From super-charged nuclei to massive nuclear density cores

Due to e+e--pair production in the field of supercritical (Z>>Zcr≅170) nucleus an electron shell, created out of the vacuum, is formed. The distribution of the vacuum charge in this shell has been determined for super-charged nuclei Ze3 > or approx. 1 within the framework of the Thomas-Fermi equation generalized to the relativistic case. For Ze3>>1 the electron shell penetrates inside the nucleus and almost completely screens its charge. Inside such nucleus the potential takes a constant value equal to V0 = -(3π2np)1/3∼-2mπc2, and super-charged nucleus represents an electrically neutral plasma consisting of e, p and n. Near the edge of the nucleus a transition layer exists with a width λ≅α-1/2h-bar/mπc∼15 fm, which is independent of Z(h-bar/mπc<<λ< or approx. 0.04(Z/A)1/2(mPlanck/mn)3 the Coulomb repulsion of protons, screened by relativistic electrons, can be balanced by gravitational forces. The overcritical electric fields E∼m2πc3/eh-bar are present in the narrow transition layer near the core surface.