It is shown, using the dielectric matrix formalism, that in the presence of free carriers the rapidly changing component of the phonon potential (i.e. that due to short-range interactions) is not screened, but produces an additional slowly changing potential component. The resulting matrix element of the total phonon potential is equal to the matrix element in the absence of free carriers divided by the free-carrier dielectric function.
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Bogulsawski et al. (1977) studied this question.
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