Collision Statistics

Abstract

Here, the statistical metrics used in the description of stochastic energy loss (or energy straggling) are derived. The stopping cross section has been previously derived and is the first moment of collision energy loss/transfer. Higher-order moments will be required in descriptions of the statistical nature of collision energy loss. Clearly, the first to be derived will be the second moment as this is necessary for the derivation of the variance of the probability distribution function. The derivation of the third moment will be deferred to Chap 18 when it is properly developed in the context of asymmetric collision energy loss probability distribution functions. The straggling parameter, a contributor to the second moment, is derived as is that due to Bohr. Finally, the effects of a condensed medium upon energy straggling are considered.