Ionization Cross Sections for ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and C${\mathrm{O}}_2$ Clusters by Electron Impact

Clusters of condensed matter which are produced under some particular conditions in supersonic molecular jets can be ionized by electrons. Measured ionization cross sections show a sharp dependence on $N$, the mean number of molecules per cluster. For small clusters ($\overline{N}<50\mathrm{}$) the cross sections increase as $N$; for larger clusters as about ${\overline{N}}^{\frac{2}{3}}$. Furthermore the electron initial energy $W_{\mathrm{eM}}$, for which the cross section is maximum, increases with $N$. In this paper we present a model for the computation of the cluster ionization cross sections which includes the energy losses inside the cluster of both primary and secondary electrons. The escape probability for secondary electrons is given as a function of their initial position and energy. This latter is related to the primary-electron energy. Results of these computations for ${\mathrm{H}}_2$, C${\mathrm{O}}_2$, and ${\mathrm{N}}_2$ clusters are in good agreement with experimental data.