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# A convexified energy functional for the Fermi-Amaldi correction

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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 $N_{1}.$

Microsoft Academic Graph classification: Molecular charge Spin-½ Physics Atom (order theory) Mathematical physics Fermi Gamma-ray Space Telescope Energy functional Electron Regular polygon

arXiv: Condensed Matter::Quantum Gases

Applied Mathematics, Discrete Mathematics and Combinatorics, Analysis

Applied Mathematics, Discrete Mathematics and Combinatorics, Analysis

Microsoft Academic Graph classification: Molecular charge Spin-½ Physics Atom (order theory) Mathematical physics Fermi Gamma-ray Space Telescope Energy functional Electron Regular polygon

arXiv: Condensed Matter::Quantum Gases

###### 6 Research products, page 1 of 1

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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 $N_{1}.$