Modified Weizsäcker Corrections in Thomas-Fermi Theories

Abstract

We consider theories in which a kinetic-energy correction $\left(\frac{\lambda h^2}{32{\pi }^{2}m}\right)\left[\frac{{\left(\nabla \rho \right)}^2}{\rho }\right]$ ($\rho =\mathrm{density}$) is added to the usual Thomas-Fermi term. A treatment based on the WKB method and expected to be valid for large $\mathcal{r}$ shows $\lambda =1\mathrm{}$ here, as found experimentally. For small $\mathcal{r}$, $\lambda =1\mathrm{}$ is needed to give proper behavior of $\rho$, but other arguments suggest that the Thomas-Fermi term be dropped here.