  In this paper, we study the exact solution of the restricted isochemical
model of $H_2$ molecule with fixed nuclei recently proposed by Santilli and
Shillady in which the two electrons are assumed to be bonded/correlated into a
quasiparticle called the {\it isoelectronium}. Under the conditions that: 1)
the isoelectronium is stable; 2) the effective size of the isoelectronium is
ignorable, in comparison to internuclear distance; and 3) the two nuclei are at
rest, the Santilli-Shillady model of the $H_2$ molecule is reduced to a
restricted {\it three-body} system essentially similar to a neutral version of
the $H_2^+$ ion, which, as such, admits exact solution. Our main result is that
the restricted three-body Santilli-Shillady approach to $H_2$ is capable to fit
the experimental binding energy, at the isoelectronium mass parameter
$M=0.308381m_e$, although under optimal internuclear distance about 19.6%
bigger than the conventional experimental value, indicating an approximate
character of the three-body model.
