Capture Collisions between Ions and Polar Molecules

Abstract

The manner in which a permanent dipole in a molecule affects capture collisions of the molecule with ions is investigated. Analytical capture cross sections are considered, and three cases are distinguished. None of these is strictly applicable to real collisions, but they are useful in establishment of the general magnitudes of cross sections. The Langevin cross section is somewhat of a lower limit. A strict upper limit to the cross section is derived; it depends on the magnitude of the dipole moment. A quantum‐mechanical treatment at small relative velocity uses the effective potential of interaction determined by the Stark effect; cross sections for this case depend explicitly on the rotational energy of the polar molecule. Molecules which have a first‐order Stark effect have a term ε⁻¹ in their cross sections, whereas the second‐order Stark effect only leads to the ε^−1/2 term of the Langevin theory (ε is the relative translational energy). Numerical cross sections are obtained by using a computer study of collisions. The classical equations of motion are solved. Spiraling collisions (predicted in the Langevin theory) are not obtained, but it is found to be possible to define ``capture'' adequately and to set up a procedure for calculation of capture cross sections. This procedure involves averaging initial conditions with proper weighting. The real molecule HCl has been used in the calculations, and the results are compared with experiment as far as possible. A hypothetical molecule with the same dipole moment and polarizability of HCl but with a moment of inertia 100 times larger is also considered.