The Magic Angle Mystery in Electron Energy Loss Spectroscopy: Relativistic and Dielectric Corrections

Recently it has been demonstrated that a careful treatment of both longitudinal and transverse matrix elements in electron energy loss spectra can explain the mystery of relativistic effects on the {it magic angle}. Here we show that there is an additional correction of order $(Zalpha)^2$ where $Z$ is the atomic number and $alpha$ the fine structure constant, which is not necessarily small for heavy elements. Moreover, we suggest that macroscopic electrodynamic effects can give further corrections which can break the sample-independence of the magic angle.