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

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.

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.