  We present a generalized nonlinear theory for large amplitude electrostatic
(ES) ion shocks in collisional quantum plasmas composed of mildly coupled
degenerate electron fluids of arbitrary degeneracy and non-degenerate strongly
correlated ion fluids with arbitrary atomic number. For our purposes, we use
the inertialess electron momentum equation including the electrostatic,
pressure gradient and relevant quantum forces, as well as a generalized
viscoelastic momentum (GVEM) equation for strongly correlated non-degenerate
ions. The ion continuity equation, in the quasi-neutral approximation, then
closes our nonlinear system of equations. When the electric field is eliminated
from the GVEM equation by using the inertialess electron momentum equation, we
then obtain a generalized GVEM and the ion continuity equations exhibiting
nonlinear couplings between the ion number density and the ion fluid velocity.
The pair of nonlinear equations is numerically solved to study the dynamics of
arbitrary large amplitudes planar and non-planar ES shocks arising from the
balance between harmonic generation nonlinearities and the ion fluid viscosity
for a wide range of the plasma mass-density and the ion atomic-number that are
relevant for the cores of giant planets (viz. the Jupiter) and compact stars
(viz. white dwarfs). Our numerical results reveal that the ES shock density
profiles strongly depend on the plasma number density and composition (the
atomic-number) parameters. Furthermore, density perturbations propagate with
Mach numbers which significantly dependent on the studied plasma fractional
parameters. It is concluded that the dynamics of the ES shocks in the
super-dense degenerate plasma is quite different in the core of a white dwarf
star from that in the lower density crust region.
