Related papers: The maximal excess charge in M\"uller density-matr…
We consider a molecule described by the Hartree-Fock model without the exchange term. We prove that nuclei of total charge $Z$ can bind at most $Z+C$ electrons, where $C$ is a constant independent of $Z$.
We will give a proof that the maximal excess charge for an atom described by a family of density-matrix-functionals, which includes Hartree-Fock and M\"uller theories, is bounded by an universal constant. We will use the new technique…
We prove that in M\"uller theory, a nucleus of charge $Z$ can bind at most $Z+C$ electrons for a constant $C$ independent of $Z$.
We prove that in Thomas-Fermi-Dirac-von Weizs\"acker theory, a nucleus of charge $Z>0$ can bind at most $Z+C$ electrons, where $C$ is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a…
Bounds are studied for the maximum number, $N_c$, of electrons that can be bound to $K$ atoms of the total nuclear charge $Z$. It is proved that $N_c < \min\{2Z+1, 1.22Z + 3Z^{1/3}\}$ in Schr\"odinger theory. This improves Lieb's bound $N_c…
This paper establishes new bounds on the maximum number of electrons $ N_c(Z) $ that an atom with nuclear charge $Z$ can bind. Specifically, we show that \begin{equation*} N_c(Z) < 1.1185Z + O(Z^{1/3}) \end{equation*} with an explicit bound…
We bound the number of electrons $Q$ that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizs\"acker functional: instead of the classical power $5/3$ more general powers $p$ are…
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge Z and the fine structure constant…
We prove that the maximum number $N_c$ of non-relativistic electrons that a nucleus of charge $Z$ can bind is less than $1.22Z+3Z^{1/3}$. This improves Lieb's upper bound $N_c<2Z+1$ [{\it Phys. Rev. A} {\bf 29}, 3018-3028 (1984)] when $Z\ge…
Due to $e^+e^-$-pair production in the field of supercritical $(Z \gg Z_{cr}\approx 170 $) nucleus an electron shell, created out of the vacuum, is formed. The distribution of the vacuum charge in this shell has been determined for…
A relativistic version of the effective charge model for computation of observable characteristics of multi-electron atoms and ions is developed. A complete and orthogonal Dirac hydrogen basis set, depending on one parameter -- effective…
We prove the ionization conjecture within the Hartree-Fock theory of atoms. More precisely, we prove that, if the nuclear charge is allowed to tend to infinity, the maximal negative ionization charge and the ionization energy of atoms…
We review some results on the ionization conjecture, which says that a neutral atom can bind at most one or two extra electrons.
Recently, we have proposed the existence of a universal relation between the maximal electric charge and total mass of any weakly self-gravitating object: $Z\leq Z^*={\alpha}^{-1/3}A^{2/3}$, where $Z$ is the number of protons, $A$ is the…
The purpose of this note is to give an elementary derivation of a lower bound on the relativistic Thomas-Fermi-Weizs\"acker-Dirac functional of Thomas-Fermi type and to apply it to get an upper bound on the excess charge of this model.
The increasing interest in the Mueller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock functional, but with a modified exchange term in…
The atomic nucleus, viewed as a system of bound quarks, should, in principle, be described within an effective theory of low-energy quantum chromodynamics. This paper provides an overview of recently developed models that embody essential…
We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom -- or the corresponding magnetic quantum dot -- the maximal number of electrons does not exceed twice the nuclear charge. It result is…
We report on a numerical study of the density matrix functional introduced by Lieb, Solovej and Yngvason for the investigation of heavy atoms in high magnetic fields. This functional describes {\em exactly} the quantum mechanical ground…
Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schr\"odinger and Born, are in…