Calculations on the cascade theory with collision loss

Abstract

A rigorous solution of the equations of the cascade theory taking the radiation and pair creation cross-sections to be those for complete screening and the collision loss to be a constant is given which exactly satisfies the given boundary conditions at the surface of the layer. The solution is in the form of an infinite series but it is not a series in powers of the collision loss β since this enters essentially into the expression for each term. The first term of the series alone gives the whole energy spectrum of cascade electrons both above and below the critical energy with very considerable accuracy. The total number of particles produced at a deptht by an electron of initial energy E₀= β exp. y₀ is given in Table III fort varying from 2 to 30 and y0 from 3 to 16. It is shown that at the maximum of the cascade the total number of particles above the critical energy is 0.8 times the number below the critical energy.