Quantum Calculations of the Velocity Dependence of the Differential and Total Cross Sections for Elastic Scattering of Molecular Beams

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Abstract
The partial wave treatment (phase shift analysis) of the elastic scattering of molecular beams [J. Chem. Phys. 33, 795 (1960)] is applied to the calculation of the velocity dependence of the differential and total cross sections for an assumed L‐J (12, 6) potential. For most of the calculations, the ε, σ values are chosen to correspond to the H2–Hg system. The range of the velocity parameter A≡kσ=μvσ/ℏ is from 3 to 30; this is equivalent to a 100‐fold variation in H2 beam temperature (approx 8.2–820°K). Computations of the angular distribution of the scattering dσ(θ)/dΩ and the total cross section Q as a function of A are reported. A correlation of the interference maxima in dσ(θ)/dΩ is presented. The Massey‐Mohr approximation for Q(A) for an inverse sixth‐power attractive potential is compared with the present calculations for the L‐J (12, 6) potential. Significant undulatory deviations are noted at low A; this effect is attributed to the existence of the broad maximum in the phase shift curve η(l), which, in turn, originates from the negative repulsive phases at low l. Consideration is given to the question of the sensitivity of the scattering to the repulsive part of the potential.