Fluctuations of the Electron-Photon Cascade - Moments of the Distribution

Abstract

The second moments of the electron-photon cascades are evaluated. It is found that the mean square fluctuation at the cascade maximum is that expected for a Poisson distribution or less; before and after the maximum the fluctuation exceeds greatly that expected for a Poisson distribution. The correlation coefficient between electrons and photons is zero for small thicknesses or near the cascade maximum. For other regions the correlation coefficient is positive. Both mean square fluctuation and correlation between electrons and photons can be understood qualitatively in terms of fluctuation of effective depth.