Transition spectra for a BCS superconductor with multiple gaps: Model calculations for MgB2

We analyze the qualitative features in the transition spectra of a model superconductor with multiple energy gaps, using a simple extension of the Mattis-Bardeen expression for probes with case I and case II coherence factors. At temperature T50, the far-infrared absorption edge is, as expected, determined by the smallest gap. However, the large thermal background may mask this edge at finite temperatures and instead the secondary absorption edges found at D i1D j may become most prominent. At finite T, if certain interband matrix elements are large, there may also be absorption peaks at the gap difference frequencies uD i2D ju/\ . We discuss the effect of sample quality on the measured spectra and the possible relation of these predictions to the recent infrared absorption measurement on MgB2.