The charged particles polarize the molecules, which then turn back rapidly to their ground state, emitting prompt radiation. The emitted light forms a coherent wavefront if v>vt; Cherenkov light is emitted under a constant Cherenkov angle with the particle trajectory, given by
The maximum emission angle is given by
and for the threshold
A more detailed treatment is given in [Allison91] and [Ypsilantis94].
The major problem of Cherenkov radiation is the modest light output: the energy loss due to ionization or excitation is two to three orders of magnitude higher than the energy lost in radiating Cherenkov light, in the energy range where photomultipliers can be used (a few eV, or about 400 nm wavelength). By its directionality, Cherenkov light can, however, be separated from the background. The useful photon yield is obtained by integrating over the range of sensitive wavelengths:
For a detailed calculation of the number of photons emitted from the photocathode, the transmission factor and the collection factor have to be taken into account both for the radiator and the light guide, and the conversion efficiency of the photocathode must be considered ( [Fabjan80], [Fernow86]).