Quantum versus classical Monte Carlo simulation of low-energy electron transport in condensed amorphous media

Classical trajectory Monte Carlo (MC) simulations modelling radiation-induced damage on subcellular length scales ignore quantum effects that may be non-negligible as electron energy decreases below 1 keV. This work investigates quantum mechanical (QM) treatments of low-energy electron transport in condensed media, comparing with classical MC.

QM calculations involve a simplified model of electron transport in water with a plane wave incident on a cylinder ("droplet") consisting of a cluster of point scatterers (positioned randomly but constrained by a minimum separation, d_min). The system of coupled equations for the electron wavefield incident on each scatterer is solved numerically and results are averaged over many clusters with different point scatterer positions. Average QM cluster cross sections and scattering event densities are compared with analogues computed within the corresponding classical MC model, and relative errors on MC results are calculated.

Differences between QM and MC results for both cluster cross section and scattering event density are sensitive to electron energy (wavelength), structure (d_min), and single-scatterer elastic/inelastic cross sections. Relative errors on cluster cross sections generally differ from errors on scattering event densities. The introduction of inelastic scatter generally increases relative errors (compared to calculations with the same single-scatterer elastic cross section) with some exceptions. Accounting for structure (d_min≠0) enhances differences between QM and MC results.

The quantum wave nature of electrons is non-negligible for simulations of low-energy electron transport within small-scale biological targets. The development of more realistic models of electron transport in condensed media is motivated for future work.