  Electron-electron correlation forms the basis of difficulties encountered in
many-body problems. Accurate treatment of the correlation problem is likely to
unravel some nice physical properties of matter embedded in this correlation.
In an effort to tackle this many-body problem, an exact partition function for
the correlation energy between two interacting states is proposed in this
study. Using this partition function, a model potential for a two-electron
system is derived. The model potential can accurately reproduce the singlet
states of a singly excited neutral helium atom with one of its electrons frozen
in the $1s$ orbital.
