Coherent bremsstrahlung from relativistic electrons in quasicrystals

In this paper we develop a Born-approximation theory of coherent bremsstrahlung (CB) production by relativistic electrons in icosahedral quasicrystals (IQCs), described by a schematic model that incorporates the presence of phonon and phason disorder. Our main result is a formula for the cross section d sigma(CB)/dk of this process, differential with respect to the photon energy k. It predicts intense low-energy CB emission (type-A CB) when an electron is incident on an IQC along a direction almost, but not exactly, parallel to that of a major axis. It also entails a scaling law that could serve as a powerful experimental signature of type-A CB emitted by these IQCs and more general ones. We illustrate our theory by discussing numerical results for type-A CB emitted by electrons of 5-MeV kinetic energy incident in a direction close to a fivefold axis of icosahedral Al-Mn-Si (i-Al-Mn-Si) described by the above model. These calculations predict the presence of CB macropeaks in d sigma(CB)/dk vs k, to which many smaller peaks contribute, and which should be experimentally detectable. This is also expected to be the case for other directions of incidence. Reasons for believing that the schematic model yields qualitatively correct predictions for this cross section for relativistic electrons incident on real i-Al-Mn-Si are stated.