Analytical Representation of Total Cross-Sections for Electron Atom Scattering: Application to Atomic Helium

Based on the series expansion formalism, an analytical approach is proposed to evaluate the total cross-sections induced by electron impact excitation. As an illustration, an analytical expression of the total cross-section of the double excitation of helium atom by electron impact is obtained for the 2p$\text{}^{2}$ $\text{}^{3}$P and 2p3p $\text{}^{1}$P transitions within the framework of the distorted wave Born approximation. The available experimental data are well reproduced by the obtained expression of the total cross-section which is function of the only parameter of the incident electron energy. Comparisons are also made with numerical calculations.