This article improves the BCS theory to include the inverse isotope effect on superconductivity. An affective model can be deduced from the model including electron-phonon interactions, and the phonon-induced attraction is simply and clearly explained on the electron Green function. The focus of this work is on how the positive or inverse isotope effect occurs in superconductors.
@article{arxiv.0909.0797,
title = {Positive and inverse isotope effect on superconductivity},
author = {Tian De Cao},
journal= {arXiv preprint arXiv:0909.0797},
year = {2009}
}