Sami M. AL-Jaber(∗)

Department of Physics, An-Najah National University - P.O. Box 7, Nablus, Palestine


Summary. 

— 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.


1. – Introduction

 2. – The helium atom in N dimensions: preliminaries 

 3. – Variational method without screening

4. – Variational method with screening

  5. – Conclusions


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https://staff.najah.edu/media/sites/default/files/Variational_Method_For_Ground-State_Energy_Of_Helium_Atom_In_N_Dimensions.pdf