Incident-energy dependence of electron-ion collision cross sections

It is shown that the dependence of electron-impact cross sections σ for the excitation of ions on the incident energy T can be represented by compact expressions for a wide range of T from thresholds to 10 keV. These expressions are σT=A lnT+B+C/T+D lnT/T for dipole- and spin-allowed transitions, σT=A+B/T+C/$T^2$+D/$T^3$ for dipole-forbidden but spin-allowed transitions, and σT=(A+BT)/(1+CT+${\mathrm{DT}}^2$) for spin-forbidden transitions, where A, B, C, and D are constants that depend on target properties but not on T. These formulas should provide accurate cross sections in applications where many atomic cross sections are needed. Examples are presented for the excitations of Be-like ${\mathrm{Fe}}^{+22\mathrm{}}$ ion by electron impact.