Symmetry-selected electron energy loss scattering

Abstract

The differential scattering cross section for EELS has long been described within the Born approximation: where v is the incident electron velocity, | ϕ0 > and | ϕn > are the initial and final one electron specimen states, and the sum is over the specimen electrons. This expression is suited to plane wave scattering where we have one well-defined momentum transfer given by q. We obtain equation by expanding the swift electron coulomb interaction in a Fourier series and picking one momentum transfer. This is not very useful for scattering in the STEM, because we must sum coherently over many plane wave states to make a small probe. This produces many cross terms in equation above, some of which may exactly cancel. Thus, the plane wave formulation can obscure a simple result by separating the scattering in a non-physical way.