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A convexified energy functional for
the Fermi-Amaldi correction
Consider the Thomas-Fermi energy functional $E$ for a spin polarized atom or
molecule with $N_{1} $ [resp. $N_{2}$] spin up [resp. spin down]
electrons and total positive molecular charge Z. Incorporating the
Fermi-Amaldi correction as Benilan, Goldstein and Goldstein did, $E$ is not
convex. By replacing $E$ by a well-motivated convex minorant $
\mathcal{E}$
,we prove that $
\mathcal{E}
$
has a unique minimizing density $( \rho _{1},\rho _{2}) \ $
when $N_{1}+N_{2}\leq Z+1\ $and $N_{2}\ $is close to $N_{1}.$