  We study a classical system of identically charged counter-ions near a planar
wall carrying a uniform surface charge density. The equilibrium statistical
mechanics of the system depends on a single dimensionless coupling parameter. A
new self-consistent theory of the correlation-hole type is proposed which leads
to a modified Poisson-Boltzmann integral equation for the density profile,
convenient for analytical progress and straightforward to solve numerically.
The exact density profiles are recovered in the limits of weak and strong
couplings. In contrast to previous theoretical attempts of the test-charge
family, the density profiles fulfill the contact-value theorem at all values of
the coupling constant, and exhibit the mean-field decay at asymptotically large
distances from the wall, as expected. We furthermore show that the density
corrections at large couplings exhibit the proper dependence on coupling
parameter and distance to the charged wall. The numerical results for
intermediate values of the coupling provide accurate density profiles which are
in good agreement with those obtained by Monte-Carlo simulations. The crossover
to mean-field behavior at large distance is studied in detail.
