Measurement of average electron densities in Si and Ge using MeV delta -rays produced by channelled high-energy projectiles

For the first time, average electron densities in silicon and germanium were measured using the channeling effect for 5 and 12 GeV/c protons,\pi^{+} and\pi^{-}. In the investigation, the yield of MeV electrons emitted through the back of the target was measured. Such delta -ray yields are proportional to the local electron density averaged along the path of the projectile in the target. For well- aligned, positive particles, the electron yield is reduced to around 15% of normal yield for germanium and 25% for silicon, whereas negatively charged, channeled projectiles give an increase in yield by a factor of three compared to normal yield. The experimental results have been compared to yield curves calculated using the Lindhard channeling model in connection with special potential models, and very good agreement is obtained for positive particles when the electron density in the middle of channels is obtained by summing the contributions from many neighbouring strings. For positive projectiles, this channeling method is most sensitive far away from the strings, where other techniques are weak. The results for negative, channeled particles agree fairly well with simplified theoretical calculations, neglecting, channeled particles agree fairly well with simplified theoretical calculations, neglecting dechanneling and the lack of equilibrium in angular momenta in the transverse plane.