On variational solution of the four-body Santilli-Shillady model of H₂ molecule

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In this paper, we apply Ritz variational approach to a new isochemical model of H₂ molecule suggested by Santilli and Shillady. We studied Gaussian, Vg, and exponential, Vₑ, screened Coloumb potential approximations, as well as the original Hulten potential, Vₕ, case. Both the Coloumb and exchange integrals have been calculated only for Vₑ owing to Gegenbauer expansion while for Vg and Vₕ cases we achieved analytical results only for the Coloumb integrals. We conclude that the Vₑ-based model is capable to fit experimental data on H₂ molecule in confirmation of the results of numerical HFR approach by Santilli and Shillady. Also, we achieved the energy-based estimation of the weight of the isoelectronium phase which is appeared to be of the order of 1%...6%, for the case of Vₑ. However, we note that this is not the result corresponding to the original Santilli-Shillady model, which is based on the Hulten potential Vₕ. An interesting result is that in order to prevent divergency of the Coloumb integral for Vₕ the correlation length parameter rc should run discrete set of values. We used this condition in our Vₑ-based model.