• Corpus ID: 246430854

Analytic bound on the excess charge for the Hartree Model

@inproceedings{Benguria2022AnalyticBO,
  title={Analytic bound on the excess charge for the Hartree Model},
  author={R D Benguria and Trinidad Tubino},
  year={2022}
}
We prove an analytic bound on the excess charge for the Hartree equation in the atomic case. 
2 Citations

New bounds on the excess charge for atomic systems

TLDR
New bounds on the excess charge for non relativistic atomic systems, independent of the particle statistics, are proved using the technique introduced by P. T. Nam in 2012 and the Coulomb Uncertainty Principle.

The ionization problem in quantum mechanics

. While it is well-known experimentally that a neutral atom can bind at most one or two extra electrons, deriving this fact rigorously from first prin-ciples of quantum mechanics remains a very

References

SHOWING 1-10 OF 47 REFERENCES

Proof of the ionization conjecture in a reduced Hartree-Fock model

SummaryThe ionization conjecture for atomic models states that the ionization energy and maximal excess charge are bounded by constants independent of the nuclear charge. We prove this for the

Bound on the ionization energy of large atoms

We present a simple argument which gives a bound on the ionization energy of large atoms that implies the bound on the excess charge of Fefferman and Seco [2].

The Hartree-Fock theory for Coulomb systems

For neutral atoms and molecules and positive ions and radicals, we prove the existence of solutions of the Hartree-Fock equations which minimize the Hartree-Fock energy. We establish some properties

On the number of electrons that a nucleus can bind

We review some results on the ionization conjecture, which says that a neutral atom can bind at most one or two extra electrons.

The ionization conjecture in Hartree-Fock theory

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

Asymptotic neutrality of large ions

It is proved that a nucleus of chargeZ can bind at mostZ+O(Za) electrons, witha=47/56.

Proof that the H − Ion Has Only One Bound State

It is rigorously demonstrated that the nonrelativistic ${\mathrm{H}}^{\ensuremath{-}}$ ion has only one bound state in the fixed (infinite-mass) nucleus approximation with Coulomb interactions only.

Geometric methods in the quantum many-body problem. Nonexistence of very negative ions

In this paper we develop the geometric methods in the spectral theory of many-body Schrödinger operators. We give different simplified proofs of many of the basic results of the theory. We prove that

Asymptotic Neutrality of Large- Z Ions

Let N(Z) denote the number of electrons that a nucleus of charge Z binds in nonrelativistic quantum theory. It is proved that N(Z)/Z → 1 as Z → ∞. The Pauli principle plays a critical role.

The Maximal Excess Charge in Müller Density-Matrix-Functional Theory

We consider an atom described by Müller theory, which is similar to Hartree–Fock theory, but with a modified exchange term. We prove that a nucleus of charge Z can bind at most $$Z+C$$Z+C electrons,