Cherenkov Radiation - Characteristics

Characteristics

The frequency spectrum of Cherenkov radiation by a particle is given by the Frank–Tamm formula. Unlike fluorescence or emission spectra that have characteristic spectral peaks, Cherenkov radiation is continuous. Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency. That is, higher frequencies (shorter wavelengths) are more intense in Cherenkov radiation. This is why visible Cherenkov radiation is observed to be brilliant blue. In fact, most Cherenkov radiation is in the ultraviolet spectrum—it is only with sufficiently accelerated charges that it even becomes visible; the sensitivity of the human eye peaks at green, and is very low in the violet portion of the spectrum.

There is a cut-off frequency above which the equation cannot be satisfied. Since the refractive index is a function of frequency (and hence wavelength), the intensity does not continue increasing at ever shorter wavelengths even for ultra-relativistic particles (where v/c approaches 1). At X-ray frequencies, the refractive index becomes less than unity (note that in media the phase velocity may exceed c without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as gamma rays) would be observed. However, X-rays can be generated at special frequencies just below those corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonance frequency (see Kramers-Kronig relation and anomalous dispersion).

As in sonic booms and bow shocks, the angle of the shock cone is directly related to the velocity of the disruption. The Cherenkov angle is zero at the threshold velocity for the emission of Cherenkov radiation. The angle takes on a maximum as the particle speed approaches the speed of light. Hence, observed angles of incidence can be used to compute the direction and speed of a Cherenkov radiation-producing charge.

Cherenkov radiation can be generated in the eye by charged particles hitting the vitreous humour, giving the impression of flashes, as in cosmic ray visual phenomena.