c-axis Raman Scattering in MgB2: Observation of a Dirty-Limit Gap in the pi-bands

Raman scattering spectra from the ac-face of thick MgB2 single crystals were measured in zz, xz and xx polarisations. In zz and xz polarisations a threshold at around 29 cm^{-1} forms in the below Tc continuum but no pair-breaking peak is seen, in contrast to the sharp pair-breaking peak at around 100 cm^{-1} seen in xx polarisation. The zz and xz spectra are consistent with Raman scattering from a dirty superconductor while the sharp peak in the xx spectra argues for a clean system. Analysis of the spectra resolves this contradiction, placing the larger and smaller gap magnitudes in the sigma and pi bands, and indicating that relatively strong impurity scattering is restricted to the pi bands.