The Structure of Electronic Excitation Levels in Insulating Crystals

In this article, a method is devised to study the energy spectrum for an excited electron configuration in an ideal crystal. The configuration studied consists of a single excited electron taken out of a full band of $N$ electrons. The multiplicity of the state is $N^2$. It is shown that because of the Coulomb attraction between the electron and its hole $N^{\frac{8}{5}}$ states are split off from the bottom of the excited Bloch band; for these states the electron cannot escape its hole completely. The analogy of these levels to the spectrum of an atom or molecule is worked out quantitatively. The bottom of the Bloch band appears as "ionization potential" and the Bloch band itself as the continuum above this threshold energy.