A note on Janossy's mathematical model of a nucleon cascade

Abstract

In a contribution (3) to these Proceedings the author considered stochastic problems in physics where one had to deal with a stochastic variable representing the number of particles distributed in a continuous infinity of states characterized by a parameter E, and where the distribution varied with another parameter t which might be continuous or discrete (if t represents time or thickness, it is of course continuous). The author introduced the concept of product densities and derived some general results relating to the functions representing these densities. Recently, Janossy(2), using a certain mathematical model for a nuclear cascade, introduced certain functions which bear a close relation to the product-density functions. The object of this note is to establish a complete correspondence between these two sets of functions and apply them to the specific problem of the development of a nucleon cascade. The diffusion equations involving product densities can be derived from the diffusion equations involving Janossy's functions.