On the Validity of the Weizs cker Inhomogeneity Correction Term

An investigation is made of Weizsacker's correction to the Thomas-Fermi statistical treatment of the many-body problem. Numerical solutions of Weizsäcker's equation were obtained for the isotropic harmonic oscillator and the step potential in plane symmetry. These particular potentials were chosen as approximations to nuclear potentials. In the case of the harmonic oscillator, the error in the energy is an order of magnitude greater than for the Thomas-Fermi equation, but a reduction in the magnitude of the Weizsäcker correction term by a factor of fraction one-eighth gives substantial improvement over the Thomas-Fermi solution. The step potential also shows that the Weizsäcker term is too great, but the reduction factor necessary to give substantial improvement is between ½ and 1. It is concluded that the Weizsäcker correction term is not reliable as such, but that a reduction in the magnitude of the term may give plausible solutions for the density. The reduction factor depends, however, upon the form of the potential.