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We study the influence of inelastic rare-earth impurity scattering onelectron-phonon mediated superconductivity and mass renormalization in(La$_{1-x}$Pr$_{x}$)Os$_{4}$Sb$_{12}$ compounds. Solving the strong couplingEliashberg equations we find that the dominant quadrupolar component of theinelastic scattering on Pr impurities yields an enhancement of thesuperconducting transition temperature T$_c$ in LaOs$_{4}$Sb$_{12}$ andincreases monotonically as a function of Pr concentration. The calculatedresults are in good agreement with the experimentally observed T$_c (x)$dependence. Our analysis suggests that phonons and quadrupolar excitationscause the attractive electron interaction which results in the formation ofCooper pairs and singlet superconductivity in PrOs$_{4}$Sb$_{12}$.

Eliashberg theory of superconductivity and inelastic rare-earth impurity scattering in filled skutterudite La$_{1-x}$Pr$_{x}$Os$_{4}$Sb$_{12}$