The polarization energies for core states of alkali halides are discussed within the context of the theory developed by Hedin and Lundqvist. It emerges from the analysis that the choice of a particular $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$-dependent dielectric function is more critical than the accuracy with which the core wave functions are described. We show that for very localized holes the use of a constant dielectric function leads to meaningless results. These results are compared with those obtained with other theoretical schemes. Comparison is also made between the theory of Hedin and Lundqvist and other theories, remarking on its more general character.