High-Energy Behavior in Quantum Field Theory

where o (E~,Ev) is the theoretical scattering cross section for electrons of initial energy E1 and final energy E2 and m and m' are the probabilities for radiation before and after scattering, respectively. For an elastic cross section, o(E~,Ev) is a delta function and the integrals of Fq. (AS) can be evaluated approximately to yield Eq. (1) of the text if E4 in that equation is replaced by Ep. Again, terms of the same order as those neglected in E'q. (A1) were neglected in Eq. (1), in addition to terms depending on (Eo—Es) but which were considerably smaller than those that were retained. If o(Ev, Ev), as a theoretical inelastic cross section, is considered to be a series of many delta functions (elastic cross sections), Eq. (2) of the text results, where the summation has been replaced by the integral sign of that expression. In deducing Eq. (2), it was assumed that the shape of o( E,sE)vas a function of Ev with fixed E1 does not change with E1. This assumption gives adequate accuracy for this work.