Integral Equations for Cascade Showers

Abstract

Integral equations of a new type are derived for the lateral and angular distribution functions in a cascade shower. The moment recursion relations of Nordheim are direct consequences of these integral equations. The method of derivation has some intrinsic interest since it involves the formal device of the introduction of negative probabilities for events in which nothing happens. This formal device may have applications in other fields. No solutions of the integral equations derived here are given in this note.