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

Abstract

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.

References in corpus (5)

• The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction
• Equivalence of Sobolev norms involving generalized Hardy operators
• Stability of atoms and molecules in an ultrarelativistic Thomas-Fermi-Weizsaecker model
• Proof of the Strong Scott Conjecture for Chandrasekhar Atoms
• On the Maximal Excess Charge of the Chandrasekhar-Coulomb Hamiltonian in Two Dimensions

Cited by in corpus (3)

• The Scott conjecture for large Coulomb systems: a review
• Mathematical Elements of Density Functional Theory
• A Statistical Theory of Heavy Atoms: Energy and Excess Charge