Signatures of interband scattering in spectroscopic experiments on   $MgB_2$
  Within a two-band, strong coupling model we analyze SIS-tunneling conductance, Raman scattering and optical conductivity measured on $MgB_2$ samples. We find that features observed in tunneling and Raman spectroscopy at intermediate energies $\omega=\Delta_{\sigma}+\Delta_{\pi}\simeq 8\div 10meV$ can be consistently explained when incoherent scattering between $\sigma$ and $\pi$ band is considered. We calculate the optical conductivity and find that strong coupling effects are important for explaining the presently available data, and predict the location and magnitude of interband scattering features for this spectroscopic probe as well. 
C. P. Moca, B. Janko