Static dielectric screen effects

This longitudinal relaxation time differs from the usual Debye relaxation time by a factor which depends on the static and optical dielectric constants of the solvent this is based on the fact that the first solvent shell is subjected to the unscreened electric field of the ionic or dipolar solute molecule, whereas in a macroscopic measurement the external field is reduced by the screening effect of the dielectric [73]. 

In TT-electron models the a and core electrons play the static role of screening the Coulomb interactions between the remaining degrees of freedom. In particular, they screen the nuclear-nuclear interactions, the interactions between the TT-electrons and the nuclei, and the mutual interactions between the Tr-electrons. This screening is often modelled by a static dielectric constant, and by the reduction of the effective charge of the nucleus to +Q at large distances. We now define Vp r R ) as the pseudopotential which models the effective interaction between the TT-electrons and the nuclei, while Vg g(r — r ) models the effective electron-electron interaction. 

A severe approximation in the weak-coupling effective model presented in this chapter is that the ground state is noninteracting, and thus there is no screening of the electron-hole interactions by the other vr-electrons. Such screening is usually modelled by a static dielectric constant in the electron-hole interaction (eqn (6.20)), and often also by a renormalization of the charge gap, 2A. 

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