On the Weizsäcker Correction to the Thomas-Fermi Theory of the Atom

In order to investigate the validity of the Weizsäcker correction to the Thomas-Fermi theory of the atom, the problem in which the Weizsäcker correction is multiplied by a constant weighting factor λ is solved for the atom neglecting the interactions between electrons completely, in view of the fact that the Weizsäcker term is essentially the correction to the statistical expression of the kinetic energy of electrons. The energy values thus obtained are compared with the exact quantum mechanical values, and it is shown that the Weizsäcker term is too large in its original form and a weighting factor λ≈1/5 (in contrast to the Kirzhnits' conclusion λ≈1/9) is necessary to give a substantial improvement over the Thomas-Fermi solution.