Asymptotics for Two-Dimensional Atoms

We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge Z > 0 and N quantum electrons of charge -1 is E(N, Z) = - 1/2 Z(2) lnZ + ( E-TF (lambda) + 1/2 c(H))Z(2) + o(Z(2)) when Z -> a and N/Z -> lambda, where E (TF)(lambda) is given by a Thomas-Fermi type variational problem and c (H) a parts per thousand -2.2339 is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when Z -> a, which is contrary to the expected behavior of three-dimensional atoms.