Inverse Isotope Effect is in principle due to the Coulomb interaction (in materials originally referred to as "bad actors"), traditionally taken into account by means of the the so-called "pseudopotential" μ*, as well as retardation effects, both in principle accounted for by the Migdal-Eliashberg equations (in the post-high-Tc era, the possibility of the Migdal theorem, according to which vertex corrections of the electron-phonon interactions would be negligible, has been subject of much debate -- P.W. Anderson has much insisted on the failure of the Migdal theorem in the high-Tc compounds; for completeness, in these compounds the band-width of electrons being relatively small, the small parameter underlying the Migdal theorem -- the square root of the ratio of the electronic effective mass and the nuclear mass -- is not small). Anharmonicity of phonon excitations can also not be neglected. For detailed theoretical considerations, see the book Superconductivity by R.D. Parks, in two volumes (Marcel Dekker, New York, 1969). See also in particular the review article by Bill, Kresin and Wolf, cited here below (the first reference):
http://www.csulb.edu/~abill/research/isotope.shtml
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