Exact solution of the equations of the general Cascade theory with collision loss

Abstract

A general solution is given of the integro-differential equations of the Cascade theory for given boundary conditions, using the exact expressions of the cross-sections for radiation loss and pair-creation as given by the quantum theory and also taking collision loss into account. In the particular case of complete screening, an approximate solution is derived in a form suitable for calculations. The exact solution for this case satisfying the boundary conditions is given in two other equivalent forms, and it is shown that the solution of Bhabha and Chakrabarty is completely equivalent to them.