大质量核密度核的相对论稳定性和电动力学稳定性
On the relativistic and electrodynamical stability of massive nuclear density cores
摘要：
我们提出了一个统一的处理核密度核心恢复中性原子与重核具有质量数$A\approx 10^2--10^6$的经典结果，并将这些结果外推到大量的核密度核心与$A\approx(m_{\rm Planck}/m_n)^3 \sim 10^{57}$。该处理包括解决相对论性的P-Fermi方程描述的$N_n$中子，$N_p$质子和$N_e$电子的β衰变平衡系统。$N_p$质子以恒定密度分布在半径为$R_c$的球形核内。发现了$A > A_R = 0.039(N_p/A)^{1/2}(m_{Planck}/m_n)^3$的一个新的稳定岛。库仑排斥，屏蔽相对论电子，是平衡的重力自我相互作用的核心。与重核类似，它们在靠近表面处呈现出超临界电场。将$A$和$N_p$之间的关系推广到质量数的任意值，并作为极限情况得到了$A < 1.5\cdot 10^2$的唯象关系。
英文摘要：
We present a unified treatment of nuclear density cores recovering the classic results for neutral atoms with heavy nuclei having a mass number $A\approx 10^2--10^6$ and extrapolating these results to massive nuclear density cores with $A\approx(m_{\rm Planck}/m_n)^3 \sim 10^{57}$. The treatment consists of solving the relativistic Thomas-Fermi equation describing a system of $N_n$ neutrons, $N_p$ protons and $N_e$ electrons in beta decay equilibrium. The $N_p$ protons are distributed at a constant density within a spherical core of radius $R_c$. A new island of stability is found for $A > A_R = 0.039(N_p/A)^{1/2}(m_{Planck}/m_n)^3$. The Coulomb repulsion, screened by relativistic electrons, is balanced by the gravitational self-interaction of the core. In analogy to heavy nuclei they present, near their surface, an overcritical electric field. The relation between $A$ and $N_p$ is generalized to an arbitrary value of the mass number, and the phenomenological relations for $A < 1.5\cdot 10^2$ are obtained as a limiting case.
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