A study of the virtual bound state dielectric constant

It is shown that existing theoretical expressions for the dielectric constant of virtual bound state alloys can only be valid in the frequency range omega tau >>1. A general expression is proposed which is valid at both low and high frequencies. Use of the conductivity sum rule then indicates changes in the electronic effective mass. Earlier expressions are not consistent with the sum rule, nor indeed with Kramers-Kronig relation between real and imaginary parts of the dielectric constant.