  Using the asymptotic iteration method (AIM) we investigate the variation in
the 1s energy levels of hydrogen and helium-like static ions in fully
degenerate electron gas. The semiclassical Thomas-Fermi (TF), Shukla-Eliasson
(SE) and corrected Shukla-Eliasson (cSE) models are compared. It is remarked
that these models merge into the vacuum level for hydrogen and helium-like ions
in the dilute classical electron gas regime. While in the TF model hydrogen
ground state level lifts monotonically towards the continuum limit with
increase in the electron concentration, in the SE and cSE models universal
bound stabilization valley through the energy minimization occurs at a
particular electron concentration range for the hydrogen-like ion which for cSE
model closely matches the electron concentrations in typical metals. The later
stabilizing mechanism appears to be due to the interaction between plasmon
excitations and the Fermi lengthscales in metallic density regime. In the case
of helium-like ions, however, no such stability mechanism is found. The
application of cSE model with electron exchange and correlation effects reveals
that cSE model qualitatively accounts for the number-density and lattice
parameters of elemental metals within the framework of free electron
assumption. According to the cSE model of static charge screening a simple
metal-insulator transition criterion is defined. Current investigation may
further elucidate the underlying physical mechanisms in the formation and
dielectric properties of metallic compounds.
