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Abstract
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In this paper, we investigate the resonant scattering of driven linear oscillations in an isothermal electron gas with an arbitrary degree of
degeneracy. The coupled pseudoforce system is obtained from the quantum hydrodynamic model and is extended to include the driving
pseudoforce and pseudodamping effect in order to study the quantum charge shielding on the resonant scattering, heat capacity, and Friedel
oscillations around an impurity charge. It is shown that the resonant scattering phenomenon takes place when the driver wavelength matches
either scale lengths of plasmon excitations, which arise due to single electron oscillations and collective electron plasma excitations. It is
remarked that in the presence of a periodic density structure such as in metals, plasmon interactions with a periodic lattice structure can lead to
resonant Bragg-like scattering. A generalized energy dispersion relation for pseudodamped plasmon excitations is obtained, which indicates a
critical screening point beyond which the plasmon excitations behave only particlelike. It is shown that the heat capacity of plasmon excitations
and the static quantum charge screening are strongly affected by interaction between the plasmon and the charge screening scale lengths.
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