$) 3 + δ$_{V}$ △ j µ V + eA $^{µ}$, (17b) ⃗ Σ µ T V = α$_{T V}$ ⃗ j µ T V + δ$_{T V}$ △ ⃗ j µ T V . (17c) 6