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

Theorem 1.1: there is a universal $C$ such that for every $M\ge1$, all distinct nuclear positions and all real charges $z_j\ge1$ with $Z=\sum z_j$, strict binding $E_n<E_{n-1}$ implies $n\le Z+CM$, and $E_n=E_{n-1}$ for $n>Z+CM$. For atoms this is Simon's bounded excess charge. Theorem 1.2: for every integer $Z\ge1$ and every neutral ground state, the radius outside which half an electron remains lies between universal constants. Corollary 1.3: the neutral first ionization energy satisfies $c\le I_1(Z)\le C$. Not shown: the value of the constants, relativistic or magnetic models, or the asymptotic (generalized) form, which is the separate generalized ionization entry.

Theorem 1.1: there is a universal $C$ such that for every $M\ge1$, all distinct nuclear positions and all real charges $z_j\ge1$ with $Z=\sum z_j$, strict binding $E_n<E_{n-1}$ implies $n\le Z+CM$, and $E_n=E_{n-1}$ for $n>Z+CM$. For atoms this is Simon's bounded excess charge. Theorem 1.2: for every integer $Z\ge1$ and every neutral ground state, the radius outside which half an electron remains lies between universal constants. Corollary 1.3: the neutral first ionization energy satisfies $c\le I_1(Z)\le C$. Not shown: the value of the constants, relativistic or magnetic models, or the asymptotic (generalized) form, which is the separate generalized ionization entry.