  The Poisson-Boltzmann (PB) theory is widely used to depict ionic systems. As
a mean-field theory, the PB theory neglects the correlation effect in the ionic
atmosphere and leads to deviations from experimental results as the
concentration or charge valance increases. A modified PB theory including ion
correlation effect while retaining its simplicity is critical for many
important applications in which ion correlation effect can be significant. In
this paper, we present a new model to incorporate ion correlations into the
original PB equation by utilizing the Green's function with a non-linear form
of the self-energy, which is different from the linear self-energy equation
obtained by the Field-Theoretic (FT) approach. Both equations are solved
numerically and compared with our molecular dynamics (MD) simulation. The
co-ion distribution calculated by the FT approach deviates significantly from
the MD simulation, while our results for both counter-ion and co-ion
distributions are justified by the MD simulation.
