Can “Two-” and “One-Dimensional” Multielectron Atoms Exist?

Abstract

The quasi-classical Thomas–Fermi method is applied to 2D and 1D multielectron atoms. In terms of this method, such atoms are shown not to exist because of the fact that the physical boundary conditions that are analogous to the 3D version of the theory, where boundary conditions are met, cannot be fulfilled. Our theoretical results can be experimentally tested. Atomic number Z_{1, 2max} (~10²?) is assumed to exist in terms of this method. At Z > Z_{1, 2max}, low-dimensional multielectron atoms cannot exist, in contrast to oneor two-electron atoms and, e.g., an experimentally detected Bose condensate of low-dimensional atoms with Z ~ 10 (Na).