Elastic Scattering of Electrons by Helium Atoms in Born Approximation
Saidou Diallo,
Louis Gomis,
Ibrahima Gueye Faye,
Moustapha Sadibou Tall,
Ismaila Diedhiou
Issue:
Volume 9, Issue 6, November 2020
Pages:
77-83
Received:
7 November 2020
Accepted:
2 December 2020
Published:
8 December 2020
Abstract: 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.
Abstract: 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...
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A Theoretical Explanation on Gell-Mann-Nishijima Formula with Singular Number and the Establishment of Lepton Quantum Number Constrained Equation
Issue:
Volume 9, Issue 6, November 2020
Pages:
84-90
Received:
11 November 2020
Accepted:
1 December 2020
Published:
8 December 2020
Abstract: In this paper, two fundamental problems of particle physics are studied theoretically. The first one is: to solve the problem of establishing general quantum number constrained equation, the symmetry transformation mechanism of charge eigenstates for elementary particles is adopted, and the general quantum number constrained equations are established, which are applicable to physical particles. For hadrons, an equation is completely consistent with Gell-Mann-Nishijima formula. For leptons, the lepton quantum numbers are exactly the solutions of an equation, which is just the lepton quantum number constrained equation. The second problem is: to solve the problem of understanding singularity and calculating singular numbers, a hypothesis that a composite particle may has virtual structure is proposed. According to this hypothesis, the singular particles must be composite particles, and have virtual structures. In a virtual structure, the particles and antiparticles of component particles can form particle-antiparticle pairs, which have great influence such as improving mass and changing life of composite particles. Therefore, the composite particle with particle-antiparticle pairs in its virtual structure is singular particle, and the singular number is the number of particle-antiparticle pairs. These two theoretical results are in good agreement with the already achieved experimental results of particle physics, can explain the related phenomena of physical particles from a deeper physical mechanism, and theoretically predict the existence of singular leptons and several new singular hadrons.
Abstract: In this paper, two fundamental problems of particle physics are studied theoretically. The first one is: to solve the problem of establishing general quantum number constrained equation, the symmetry transformation mechanism of charge eigenstates for elementary particles is adopted, and the general quantum number constrained equations are establish...
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