Quantal aspects of the spatial resolution of energy-loss measurements in electron microscopy I. Broad-beam geometry

Abstract Quantal aspects of spatial resolution in combined energy-loss—electron microscopy are considered. Working in the first Born approximation, it is shown that for coherent broad-beam irradiation the probability of stimulating a localized excitation in matter may be calculated as if the electron executed classical rectilinear motion at constant velocity, v, as v becomes very large. Corrections to this expression may be expressed as a power series in inverse powers of v and may be considered to originate in the quanta1 properties of the electron. The first correction term is displayed explicitly. The impact-parameter dependence of excitation of some localized systems is studied numerically.