  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
$\beta$-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.
