Scaling of plane-wave Born cross sections for electron-impact excitation of neutral atoms and molecules

We review the scaling of plane-wave Born cross sections for electron-impact excitation of neutral atoms and molecules. The scaling method is applied to integrated cross sections for electric dipole-allowed transitions. As introduced in the BEB scaling model for ionization cross sections, this scaling replaces the incident electron energy $T$ in the first-order PWB cross sections by $T + B + E$, where $B$ is the ionization energy, or the binding energy, of the target electron, and $E$ is the excitation energy. Note in a generic form, first-order PWB cross sections are defined as $\sigma _{PWB} =$ (4$\pi a_{0}^{2}R$/$T)$ GOS$_{PWB}(T)$, where $a_{0}$ is the Bohr radius, $R$ is the Rydberg energy, and GOS is the \textit{Bethe} generalized oscillator strength. In the scaling, though two approaches, computational and experimental have been applied, the latter is presented at this meeting in which the \textit{Bethe} GOS is replaced by the \textit{apparent} GOS determined by the experiments. Representative examples show that an simple improvement scaled by $T + B + E$ extends the usage of the Born-Bethe approximation into the \textit{intermediate} region, thereby bridging the gap between the two regions categorized conventionally as slow and fast collisions.