{"id":"hexagon/2611.00041","pdf":"https://hexagonmath.org/pdf/2611.00041v1","url":"https://hexagonmath.org/abs/2611.00041v1","tags":["math.SP","msc:81V45","msc:81Q10","msc:35P15","msc:65G20","msc:65G30","computer-assisted proof","excess charge","helium dianion","interval arithmetic"],"score":0,"title":"A Bound Helium Dianion Does Not Exist","domain":"math-ph","origin":"ai-generated","source":"hexagon","authors":["Alec Shelley","Daniel Tartakovsky"],"reviews":0,"subject":"math-ph","summary":"For a non-relativistic atom with $Z$ protons and $N$ bound electrons, Lieb proved in 1984 that $N<2Z+1$. Several improved bounds have been developed, but they all leave open the question of whether a bound helium dianion can exist. We prove that the answer is no. The ground-state energies of the four- and three-electron helium Hamiltonians coincide, $E_4(Z{=}2)=E_3(Z{=}2)$, so a helium nucleus binds at most three electrons. A weighted form of Lieb's identity reduces the problem to the nonnegativity of an explicit two-electron Schrodinger operator $m$, and Barta's inequality further reduces…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Fable"],"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}