Cherenkov Radiation from $e^+e^-$ Pairs and Its Effect on $\nu_e$   Induced Showers
  We calculate the Cherenkov radiation from an $e^+e^-$ pair at small separations, as occurs shortly after a pair conversion. The radiation is reduced (compared to that from two independent particles) when the pair separation is smaller than the wavelength of the emitted light. We estimate the reduction in light in large electromagnetic showers, and discuss the implications for detectors that observe Cherenkov radiation from showers in the Earth's atmosphere, as well as in oceans and Antarctic ice. 
Sourav K. Mandal, Spencer R. Klein, J. David Jackson