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Based on the Thomas-Fermi solution for compressed electron gas around a giant nucleus, $Zapprox 10^6$, 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 Maxwells equations, as well as physical boundary conditions. We choose a proton number of $Z=10^6$ and assume the nucleons in $beta$-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.
We derive and solve by the spectral method the equations for a neutral system of ultra-relativistic electrons that are compressed to the radius of the nucleus and subject to a driving force. This driving force can be thought of as originating from a
We have studied the collective plasma excitations of a two-dimensional electron gas with an arbitrary lateral charge-density modulation. The dynamics is formulated using a previously developed hydrodynamic theory based on the Thomas-Fermi-Dirac-von W
We predict the emergence of novel collective electronic excitations in warm dense matter with an inhomogeneous electronic structure based on first-principles calculations. The emerging modes are controlled by the imposed perturbation amplitude. They
Bright sources of high energy electromagnetic radiation are widely employed in fundamental research as well as in industry and medicine. This steadily growing interest motivated the construction of several facilities aiming at the realisation of sour
We present a general method for obtaining the exact static solutions and collective excitation frequencies of a trapped Bose-Einstein condensate (BEC) with dipolar atomic interactions in the Thomas-Fermi regime. The method incorporates analytic expre