Solovej's generalized ionization conjecture for neutral Coulomb atoms (energies and radii)

Lineage and corrections

Solovej's generalized ionization conjecture for neutral Coulomb atoms (energies and radii) parent of this event

This event attributed to Unreleased internal OpenAI model

Companion: Generalized outer-electron radii of neutral Coulomb atoms evidence for this event

Solovej, A new look at Thomas-Fermi theory (2016) evidence for this event

Lean proof (OAI.CoulombAtom.generalized_ionization) evidence for this event

Lean proof, radii (OAI.NeutralAtom.generalized_outer_radii, not in the catalogue) evidence for this event

Energy (principal, Theorem 1.1): $I_m(Z)/m^{7/3}\to a_{TF}>0$ whenever $m\to\infty$ and $Z/m\to\infty$, with $a_{TF}$ the Thomas-Fermi constant; this is stronger than and implies Solovej's iterated limits, which are stated as (1.4)-(1.5). Radius (companion, Theorem 1.1): for every choice of neutral ground states, $m^{1/3}\limsup_Z R_m(Z)$ and $m^{1/3}\liminf_Z R_m(Z)$ both tend to $(81\pi^2/2)^{1/3}$, with $Z\to\infty$ first. Not shown: convergence of $I_m(Z)$ or $R_m(Z)$ at fixed $m$, a joint limit for radii, or relativistic and molecular versions. parent of this event

Companion: Generalized ionization energies for full Coulomb atoms evidence for this event

The ionization conjecture: bounded excess charge, ionization energy and radius for Coulomb atoms and molecules (Simon's Problem 9) evidence for this event

VibeMathed record: Solovej's generalized ionization conjecture for neutral Coulomb atoms (energies and radii) evidence for this event