Quantum Vibrational Transition Probabilities in Atom-diatomic Molecule Collisions. A Tractable Three-Dimensional Model

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Abstract
The method of Cheung and Wilson [J. Chem. Phys. 51, 3448, 4733 (1969)] is applied to the computation of vibrational transition probabilities for collisions of atoms with spherically symmetric oscillators (``breathing spheres'') in three dimensions. Effects of the angular momenta associated with rotation of the sphere and with the relative motion of the atom and sphere are taken into account. Takayanagi's modified wave number method [Progr. Theoret. Phys. (Kyoto) 8, 497 (1952); J. Phys. Soc. (Japan) 14, 75 (1959)] is employed to obtain approximations in closed form to the integrals which are needed.