On the excess charge of a relativistic statistical model of molecules with an inhomogeneity correction

On the excess charge of a relativistic statistical model of molecules with an inhomogeneity correction

We show that the molecular relativistic Thomas-Fermi-Weizsäcker functional consisting of atoms of atomic numbers Z 1, ..., Z k has a minimizer, if the particle number N is constrained to a number less or equal to the total nuclear charge Z ≔ Z 1 + ⋯ + Z K . Moreover, there is no minimizer, if the pa...

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Veröffentlicht in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-10, Vol.53 (39), p.395201
Hauptverfasser: Chen, Hongshuo, Siedentop, Heinz
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Sprache:eng
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excess charge
existence of minimizers
relativistic Thomas-Fermi-Weizsäcker functional
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Siedentop, Heinz
description We show that the molecular relativistic Thomas-Fermi-Weizsäcker functional consisting of atoms of atomic numbers Z 1, ..., Z k has a minimizer, if the particle number N is constrained to a number less or equal to the total nuclear charge Z ≔ Z 1 + ⋯ + Z K . Moreover, there is no minimizer, if the particle number exceeds 2.56Z. This gives lower and upper bounds on the maximal ionization of heavy atoms.
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subjects excess charge
existence of minimizers
relativistic Thomas-Fermi-Weizsäcker functional
title On the excess charge of a relativistic statistical model of molecules with an inhomogeneity correction
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