An-Najah Staff

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.