  Various strong coupling theories of the one-component plasma have
successfully predicted the thermodynamic and structural properties by
separating the Coulomb potential into short- and long-ranged parts in {\itshape
ad hoc} ways. Moreover, it has been demonstrated that the density-density
correlation function in a mimic system with only the short-ranged interactions
resembles that of the full Coulomb system, revealing that the van der Waals
picture applies to the strongly coupled Coulomb systems. Here we provide a
variational theory forming the basis of the van der Waals picture. Our approach
provides hybrid formulations which combine both the liquid state theory and
statistical field theory; essential use is made of the coarse-grained system
with only long-raged part of Coulomb interactions as a reference system in
introducing both lower bound variational principle and strong coupling
expansion.
