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Replacement of hydrogen by deuterium in palladium hydride results in highersuperconducting temperatures and an anomalous isotope effect that has not beenyet fully explained. In this work, we try a new approach to the explanation ofthe inverse isotope effect in PdH(D). Our approach introduces two new aspects.First, we took into account the experimental evidence that at temperaturesbelow 50 K, the crystal structure of PdH and of PdD is zincblende. Second, wetake into account not only the influence of the electron-phonon interaction butalso the electron-electron interaction contribution to the isotope coeffiecientdue tothe replacement of deuterium in the place of hydrogen. We used theMigdal-Eliashberg theory to perform our ab initio calculations. We found inthis picture that the electron-electron interaction is considerably reduced bythe isotope substitution and is the most important factor to explain theinverse isotope effect. We found $\Delta T_c^{total}=2.224\:K$ and $\alpha=-0.3134$ in excellent agreement with the values found experimentally.

On the Calculation of the Inverse Isotope Effect in PdH(D): A Migdal-Eliashberg Theory Approach