| Popis: |
Purpose Monte Carlo simulations are being applied to study radiation interactions and energy deposition on sub-micron length scales within cells, e.g., DNA, in diverse contexts across medical physics. While these classical trajectory Monte Carlo simulations ignore the quantum wave nature of the electron, quantum effects may become non-negligible as electron energy decreases below 1 keV, with electron wavelength becoming considerable relative to the size of biological targets. This work investigates quantum mechanical (QM) treatments of low energy electron transport in condensed media and compares results with those from the corresponding classical trajectory Monte Carlo (MC) model. Methods For QM calculations, a simplified model of electron transport in water is developed consisting of a plane wave (representing an electron) incident on a collection of ∼103 point scatterers (molecules) representing a water droplet. Scatterer positions are random but are constrained by a minimum scatterer-to-scatterer separation, dmin, in some simulations. Cross sections for isotropic elastic and inelastic (absorption) interactions are varied. QM calculations involve numerically solving the system of ∼103 coupled equations for the electron wavefield incident on each scatterer. Results are averaged over 105 droplets with different point scatterer positions but otherwise same parameters (incident electron energy, cross sections). Average QM droplet incoherent cross sections and scattering event densities are compared with analogues computed within the corresponding classical MC model, and estimates of relative errors on MC results are computed. Results Relative errors on MC results vary with electron wavelength, droplet shape and structure (dmin), and interaction cross section. Relative errors on droplet differential cross sections generally differ from errors on scattering event density. The introduction of inelastic scatter generally increases relative errors (compared to calculations with the same elastic scatter cross section) with some exceptions (e.g. longer wavelength, relatively large inelastic cross section). Accounting for structure (non-zero dmin) enhances differences between QM and MC results. Conclusions The quantum wave nature of electrons may be non-negligible for simulations of electron transport within small-scale biological targets. Future work will involve the development of more realistic models of electron transport in condensed media. |
Full Text from ScienceDirect