Excitation of Molecular Vibration on Collision: Role of the High-Order Angular Momenta

Excitation of molecular vibration in the collision between two diatomic molecules is studied. The specific aims are to calculate the partial cross sections for general values of the collision angular momentum l and to show the important role of the high‐order partial waves in the calculation of total cross sections. It is shown that the partial cross section becomes largest at $l_{\max }=\frac{1}{2}{\text{[(2/L)}}^{\frac{1}{2}}\text{−1]}$ , where L is dependent on the collision parameters and is of the order of 10⁻³−10⁻⁴; in H₂–H₂ values of l up to about 30, 55, 90, and 125 must be considered for the relative energy of 0.5, 1, 2, and 3 eV, respectively, for the calculation of total cross sections. In O₂–O₂ the corresponding l values are 125, 200, 340, and 450. It is also shown that the modified wavenumber approximation underestimates the average total cross section by a factor of 1.7 at 300°K and 1.3 at 4000°K for H₂–H₂ and for O₂–O₂ by 1.8 and 1.4 at the corresponding temperatures. The connection between the cross section for inverse power potentials and those for exponential potentials is discussed analytically.