Modification of the isotope effect due to energy-dependent electronic density of states

We study how energy dependence in the electronic density of states N(ɛ) affects the isotope-effect coefficient β within a realistic Eliashberg formalism. For structure in N(ɛ), sharp on the scale of the Debye energy, the value of β can be significantly affected and can be smaller or larger than the canonical value 0.5. In some cases, when coupled with large values of the Coulomb pseudopotential ${\mathrm{\mu }}^{\mathrm{*}}$, β can be quite small with otherwise fairly unremarkable values of the other parameters.