Cross section of electron-nucleus bremsstrahlung near the short-wavelength limit

Abstract

Using the partial-wave formalism the cross section of bremsstrahlung for a pure Coulomb field is calculated for various atomic numbers of the target nucleus and various incident electron energies. The results are compared to those of previous theories. For intermediate and large atomic numbers the latter cross sections undervalue significantly the present ones. Except for low atomic numbers the cross sections in Born approximation with the Coulomb correction by Elwert yield more accurate results than the cross sections obtained by using the approximate Sommerfeld-Maue wave function. The effect of screening is small for low atomic numbers. At nonrelativistic energies the number of required partial waves is rather large for target nuclei with high atomic numbers, contrary to the expectations. The pertinent results exceed the numerical values including screening by factors of up to five. They verify the assumption that the nonrelativistic cross section of Sommerfeld is fairly accurate even for high atomic numbers.