The Airy gas model is used to derive an expression for the local kinetic energy in the linear potential approximation. The expression contains an explicit Laplacian term $\frac{2}{5}({ħ}^2/2m){\nabla }_{\mu }^2\left(\mathbf{r}\right)$ that, according to jellium surface calculations, must be a universal feature of any accurate local description. Applied to the noble gases the expression reduces the errors by a factor of $50$ over previous results obtained by the linear potential approximation.

• Received 30 November 1999

DOI:https://doi.org/10.1103/PhysRevA.61.052511