Title: A Z-dependent variational solution of Thomas-Fermi-Dirac equation

Authors: O.H. Mobarek, A.Z. Alzahrani

Addresses: Department of Physics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. ' Department of Physics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Abstract: Using Thomas-Fermi-Dirac equation within the exchange-correlation scheme and a Z-dependent trial solution, the ground state binding energy for neutral, positively, and negatively charged atoms are calculated. Comparing to the results obtained in earlier works, the values of the binding energy estimated here for both light and heavy atoms agree nicely with the Hartree-Fock values. We have also calculated the radial expectation values and diamagnetic susceptibilities for some neutral and single ionised atoms. Our results are compared with the available theoretical and experimental findings.

Keywords: Thomas-Fermi-Dirac equation; Z-dependent variational principle; binding energy; exchange correlation; diamagnetic susceptibility; heavy atoms; light atoms; neutral atoms.

DOI: 10.1504/IJMMNO.2011.037200

International Journal of Mathematical Modelling and Numerical Optimisation, 2011 Vol.2 No.1, pp.69 - 84

Published online: 30 Nov 2010 *

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