Configuration average for energy transfer to randomly distributed acceptors in the fast-migration limit

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Abstract
In a recent theory of concentration quenching in rare-earth pentaphosphates a crucial step in the derivation of the quenching rate was not proven. This step consists of an average over acceptor-ion configurations and yields the often-observed linear concentration dependence of the quenching rate. Here this average is rigorously carried out including the restriction that not more than one ion can occupy a site. Somewhat surprisingly, the result is the same as that obtained with an unrestricted average.