A Closed Form Solution for the Hopping Rate of Charged Particles in Metals

Abstract

The hopping rate of charged particles in metals is obtained in a closed form, by extending the Nozières-Dominicis theory. The hopping rate at low temperatures is proportional to T2K-1Γ(K)/Γ(½+K), where Γ and T are the gamma function and the absolute temperature, respectively. The constant K determining the temperature-dependence coincides with that derived from the generalized theory by Yamada and Yosida for the overlap integral between electron clouds.