Scaled adiabatic-nuclear-rotation theory for near-threshold rotational excitation in electron-molecule scattering

The adiabatic-nuclei theory, which is widely used in electron-molecule scattering calculations of cross sections for nuclear excitation, is known to be invalid near threshold. A new "scaling procedure" for correcting the adiabatic-nuclei theory for rotational excitation is introduced and applied to $e$-${\mathrm{H}}_2$ collisions in the rigid-rotor approximation. At near-threshold energies, the resulting cross sections are shown to be in very good agreement with accurate laboratory-frame close-coupling results.