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

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.