Gradient-free representation of the Weizsäcker term for atoms

It has been demonstrated that the Weizs\"acker inhomogeneity term may be replaced by a gradient-free form for atomic systems. This forms a realization of a previous conjecture made by the authors [Phys. Rev. A 25 668 (1982)]. In the variational context, numerical computations have been performed with such a representation with the first-row atoms employed at test cases. The resulting energies are seen to match very well with their Hartree-Fock counterparts.