Differential bremsstrahlung and pair production cross sections at high energies

Abstract

Detailed differential cross sections for high energy bremsstrahlung and pair production are derived with specific attention to the differences between the two processes, which are considerable. For the integrated cross sections, which are the only cross sections specifically known until now, the final state integration theorem guarantees that the exact cross section formulas can be exchanged between bremsstrahlung and pair production by the same substitution rules as for the Born-approximation Bethe-Heitler cross sections, for any amount of atomic screening. In fact the theorem states that the Coulomb corrections to the integrated bremsstrahlung and pair production cross sections are identical for any amount of screening. The analysis of the basic differential cross sections leads to fundamental physical differences between bremsstrahlung and pair production. Coulomb corrections occur for pair production in the strong electric field of the atom for ``large'' momentum transfer of the order of mc. For bremsstrahlung, on the other hand, the Coulomb corrections take place at a ``large'' distance from the atom of the order of $(\ensuremath{\Elzxh}/mc)\ensuremath{\epsilon},$ with a ``small'' momentum transfer $mc/\ensuremath{\epsilon},$ where $\ensuremath{\epsilon}$ is the initial electron energy in units of ${\mathrm{mc}}^{2}.$ And the Coulomb corrections can be large, of the order of larger than ${(Z/137)}^{2},$ which is considerably larger than the integrated cross section corrections.