Discrete Deposition of Energy by Electrons in Gases

Much previous work on the energy deposition of electrons in gases has centered on the continuous-slowing-down approximation, the key element being the loss function $-\left(\frac{1}{n}\right)\frac{\mathrm{dE}}{\mathrm{dx}}$. Calculations generally reduce to energy integrals involving cross sections and this loss function. The limits of the continuous approximation are now examined by comparing it over various energy intervals with a method which takes into account the discrete nature of the energy lost in each collision. The calculation at each stage considers how an electron at a particular energy will redistribute itself on average at all lower energies, with the distribution depending on cross sections and transition energies. Results of the present work for He and ${\mathrm{N}}_2$, and comparisons to the continuous approximation, are given.