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Prove from the many-electron Schrodinger equation that the size of a neutral atom does not grow with Z.","posed_since":"","precise":"For a neutral ground state $\\psi$ of $H_{Z,Z}$ with one-electron density $\\rho$, define $R(Z)$ as the radius with $\\int_{|x|>R(Z)}\\rho(x)\\,dx=1$. Prove $c a_0\\le R(Z)\\le C a_0$ with $a_0=\\hbar^2/(m e^2)$ and constants c, C independent of Z, or show R(Z) grows or shrinks without bound.","problem_ref":"bf2a52b11695356d77880e63de63d68f319926af8817c69f4871dbeccdaba5d3","references":"","settled_by":"Z-independent upper and lower bounds on R(Z) for the neutral many-body ground state.","status_note":"Proved in Hartree-Fock theory (Solovej 2003); open for the Schrodinger Hamiltonian.","title":"Atomic radius bounded independently of nuclear 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