  An approximate analytical solution to the fluctuation potential problem in
the modified Poisson-Boltzmann theory of electrolyte solutions in the
restricted primitive model is presented. The solution is valid for all
inter-ionic distances, including contact values. The fluctuation potential
solution is implemented in the theory to describe the structure of the
electrolyte in terms of the radial distribution functions, and to calculate
some aspects of thermodynamics, viz., configurational reduced energies, and
osmotic coefficients. The calculations have been made for symmetric valence 1:1
systems at the physical parameters of ionic diameter $4.25 \times 10^{-10}$ m,
relative permittivity 78.5, absolute temperature 298 K, and molar
concentrations 0.1038, 0.425, 1.00, and 1.968. Radial distribution functions
are compared with the corresponding results from the symmetric
Poisson-Boltzmann, and the conventional and modified Poisson-Boltzmann
theories. Comparisons have also been done for the contact values of the radial
distributions, reduced configurational energies, and osmotic coefficients as
functions of electrolyte concentration. Some Monte Carlo simulation data from
the literature are also included in the assessment of the thermodynamic
predictions. Results show a very good agreement with the Monte Carlo results
and some improvement for osmotic coefficients and radial distribution functions
contact values relative to these theories. The reduced energy curve shows
excellent agreement with Monte Carlo data for molarities up to 1 mol/dm$^{3}$.
