Theory of the isotope effect in superconducting compounds

We present a theoretical analysis of the isotope effect on the superconducting transition temperature. Our method is to calculate via formal perturbation theory the response of the transition temperature to small changes of the masses of the various constituents of the compound. We discuss the relation between the isotope effect and various more fundamental parameters in strong coupling superconductors, such as $\mu$* and $\alpha$2 F($\omega$). As illustrative examples, we consider the systems Pd-H(D) alloys and the binary Chevrel phase superconductor Mo$_{6}$Se$_{8}$, and show that analysis of the isotope effect can yield useful information concerning interaction mechanisms in these compounds