Resonances and threshold effects in low-energy electron collisions with methyl halides

Cross sections for elastic and inelastic electron collisions with CH$_3$X (X=Cl, Br, I) molecules are calculated. For the lowest partial wave the resonance R-matrix theory, and for the higher partial waves the theory of scattering by dipolar plus polarization potential, are used. It is shown that the rotationally elastic scattering amplitude for a polar molecule in the fixed-nuclei approximation is logarithmically divergent for the forward direction, and a new closure formula is derived to speed up the convergence at small angles. The dipole moment as a function of the C--X distance is modeled semiempirically. This is supplemented by {\it ab initio} calculations of the dipole moment function for CH$_3$Br using the multi-configurational valence bond method. The results for scattering cross sections show pronounced features caused by vibrational Feshbach resonances and threshold cusps. The features are most noticeable at the $v=6$, 7, and 8 thresholds in CH$_3$Cl, at the $v=3$ and 4 thresholds in CH$_3$Br and at the $v=1$ threshold in CH$_3$I. The authors are grateful to H. Hotop for many stimulating discussions.