The Influence of Multiple Scattering on the Angular Width of Čerenkov Radiation

Abstract

One may measure the angle at which visible Čerenkov radiation appears from fast charged particles as they pass through a thin transparent plate. This angle is related to the velocity of the particle in a simple manner, and therefore offers a method of measuring the velocity. The angular width of the radiation is important in that it determines the resolution of the velocity measurement. This width contains contributions due to diffraction, energy loss of the charged particle, and multiple scattering. In this paper, the effects of multiple scattering and diffraction are considered in the following manner. The path of the particle through the transparent plate is considered to be a series of connected short straight-line segments. The radiation is calculated classically from this path, and with the aid of the results of multiple scattering theory, an ensemble average is taken over all possible paths. Two different methods are used in evaluating the radiation average. One is valid at viewing angles near the radiation maximum, and the other at viewing angles differing appreciably from the maximum. Curves are presented that give the radiation intensity as a function of the viewing angle for a variety of cases.