Atomic Properties of the Two-Electron System using Variational Monte Carlo Technique

S.B. Domaa and F.N. El-Gammalb aMathematics Department, Faculty of Science, Alexandria University, Alexandria, Egypt bMathematics Department, Faculty of Science, Menofia University, Shebin El-Kom, Egypt

Received: September 25, 2011

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Using variational Monte Carlo method we calculated the lowest order relativistic corrections for the ground state energies of the helium-like atoms, up to Z = 10, and also for some excited state energies of the helium atom. These relativistic corrections include: mass-velocity effect, orbit-orbit interaction, spin magnetic and dipole moments of the two electrons and the Darwin effect. Moreover, correction due to the nucleus motion has been also calculated. Our results were obtained by using two new types of compact and accurate trial wave functions for the helium ions. For excited states we used simple trial wave functions of good quality and accurate results. The obtained results are in good agreement with the most recent previous accurate values and also with the exact values.

DOI: 10.12693/APhysPolA.122.42 PACS numbers: 02.70.-c, 31.15.-p, 31.15.B-