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

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.The work of D.E. and I.K. has been financially supported by the European Union FP7 (Marie Curie Actions) program "RADDEL" (REA Grant Agreement No. 290023). The work of R.G.M. and I.A. has been supported by the European Regional Development Fund and the Spanish Ministerio de Economía y Competitividad (Project No. FIS2010-17225)