  It is difficult to derive the solid-fluid transition theoretically from
microscopic models, although this phenomenon itself has been investigated for a
long time. We previously constructed an exactly-solvable model with the
solid-fluid transition. This model resembles the infinite-range (or mean-field)
model in spin systems in some points, hence it can be called a "mean-field
model" of the solid-fluid transition. In the present paper, we construct a
"mean-field approximation" of the solid-fluid transition by using the
"mean-field model" introduced in our previous study, and tries to describe the
phase transitions of the three-dimensional Lennard-Jones model as an example.
This approximation succeeds in describing the phase diagram which contains
three (gas, liquid, and fcc-solid) phase, at least qualitatively.
