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arXiv · 1002.4810

From super-charged nuclei to massive nuclear density cores

Vladimir Popov
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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 $V_0=-(3π^2 n_p)^{1/3} \sim -2m_πc^2$, 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 $λ\approx α^{-1/2} \hbar/m_π c\sim 15$ fm, which is independent of $Z (\hbar/m_π c \ll λ\ll \hbar/m_e c)$. The electric field and surface charge are concentrated in this layer. These results, obtained earlier for hypothetical superheavy nuclei with $Z \sim A/2\la 10^4 ÷10^6$, 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 $E\sim m^2_π c^3/e\hbar$ are present in the narrow transition layer near the core surface.

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Vladimir Popov. 2010-02-25. From super-charged nuclei to massive nuclear density cores. https://doi.org/10.1063/1.3382318

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