From super-charged nuclei to massive nuclear density cores

Abstract

Due to $e^+e^-$-pair production in the field of supercritical $(Z \gg Z_{cr}\approx 170$) 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 Ze^3 \ga 1 within the framework of the Thomas-Fermi equation generalized to the relativistic case. For $Ze^3 \gg 1$ the electron shell penetrates inside the nucleus and almost completely screens its charge. Inside such nucleus the potential takes a constant value equal to $V_0=-(3\pi^2 n_p)^{1/3} \sim -2m_{\pi}c^2$, 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 $\lambda \approx \alpha^{-1/2} \hbar/m_{\pi} c\sim 15$ fm, which is independent of $Z (\hbar/m_{\pi} c \ll \lambda \ll \hbar/m_e c)$. The electric field and surface charge are concentrated in this layer. These results, obtained earlier for hypothetical superheavy nuclei with Z \sim A/2\la 10^4 \div 10^6, are extrapolated to massive nuclear density cores having a mass number $A \approx (m_{Planck}/m_n)\sim 10^{57}$. The problem of the gravitational and electrodynamical stability of such objects is considered. It is shown that for A \ga 0.04 (Z/A)^{1/2}(m_{Planck}/m_n)^3 the Coulomb repulsion of protons, screened by relativistic electrons, can be balanced by gravitational forces. The overcritical electric fields $E\sim m^2_{\pi} c^3/e\hbar$ are present in the narrow transition layer near the core surface.Comment: To appear in the proceedings of the international conference "The Sun, the Stars, The Universe and General Relativity" in honor of Ya.B. Zeldovich 95th Anniversary, held in Minsk, Belarus on April 20-23, 2009. AIP Conf. Proc. Vol. 1205 (2010