distance from the surface, z ∗ , which is found from the condition m$_{e}$ − V ( z ∗ ) = µ , see Eq. (4). The value of µ is determined from the condition of global charge neutrality: where σ$_{+}$ and σ − are the areal densities of positive and negative charges accumulated at z < z$_{0}$ and z > z$_{0}$ respectively. Since calculated µ values are very close to m$_{e}$ , we use µ = m$_{e}$ for our estimates. Another boundary condition follows from the requirement that far inside the star the electron charge density must completely compensate the positive charge density, i.e. ρ$_{ch}$ ( z → −∞ ) = 0, that means that k$_{Fe}$ ( z → −∞ ) ≡ k$_{F}$$_{0}$ = (3 π $^{2}$ρ$_{p}$$_{0}$ ) 1 / 3 and e ∞ ∫ −∞ [ ρ$_{p}$ ( z ) − ρ$_{e}$ ( z )] dz ≡ σ$_{+}$ + σ − = 0 , (7) V ( z → −∞ ) = √ k 2 F 0 + m 2 e − µ = √ (3 π $^{2}$ρ$_{p}$$_{0}$ ) 2 / 3 + m 2 e − µ . (8) These conditions are sufficient to determine the electron density distribution ρ$_{e}$ ( z ). Unfor- tunately, no analytical solution can be found without further approximations, and therefore numerical methods must be applied. We have performed numerical calculations for different values of the diffuseness parameter a ranging from 1 fm, typical for nuclear surfaces, up to 1 nm, typical for solid-state surfaces. As an example, in Fig. 1 we present results for a =5 fm which is rather close to a “sharp surface” limit. The upper, middle and lower panels show, respectively, the electron density, electric potential and electric field calculated for the given proton density (dashed line in the upper panel). One can clearly see the deviation of the electron density from the proton one in the layer of ± 50 fm around the surface. This gives rise to a sharp fall of the potential, and as a consequence, to a very strong electric field generated in this layer. The maximum of the field, about 1.5 MV/fm, is reached at z = z$_{0}$ . This value is almost 600 times higher than the critical electric field for spontaneous electron-positron pair production [19], E$_{c}$ = 2 m $^{2}$c$^{3}$/e ℏ = 0 . 0026 MV/fm=2 . 6 · 10 16 V/cm. However, in the considered system the pair production does not happen because all electron states with ϵ$_{e}$ ( k, z ) < m$_{e}$ are occupied and therefore Pauli- blocked. This situation is clarified in Fig. 2, where the electron levels in a strong electric potential, − V ( z ), are shown schematically. As explained above, the negative potential inside the medium ( z < z$_{0}$ ) is generated by the charge separation at the surface. In the vacuum such 4