Bragg–Gray cavity theory

According to the Bragg–Gray cavity theory, the ionization produced in a small cavity within an irradiated medium or object is related to the energy absorbed in that medium as a result of its radiation exposure. It was developed in 1936 by British scientists Louis Harold Gray, William Henry Bragg, and William Lawrence Bragg.

If the cavity is small enough that it does not change the number or energy distribution of the electrons that would exist in the medium in the absence of the cavity, and the energy is deposited only by electrons passing through the gas-filled cavity, then

where

E ν is the energy absorbed per unit volume of the medium J ν is the ionization per unit volume produced in the gas W is the average energy lost by the secondary electrons per pair of ions formed in the gas ρ is the ratio of the stopping power of the medium and the gas for the secondary electrons