An-Najah National University

Professor Sami M. AL-Jaber - Physics Department

Editorial Board member of Journal of Modern Physics (JMP). Recipient of PFDP Teaching Excellence Award 2010.

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  • Wednesday, September 15, 2010
  • Variational method for ground-state energy of helium atom in N dimensions
  • Published at:IL NUOVO CIMENTO Vol. 125 B, N. 9, (2010).
  • Sami M. AL-Jaber(∗)
    Department of Physics, An-Najah National University - P.O. Box 7, Nablus, Palestine.


    Abstract: The ground-state energy of the N-dimensional helium atom is presented
    by applying the variational principle. The calculations are made for the
    unscreened and screened cases. It is shown that, in both cases, the magnitude of
    the ground-state energy decreases (less negative) as the spatial dimension N increases.
    For the unscreened case, the relative contribution of the electron-electron
    interaction term to the ground-state energy is calculated for different dimensions,
    and it is found that this ratio approaches one half as N → ∞. For the screened
    case, the effective nuclear charge is computed for different dimensions and its limiting
    value is found to be 3/2 in the infinite-dimensional space. In addition, the
    relative contribution of screening to ground-state energy is calculated in different
    dimensions and it is shown that it reaches 1/8 as N →∞. Furthermore, the asymptotic
    behavior of ground-state energy, contribution of electron-electron interaction
    and contribution of screening effect are presented.

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Sami Mohammad Jaber
Theoretical Physics
Professor, Theoretical Physics, Physics Department, AN-Najah National UniversityNablus, Palestine.
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