High-Frequency Limit of Bremsstrahlung in the Sauter Approximation

The expansion in powers of $\frac{Z}{137}$ utilized in the Sauter theory of the photoelectric effect yields a nonzero cross section proportional to $Z^3$ at the high-frequency limit of the bremsstrahlung spectrum, and also at the low electron energy limit of the pair production spectrum. These cross sections are related to the Sauter photoelectric cross section by detailed balancing. The results apply equally when the effects of spin orientations and x-ray polarization are considered.