  We study thermal equilibrium of classical pointlike counterions confined
between symmetrically charged walls at distance $d$. At very large couplings
when the counterion system is in its crystal phase, a harmonic expansion of
particle deviations is made around the bilayer positions, with a free lattice
parameter determined from a variational approach. For each of the two walls,
the harmonic expansion implies an effective one-body potential at the root of
all observables of interest in our Wigner Strong-Coupling expansion. Analytical
results for the particle density profile and the pressure are in good agreement
with numerical Monte Carlo data, for small as well as intermediate values of
$d$ comparable with the Wigner lattice spacing. While the strong-coupling
theory is extended to the fluid regime by using the concept of a correlation
hole, the Wigner calculations appear trustworthy for all electrostatic
couplings investigated. Our results significantly extend the range of accuracy
of analytical equations of state for strongly interacting charged planar
interfaces.
