Energy loss by slow electrons in polar gases

The mean energy loss by slow electrons moving in a gas and rotationally exciting the molecules is proportional to the rotational stopping cross section (RSCS) defined by multiplying the cross section for a rotational transition Γ→Γ' by the transition energy and by summing the product over Γ'. The RSCS for linear and symmetric-top polar molecules are studied in the adiabatic-rotation approximation at scattering angles θ larger than a critical value θc and in the first-Born approximation for θ<θc. Formulas independent of θc are derived for the RSCS for any Γ as the sum of the RSCS for the ground rotational state Γ=0 and a term that depends on Γ in a simple analytic form and is proportional to the dipole moment D squared. For a vanishing D, this term vanishes and the formulas reduce to a previously proven theorem for nonpolar molecules that the RSCS is independent of Γ. Useful expressions are also derived for the average of the RSCS over the Boltzmann distribution of Γ