巨核周围的集体电子脉动
Collective electronic pulsation around giant nuclei in the Thomas-Fermi model
摘要：
本文从巨核周围压缩电子气的Escheras-Fermi解$Z\approx 10^6$出发，研究了外界扰动作用于核或电子本身所引起的电子数密度、压强和电场的电脉动。我们数值计算得到了满足电子数和能量动量守恒、状态方程、热力学热力学定律和麦克斯韦方程所建立的边值问题以及物理边界条件的定态脉动模的本征频率和本征函数。我们选择质子数为$Z=10^6$，并假设核子在核密度下处于$β$平衡。类似的非球形几何系统被假设存在于中子星的下地壳中，通常被称为\textit{pasta equation of state}。结果表明，最低模受原子核中正电荷背景所引起的相对论等离子体频率的影响很大。我们讨论了将我们的结果应用于动态核的光谱方法的可能性，并提到机制，可以刺激这种动态的天体物理背景下。
英文摘要：
Based on the Thomas-Fermi solution for compressed electron gas around a giant nucleus, $Z\approx 10^6$, we study electric pulsations of electron number-density, pressure and electric fields, which could be caused by an external perturbations acting on the nucleus or the electrons themselves. We numerically obtain the eigen-frequencies and eigen-functions for stationary pulsation modes that fulfill the boundary-value problem established by electron-number and energy-momentum conservation, equation of state, laws of thermodynamics, and Maxwell's equations, as well as physical boundary conditions. We choose a proton number of $Z=10^6$ and assume the nucleons in $β$-equilibrium at nuclear density. Similar systems with non-spherical geometry are hypothesized to exist in the lower crust of neutron stars, commonly referred to as \textit{pasta equation of state}. The lowest modes turn out to be heavily influenced by the relativistic plasma frequency induced by the positive charge background in the nucleus. We discuss the possibility to apply our results to dynamic nuclei using the spectral method and mention mechanisms that could stimulate such dynamics in the astrophysical context.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
