For a system with time reversal invariance, the space-like components of the currents j$_{i}$ in Eq. (13) and the vector potential V ( r ) in Eq. (16) vanish. Furthermore, one can assume that the nucleon single-particle states do not mix isospin, i.e., the single-particle states are eigenstates of τ$_{3}$ . Therefore only the third component of isovector potentials ⃗ Σ µ T V survives. The Coulomb field A$_{0}$ is determined by Poisson’s equation. In addition to the self-consistent mean-field potentials, for open-shell nuclei, pairing cor- relations are taken into account by the BCS method with a smooth cutoff factor f$_{k}$ to simulate the effects of finite-range [16, 17], i.e., we have to add to the functional Eq. (9) a pairing energy term of the form depending on the pairing tensor κ , with the smooth cut-off weight factor where ϵ$_{k}$ is the eigenvalue of the self-consistent single-particle field, and ϵ$_{F}$ is the chemical potential determined by the particle number, 〈 Φ | ˆ N$_{τ}$ | Φ 〉 = N$_{τ}$ , with N$_{τ}$ the particle number of neutron or proton. The cut-off parameters Δ E$_{τ}$ and µ$_{τ}$ = Δ E$_{τ}$ / 10 are chosen in such a way that 2 ∑ k> 0 f$_{k}$ = N$_{τ}$ + 1 . 65 N 2 / 3 τ [17]. In the following calculations, a density-independent δ -force in the pairing channel is adopted. Thus, the pairing energy is given by where V$_{τ}$ is the constant pairing strength and the pairing tensor κ ( r ) reads The pairing strength parameters V$_{τ}$ can be adjusted by fitting the average single-particle pairing gap to the data obtained with a five-point formula. As the translational symmetry is broken in the mean-field approximation, proper treat- ment of center-of-mass (c.m.) motion is very important and here the c.m. correction energy 〈 Δ 〉 ≡ ∑ k f$_{k}$u$_{k}$v$_{k}$ Δ$_{k}$ k f$_{k}$u$_{k}$v$_{k}$ (22) κ ( r ) = − 2 ∑ k> 0 f$_{k}$u$_{k}$v$_{k}$ | ψ$_{k}$ ( r ) | $^{2}$. (21) E$_{pair}$ [ κ, κ $^{∗}$] = − ∑ τ = n,p V$_{τ}$ 4 ∫ d $^{3}$rκ ∗ $_{τ}$( r ) κ$_{τ}$ ( r ) , (20) f$_{k}$ = 1 1 + exp[( ϵ$_{k}$ − ϵ$_{F}$ − Δ E$_{τ}$ ) /µ$_{τ}$ ] , (19) E$_{pair}$ [ κ, κ $^{∗}$] = ∑ kk ′ > 0 f$_{k}$f$_{k}$ ′ 〈 k ¯ k | V $^{pp}$| k ′ ¯ k $^{′}$〉 κ ∗ $_{k}$κ$_{k}$ ′ , (18) 7