Long-Range Scattering from Anisotropic Potentials: Dipole—Dipole Scattering

Abstract

Total cross sections were calculated for collisions of polar molecules. They were found to be determined chiefly by the rotationally inelastic collisions occurring at large impact parameters and to be highly sensitive to the amount of energy transferred from translation to rotation. The calculations were done by using either the Born approximation or a semiclassical method based on time‐dependent perturbation theory to obtain the scattering matrix for large impact parameters (both methods yield the same results). Scattering at smaller impact parameters was handled using a generalized Massey—Mohr treatment. The cross sections were found to be large and strongly dependent on the rotational states. Averaged cross sections were calculated for Boltzmann distributions of rotational states. These depend, as expected, on both the rotation constants and on the rotational temperature. Cross sections for linear dipoles such as alkali halides scattered by CH₃I are around 4000 Ų. Cross sections for two symmetric tops are much higher. The averaged velocity derivative is quite different from that found for atom—atom scattering. A calculation of the second‐order elastic scattering was done for the case where the rotational energy levels of the two molecules are badly mismatched. Comparison is made with several other treatments which use the sudden approximation or some sort of averaged potential. The methods developed here are also applicable to scattering of polarized beams or to the calculation of small‐angle inelastic scattering.