Exact solution of the restricted three-body Santilli-Shillady model of $H_2$ molecule

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.