Abstract
In the Van Vleck metals such as Pr, an indirect interaction arises between the conduction electrons through the virtual excitation of the crystal-field singlet ground state. By solving the Eliashberg equations, it is shown that this effective interaction can bring about superconductivity in a way similar to the spin-fluctuation-mediated pairing due to the repulsive short-range interaction. For the free-electron band the triplet p-wave pairing is formed. Spin degeneracy of the triplet states is lifted by the crystal-field anisotropy to choose the highest ${\mathit{T}}_{\mathit{c}}$. The retardation effect brought by the effective interaction and the depairing effects due to the scattering of the conduction electrons by the crystal-field states are analyzed in detail. Of all these effects, it is the mass renormalization effect that strongly depresses ${\mathit{T}}_{\mathit{c}}$.
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