标题： 从超充电核到大核密度核心 显示英文标题

标题： From super-charged nuclei to massive nuclear density cores

摘要： 由于在超临界$e^+e^-$核场中的$(Z \gg Z_{cr}\approx 170 $对产生，一个由真空产生的电子壳层形成。 根据推广到相对论情况的托马斯-费米方程，在超电荷核$Ze^3 \ga 1$中确定了这种壳层中真空电荷的分布。 对于$Ze^3 \gg 1$，电子壳层会穿透进入原子核，并几乎完全屏蔽其电荷。 在这种核内部，势能取一个等于$V_0=-(3\pi^2 n_p)^{1/3} \sim -2m_{\pi}c^2$的常数值，超电荷核表现为由$e,p$和$n$组成的电中性等离子体。 在核边缘附近存在一个宽度为$\lambda \approx \alpha^{-1/2} \hbar/m_{\pi} c\sim 15$fm 的过渡层，该宽度与$Z (\hbar/m_{\pi} c \ll \lambda \ll \hbar/m_e c)$无关。 电场和表面电荷集中在这一层。 这些结果先前是基于假设的超重核（$Z \sim A/2\la 10^4 \div 10^6$）得出的，并被外推到具有原子量$A \approx (m_{Planck}/m_n)\sim 10^{57}$的大核密度核心。 考虑了此类物体的引力和电磁稳定性问题。 研究表明，对于$A \ga 0.04 (Z/A)^{1/2}(m_{Planck}/m_n)^3$，由相对论电子屏蔽的质子的库仑排斥力可以被引力力量平衡。 过临界电场$E\sim m^2_{\pi} c^3/e\hbar$存在于靠近核表面的狭窄过渡层中。 显示英文摘要

摘要： 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.