Thomas-Fermi theory of an inhomogeneous electron liquid generalized to incorporate density gradients
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abstract
Motivated by exact results for many closed shells in a bare Coulomb field, a generalization of the Thomas-Fermi statistical model is proposed. This generalization includes density gradients in the density-potential relation, and offers the possibility of avoiding the singularity (of the original method) in the density at an atomic nucleus and of embodying Kato's theorem.