Field Correction for Ionic Dielectric Function

Appendix Internal Field Correction for Ionic Dielectric Function 

Some solid-state physics texts (e.g., Kittel) include the correction for internal fields in calculating the electronic dielectric function but ignore it when calculating the ionic dielectric function and obtain the same result as Equation 23.17. Instead of computing the internal field corrections for ionic and electronic contributions to the dielectric function separately and then adding them, Ashcroft and Mermin combine the polarizabilities of the ions and the electrons and then apply the Clausius-Mossotti equation to the sum  

It would be more convenient to be able to write Equation A.23.4 in the form 

Since s(oo) s(0), the effect of the internal field is to lower the resonance frequency. 

The final result. Equation A.23.5 is the same as the real part of the electronic and ionic dielectric fimction foimd in Equation 23.19. The question is whether it is more accurate to calculate the ionic contribution with or without the correction for the local field (see Problems 6-8). 

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