The effect of static many-body local-field corrections to inelastic electron scattering in condensed media

Abstract

We present a manageable approach to include, within the context of optical-data models of the dielectric response function, exchange and correlation (XC) effects in inelastic electron scattering, thus, going beyond the standard random-phase approximation (RPA). The many-body local-field correction in its static limit, G(q) , is employed to incorporate XC effects to all orders in q at both the level of “screening” and the level of “scattering” by computing the so-called test-charge–test-charge (t–t), electron–test-charge (e–t), and electron–electron (e–e) dielectric functions. Some of the most used analytic approximations for G(q) are examined, ranging from the early Hubbard-like expressions to more recent parameterized formulations that satisfy some of the known asymptotic limits. The effect of the different G(q) models upon the inelastic scattering of low-medium energy electrons in condensed matter is examined using solid (amorphous) carbon as an example. It is shown that when XC corrections at all levels are considered, a net reduction of the inelastic scattering cross section by up to 20%–30% from the corresponding RPA value is obtained. Interestingly, a screened Hubbard approximation to G(q) reproduces (to a few %) the results of more accurate representations. Based on the present results, the controversial high-q asymptotic behaviour of G(q) is inconsequential to inelastic electron scattering in the examined energy range.