Abstract
A method to calculate the self-consistent field (SCF) potential and wave functions for atoms and ions in analytical forms is described. The numerical SCF potential for atoms and ions is fitted to an analytical function by the use of the nonlinear least-squares method. The SCF wave functions are obtained numerically by solving the Schrödinger equation with the analytical SCF potential. The analytical wave functions are calculated with the nonlinear least-squares fitting technique. The obtained results are tested by comparing energy eigenvalues and radiative transition probabilities with those from numerical calculations.
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