Thomas-Fermi calculations for atoms in high magnetic field using realistic model

An approximate solution of the Thomas-Fermi equation for positive ions in a high magnetic field is obtained by making use of the variational principle. The radial wavefunctions of the hydrogen-like atom are used as the trial function that contains some variational parameters and satisfies the appropriate boundary and the normalization conditions. These parameters are determined, by externalizing the variational expression with respect to the parameters. These parameter values are then used to obtain the desired physical quantities. The initial slope of the variational trial function for several ions is obtained from which the energy and the ionization energy can be found. The results of the present calculation are in good agreement with those available in literature.