- 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.