Many electron-molecule collision cross sections have been measured, calculated, analyzed and compiled in the literature. Also, data on positron scattering are increasing recently. The present work is to issue a warning about the reliability of the reported cross sections for polar polyatomic molecules.

Differential cross sections for elastic scattering by polar molecules rise sharply toward forward angles. For obtaining the integral cross section (ICS) in such a case, the angular distribution measured with a crossed-beam technique needs to be extrapolated carefully to small angles; empirical extrapolation may easily fail. On the other hand, the ICS are often determined directly by the beam transmission method, in which the attenuation of the incident beam after passing through a gas chamber is measured. Such measurement also requires a careful correction for forward scattering that is only imperfectly discriminable from the unscattered part of the beam. This correction can be easily underestimated for polar molecules if it is based on the experience on nonpolar molecules.

For polar molecules, an estimation of the contribution from forward scattering would be reliable only with the help of theory taking proper account of the rotational motion. Some molecules may be regarded as linear rotators, others as symmetric-top or asymmetric-top rotators. The internal rotation could be important. Nevertheless, well-known cross section formulas valid only for linear rotators are often used also for nonlinear rotators in the literature, leading to unreliable cross sections.

An outstanding case is that of symmetric-top polar molecules, such as NH₃, CH₃X, and CHX₃ (X = F, Cl, Br, I), since the use of the symmetric-top wave functions, rather than the linear-rotator wave functions, makes the elastic ICS diverge unless the rotational temperature T of the molecular gas is exactly zero degrees Kelvin. This is a serious difficulty usually unnoticed in the literature. Theoretical papers often assume that the molecules are initially in the ground rotational state, meaning T = 0. This happens to make the ICS finite. Experimentalists often compare their "measured cross sections" at T ≠ 0 with these theoretical cross sections at T = 0. This comparison is naturally meaningless for polar molecules. Note that it makes sense for nonpolar molecules, for which the ICS is usually nearly independent of the rotational temperature.

It should be noted also that theoretically calculated elastic ICS in the literature are unreliable, if they are based on approximate interaction potentials without the correct long-range dipole potential, if incorrect rotational wave functions for that molecule are used (e.g., linear rotators used for nonlinear polyatomics), or if the rotational motion is not taken into account.

In this way, the cross section data in the literature for electron and positron scattering by polar molecules need to be re-examined carefully.