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Atomic Form Factor Calculations of S-states of Helium
American Journal of Modern Physics
Volume 8, Issue 4, July 2019, Pages: 66-71
Received: Sep. 12, 2019; Accepted: Oct. 4, 2019; Published: Oct. 15, 2019
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Saïdou Diallo, Department of Physics, Faculty of Sciences, University Cheikh Anta Diop, Dakar, Senegal
Ibrahima Gueye Faye, Department of Physics, Faculty of Sciences, University Cheikh Anta Diop, Dakar, Senegal
Louis Gomis, Department of Physics, Faculty of Sciences, University Cheikh Anta Diop, Dakar, Senegal
Moustapha Sadibou Tall, Department of Physics, Faculty of Sciences, University Cheikh Anta Diop, Dakar, Senegal
Ismaïla Diédhiou, Department of Physics, Faculty of Sciences, University Cheikh Anta Diop, Dakar, Senegal
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Variational calculations of the helium atom states are performed using highly compact 26-parameter correlated Hylleraas-type wave functions. These correlated wave functions used here yield an accurate expectation energy values for helium ground and two first excited states. A correlated wave function consists of a generalized exponential expansion in order to take care of the correlation effects due to N-corps interactions. The parameters introduced in our model are determined numerically by minimization of the total atomic energy of each electronic configuration. We have calculated all integrals analytically before dealing with numerical evaluation. The 1S2 11S and 1S2S 21, 3S states energies, charge distributions and scattering atomic form factors are reported. The present work shows high degree of accuracy even with relative number terms in the trial Hylleraas wave functions definition. The results presented here, indicate that the highly compact twenty-six variational parameters model will have the quantitative and qualitative applicability for the study of electronic correlation. The correlated wave functions are used to calculate the atomic form factor for the diffusion of electrons by the helium atom. The atomic form factor is evaluated as the Fourier transform of the electron density distribution of an atom or ion, which is calculated from theoretical correlated wave functions for free atoms. Finally, suggestions are made as to the way the atomic form factor of the helium atom may be approximated by a sum of Gaussians for efficiency use.
Helium, Variational Method, Correlation Effect, Charge Distribution, Scattering
To cite this article
Saïdou Diallo, Ibrahima Gueye Faye, Louis Gomis, Moustapha Sadibou Tall, Ismaïla Diédhiou, Atomic Form Factor Calculations of S-states of Helium, American Journal of Modern Physics. Vol. 8, No. 4, 2019, pp. 66-71. doi: 10.11648/j.ajmp.20190804.12
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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