Exact Solution of the Three-Body Santilli-Shillady Model of the Hydrogen Molecule

The conventional representation of the H 2 molecule characterizes a 4-body system due to the independence of the orbitals of the two valence electrons as requested by quantum chemistry, under which conditions no exact solution is possible. To overcome this problem, Santilli and Shillady introduced in 1999 a new model of the H 2 -molecule in which the two valence electrons are deeply bounded-correlated into a single quasi-particle they called isoelectronium that is permitted by the covering hadronic chemistry. They pointed out that their new H 2 -model is a restricted 3-body system that, as such, is expected to admit an exact solution and suggested independent studies for its identification due to its relevance, e.g., for other molecules. In 2000, Aringazin and Kucherenko did study the Santilli-Shillady restricted 3-body model of the H 2 molecules, but they presented a variational solution that, as such, is not exact. In any case, the latter approach produced significant deviations from experimental data, such as a 19.6% inter-nuclear distance greater than the experimental value. In this paper we present, apparently for the first time, an exact solution of the Santilli-Shillady restricted 3-body model of the Hydrogen molecule along the lines of its originators and show that it does indeed represent correctly all basic data. Intriguingly, our solution confirms that the orbital of the isoelectronium (referred to as its charge distribution around the nuclei) must be concentrated in a limited region of space given by the Santilli-Shillady oo-shaped orbits. Our exact solution is constructed by following the Ley-Koo solution to the Schr¨ odinger equation for a confined hydrogen molecular ion, H + . We show that a confined model to the 3-body molecule reproduces the ground state curve as calculated by Kolos, Szalewics and Monkhorst with a precision up to the 4-th digit and a precision in the representation of the binding energy up to the 5-th digit.