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.
| Published in | American Journal of Modern Physics (Volume 8, Issue 4) |
| DOI | 10.11648/j.ajmp.20190804.12 |
| Page(s) | 66-71 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2019. Published by Science Publishing Group |
Helium, Variational Method, Correlation Effect, Charge Distribution, Scattering
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APA Style
Saïdou Diallo, Ibrahima Gueye Faye, Louis Gomis, Moustapha Sadibou Tall, Ismaïla Diédhiou. (2019). Atomic Form Factor Calculations of S-states of Helium. American Journal of Modern Physics, 8(4), 66-71. https://doi.org/10.11648/j.ajmp.20190804.12
ACS Style
Saïdou Diallo; Ibrahima Gueye Faye; Louis Gomis; Moustapha Sadibou Tall; Ismaïla Diédhiou. Atomic Form Factor Calculations of S-states of Helium. Am. J. Mod. Phys. 2019, 8(4), 66-71. doi: 10.11648/j.ajmp.20190804.12
AMA Style
Saïdou Diallo, Ibrahima Gueye Faye, Louis Gomis, Moustapha Sadibou Tall, Ismaïla Diédhiou. Atomic Form Factor Calculations of S-states of Helium. Am J Mod Phys. 2019;8(4):66-71. doi: 10.11648/j.ajmp.20190804.12
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Download@article{10.11648/j.ajmp.20190804.12,
author = {Saïdou Diallo and Ibrahima Gueye Faye and Louis Gomis and Moustapha Sadibou Tall and Ismaïla Diédhiou},
title = {Atomic Form Factor Calculations of S-states of Helium},
journal = {American Journal of Modern Physics},
volume = {8},
number = {4},
pages = {66-71},
doi = {10.11648/j.ajmp.20190804.12},
url = {https://doi.org/10.11648/j.ajmp.20190804.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20190804.12},
abstract = {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.},
year = {2019}
}
TY - JOUR T1 - Atomic Form Factor Calculations of S-states of Helium AU - Saïdou Diallo AU - Ibrahima Gueye Faye AU - Louis Gomis AU - Moustapha Sadibou Tall AU - Ismaïla Diédhiou Y1 - 2019/10/15 PY - 2019 N1 - https://doi.org/10.11648/j.ajmp.20190804.12 DO - 10.11648/j.ajmp.20190804.12 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 66 EP - 71 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.20190804.12 AB - 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. VL - 8 IS - 4 ER -
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