An approximate analytical solution for the energy distribution of beta particles transmitted through metal foils

The energy distributions of beta particles which penetrated a certain matter thickness were studied experimentally and theoretically by using a surface barrier solid state detector. A valid theoretical expression based on average values between energy and distance traveled during the slowing down of the electron was obtained. Two analytical expressions were proposed; one for the energy distribution of monoenergetic electrons which penetrated a certain matter thickness, and one for the response function in the detector for monoenergetic electrons detected with its entire energy. Response functions of the detector for beta particles emitted from 204Tl isotope which penetrated a certain matter thickness were obtained for two different aluminum thicknesses, and the results were discussed by comparing with experimental energy spectra.