Collective electronic pulsation around giant nuclei in the Thomas-Fermi model

Based on the Thomas-Fermi solution for compressed electron gas around a giant nucleus, 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, and Maxwell's equations, as well as physical boundary conditions, and assume the nucleons in β-equilibrium at nuclear density. We particularly study the configuration of ultra-relativistic electrons with a large fraction contained within the nucleus. Such configurations can be realized for a giant nucleus or high external compression on the electrons. The lowest modes turn out to be heavily influenced by the relativistic plasma frequency induced by the positive charge background in the nucleus. Our results can be applied to heavy nuclei in the neutron star crust, as well as to the whole core of a neutron star. We discuss the possibility to apply our results to dynamic nuclei using the spectral method.