Asymptotics for Two-dimensional Atoms

الأصل · EN

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)=-1/2Z² Z+(E(λ)+1/2c H)Z²+o(Z²) when Z→ ∞ and N/Z→ λ, where E(λ) is given by a Thomas-Fermi type variational problem and c H≈ -2.2339 is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when Z→ ∞, which is contrary to the expected behavior of three-dimensional atoms.