An update to the Mathematica package PCR for simulation of planar channeling of electrons

The presented Mathematica package is an upgrade of the Mathematica package PCR presented by B. Azadegan [1]. The purpose of the package is to accurately and efficiently calculate the characterizing features of planar channeling radiation of relativistic electrons along major crystallographic planes of diamond, silicon, and germanium crystal. The package is based on the quantum theory of electron channeling as written by Azadegan in his dissertation which has been successfully applied to model planar channeling of electrons at energies between 10 and 100 MeV [2]. It will be shown that the PCR code is successful in calculating peak photon energies, but fails to generate accurate spectral linewidths and photon yields. The presented package adopts the successes of the PCR code: calculation of the continuum potentials for different planes of diamond, silicon, and germanium crystals; numerical solution of the one-dimensional Schrödinger equation; and calculation of the transition probabilities between channeling states. The package improves upon the spectral linewidths generated by the PCR code by including the effects of multiple scattering of electrons and Bloch-wave broadening as well as calculating a more accurate expression for the linewidth due to multiple scattering than is presented in Azadegan’s dissertation. Finally, the package generates more accurate photon yields by including the dechanneling of electrons due to multiple scattering and the self-absorption of photons by the crystal, and convolving the Lorentzian line-shape of the PCR code with a Gaussian line-shape. The simulation of channeling radiation spectra is a useful tool in the comparison of theory with experimental data.