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The ionization and generalized ionization conjectures

For the full nonrelativistic Coulomb model with two electron spin states, proves that a molecule with M fixed nuclei of charges at least one and total charge Z strictly binds at most

Z+CM

electrons. Neutral-atom first ionization energies and radii containing all but an expected half-electron have universal positive upper and lower bounds. The energy cost of removing m electrons has Thomas–Fermi asymptotics as

m\to\infty

and

Z/m\to\infty

; neutral-atom outer radii have the corresponding iterated-limit asymptotics, taking

Z\to\infty

first.

Manuscripts in this family · 3

Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms

Sep 24, 2026·paper.pdf

We prove that a molecule with M fixed nuclei of real charges at least one and total nuclear charge Z strictly binds at most

Z+CM

electrons, where C is universal. The result holds for the full nonrelativistic Coulomb Hamiltonian with two spin states and arbitrary distinct nuclear positions. For neutral atoms with integer nuclear charge Z ≥ 1, the first ionization energy and, for every ground state, the radius outside which one half of an electron remains are each bounded above and below by positive universal constants.

Full abstract

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Generalized ionization energies for full Coulomb atoms

Sep 24, 2026·paper.pdfLean

We prove the energy part of the generalized ionization conjecture for full nonrelativistic Coulomb atoms with two electron spin states. The energy needed to remove m electrons is asymptotic to

a_{\mathrm{TF}}m^{7/3}

whenever

m\to\infty

and

Z/m\to\infty

, with the Thomas–Fermi constant in atomic units. We also obtain both conjectured iterated limits.

Full abstract

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Generalized outer-electron radii of neutral Coulomb atoms

Sep 24, 2026·paper.pdf

We prove the radius part of the generalized ionization conjecture for neutral nonrelativistic Coulomb atoms with two spin states. For every choice of ground states, the upper and lower large-nuclear-charge limits of the radius defined by an expected exterior electron mass m are both asymptotic to

(81\pi^2/2)^{1/3}m^{-1/3}

as m tends to infinity.

Full abstract

PDF on GitHub LaTeX source