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({ε}) affects the isotope-effect coefficient {β} within a realistic Eliashberg formalism. For structure in N({ε}), 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 μ*, {β} can be quite small with otherwise fairly unremarkable values of the other parameters.