dorsal/arxiv
View SchemaOn variational solution of the four-body Santilli-Shillady model of $H_2$ molecule
| Authors | A. K. Aringazin |
|---|---|
| Categories | |
| ArXiv ID | physics/0001057 |
| URL | https://arxiv.org/abs/physics/0001057 |
| Journal | Hadronic J. 23 (2000) 59 |
Abstract
In this paper, we apply Ritz variational approach to a new isochemical model of $H_2$ molecule suggested by Santilli and Shillady. We studied Gaussian, $V_g$, and exponential, $V_e$, screened Coloumb potential {\it approximations}, as well as the original Hulten potential, $V_h$, case. Both the Coloumb and exchange integrals have been calculated only for $V_e$ owing to Gegenbauer expansion while for $V_g$ and $V_h$ cases we achieved analytical results only for the Coloumb integrals. We conclude that the $V_e$-based model is capable to fit experimental data on $H_2$ 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 $V_e$. However, we note that this is {\it not} the result corresponding to the original Santilli-Shillady model, which is based on the Hulten potential $V_h$. An interesting result is that in order to prevent divergency of the Coloumb integral for $V_h$ the correlation length parameter $r_c$ should run discrete set of values. We used this condition in our $V_e$-based model.
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"abstract": "In this paper, we apply Ritz variational approach to a new isochemical model\nof $H_2$ molecule suggested by Santilli and Shillady. We studied Gaussian,\n$V_g$, and exponential, $V_e$, screened Coloumb potential {\\it approximations},\nas well as the original Hulten potential, $V_h$, case. Both the Coloumb and\nexchange integrals have been calculated only for $V_e$ owing to Gegenbauer\nexpansion while for $V_g$ and $V_h$ cases we achieved analytical results only\nfor the Coloumb integrals. We conclude that the $V_e$-based model is capable to\nfit experimental data on $H_2$ molecule in confirmation of the results of\nnumerical HFR approach by Santilli and Shillady. Also, we achieved the\nenergy-based estimation of the weight of the isoelectronium phase which is\nappeared to be of the order of 1%...6%, for the case of $V_e$. However, we note\nthat this is {\\it not} the result corresponding to the original\nSantilli-Shillady model, which is based on the Hulten potential $V_h$. An\ninteresting result is that in order to prevent divergency of the Coloumb\nintegral for $V_h$ the correlation length parameter $r_c$ should run discrete\nset of values. We used this condition in our $V_e$-based model.",
"arxiv_id": "physics/0001057",
"authors": [
"A. K. Aringazin"
],
"categories": [
"physics.gen-ph"
],
"journal_ref": "Hadronic J. 23 (2000) 59",
"title": "On variational solution of the four-body Santilli-Shillady model of $H_2$ molecule",
"url": "https://arxiv.org/abs/physics/0001057"
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