Inelastic mean free path of low-energy electrons in condensed media: beyond the standard models

The most established approach for ‘practical’ calculations of the inelastic mean free path (IMFP) of low-energy electrons (~10 eV to ~10 keV) is based on optical-data models of the dielectric function. Despite nearly four decades of efforts, the IMFP of low-energy electrons is often not known with the desired accuracy. A universal conclusion is that the predictions of the most popular models are in rather fair agreement above a few hundred electron volts but exhibit considerable differences at lower energies. However, this is the energy range where their two main approximations, namely, the random-phase approximation (RPA) and the Born approximation, may be invalid. After a short overview of the most popular optical-data models, we present an approach to include exchange and correlation (XC) effects in IMFP calculations, thus going beyond the RPA and Born approximation. The key element is the so-called many-body local-field correction (LFC). XC effects among the screening electrons are included using a time-dependent local-density approximation for the LFC. Additional XC effects related to the incident and struck electrons are included through the vertex correction calculated using a screened-Hubbard formula for the LFC. The results presented for liquid water reveal that XC may increase the IMFP by 15–45% from its Born–RPA value, yielding much better agreement with available experimental data. The present work provides a manageable, yet rigorous, approach to improve upon the standard models for IMFP calculations, through the inclusion of XC effects at both the level of screening and the level of interaction.D. E. and I. K. acknowledge financial support from the European Union FP7 (Marie Curie Actions) programme ‘RADDEL’ (REA grant agreement no. 290023). R.G.M. and I. A. acknowledge financial support from the European Regional Development Fund and the Spanish Ministerio de Economía and Competitividad (project no. FIS2014-58849-P)