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Elastic Scattering of Electrons by Helium Atoms in Born Approximation
American Journal of Modern Physics
Volume 9, Issue 6, November 2020, Pages: 77-83
Received: Nov. 7, 2020; Accepted: Dec. 2, 2020; Published: Dec. 8, 2020
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Saidou Diallo, 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
Ibrahima Gueye Faye, 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
Ismaila Diedhiou, Department of Physics, Faculty of Sciences, University Cheikh Anta Diop, Dakar, Senegal
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Elastic scattering phenomena arising in electron-helium scattering are dominant processes. The determination of accurate elastic differential cross sections for electron-helium scattering has a considerable importance. An accurate calculation of the plane-wave first Born exchange amplitude of electrons elastic scattering by helium atoms is reported. The direct and exchange amplitudes are calculated analytically from the Hartree-Fock orbital wave functions by using a variational method. The forms of these wave functions are very suitable for analytical calculations and powerful to generalize to more complex atomic systems. The interaction potential is modelled by the static Coulomb interaction between the incident electron and the atomic system. The differential cross sections are calculated at intermediate energies taking into account the exchange effects. We have established in the high energies region, by neglecting the exchange effects, the analytical expressions of the total and momentum transport cross sections suitable for the calculation of the plasma transport properties. A very compact form of the Born amplitude has been proposed as a finite series of Gaussian functions, which represents a major tool in the calculations of differential cross sections of two-electron atomic systems. Numerical results are used to analyze the contribution of the exchange amplitude to the differential cross sections at intermediate and high energies. The differential cross sections are calculated for the energy range 30-400 eV. We find good agreement in high energy domain scattering with experimental results and other sophisticated calculations without using any adjustable parameter.
Differential Cross Section, Elastic Scattering, Exchange Amplitude, Electron Transport, Helium
To cite this article
Saidou Diallo, Louis Gomis, Ibrahima Gueye Faye, Moustapha Sadibou Tall, Ismaila Diedhiou, Elastic Scattering of Electrons by Helium Atoms in Born Approximation, American Journal of Modern Physics. Vol. 9, No. 6, 2020, pp. 77-83. doi: 10.11648/j.ajmp.20200906.11
Copyright © 2020 Authors retain the copyright of this article.
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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