The cross section for double bremsstrahlung differential in the radiated photon energies and angles has been measured for 70-keV electrons on targets of Al, Cu, Ag, Tb, and U for photons radiated at ±45° to the incident beam for photon energies in windows from 10 to 30 keV. In contrast with previous experiments at ±90°, the results are in reasonable agreement with the relativistic first Born approximation at lower Z. However, the results exhibit a Z dependence which disagrees with the first Born Z^ dependence, suggesting the need for consideration of a second Born approximation.PACS numbers: 34.80.-i Double bremsstrahlung is a quantum electrodynamic process in which two photons are radiated simultaneously in the scattering of an electron by an atom. This process was first mentioned by Heitler and Nordheim [I] who estimated that the cross section would be about 137 times smaller than that of single bremsstrahlung, or essentially smaller by a factor of the fine-structure constant due to the emission of the second photon. While the two-photon process is too small to make much contribution to the production of radiation, it is nevertheless especially interesting as an example of a quantum radiative process for which, unlike single bremsstrahlung, there seems to be no prescription for a classical calculation of the cross section. Although recently there has been much interest in two-photon and multiphoton processes, the radiative two-photon process has been studied in only two experiments [2,3], both in a ±90° geometry. In both experiments, a significant discrepancy, as large as 2 orders of magnitude, with theories has been observed.The first measurement of the cross section was made in 1985 by Altman and Quarles [2]. They measured the cross section for two-photon emission for 75-keV electrons on thin targets of silver, terbium, gold, and uranium. The electron was not observed, so a differential cross section integrated over the unobserved electron was measured. Altman and Quarles also evaluated the theoretical cross section by numerical integration of the very complicated formula for the cross-section differential in the two photon energies and angles and the electron angles worked out by Smirnov [4] in the relativistic first Born approximation. The experimental result for gold was about 300 times the computed theoretical value. It was not clear whether the discrepancy was due to an error in the theoretical formula, the numerical integration of the formula, or the experimental data. An independent evaluation of the theory in the nonrelativistic Coulomb approximation was then provided by Veniard, Gavrila, and Maquet [5] and also by Florescu and Djamo [6]. The result for the particular geometry of Ref. [2] was larger by about a factor of 3 than the relativistic Born approximation but was still about a factor of 100 smaller than the observed cross section. These nonrelativistic calculations when evaluated in the Born rather than the Coulomb approximation were close to the relativistic result computed in Ref. [2], sug...
