Absence of a Scott Correction for the Total Binding Energy of Noninteracting Fermions in a Smooth Potential Well

Author: Huxtable, Barton Duane

Year: 1988

Degree: Dissertation (Ph.D.)

Advisor: Simon, Barry M.

Committee Members: Simon, Barry M.; Barnes, Charles A.; Cross, Michael Clifford; Koonin, Steven E.

Option: Physics

DOI: 10.7907/87FQ-5X29

Abstract

It is shown, for V in a particular class of smooth functions, that the total binding energy, E(Z), of Z noninteracting Fermions in the potential well Z^4/3V(Z^1/3x), obeys E(Z) = c_TF(V)Z^7/3 + 0(Z^5/3) as Z → ∞. Here c_TF(V) is the coefficient predicted by the Thomas-Fermi theory. This result is consistent with the conjectured Scott correction, which occurs at order Z², to the total binding energy of an atom of atomic number Z. This correction is thought to arise only because V(x) ~ - |x|¹ near x - 0 in the atomic problem, and so V is not a smooth function.

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