Transition state theory inelastic scattering

These results apply specifically to Rayleigh, or elastic, scattering. For Raman, or inelastic, scattering the same basic CID expressions apply but with the molecular property tensors replaced by corresponding vibrational Raman transition tensors between the initial and final vibrational states nv and rn . In this way a s are replaced by (mv aap(Q) nv), where aQ/3(<3) s are effective polarizability and optical activity operators that depend parametrically on the normal vibrational coordinates Q such that, within the Placzek polarizability theory of the Raman effect [23], ROA intensity depends on products such as (daaf3 / dQ)0 dG af3 / dQ) and (daaf3 / dQ)0 eajS dAlSf / dQ)0. 

Utilization of both ion and neutral beams for such studies has been reported. Toennies [150] has performed measurements on the inelastic collision cross section for transitions between specified rotational states using a molecular beam apparatus. T1F molecules in the state (J, M) were separated out of a beam traversing an electrostatic four-pole field by virtue of the second-order Stark effect, and were directed into a noble-gas-filled scattering chamber. Molecules which were scattered by less than were then collected in a second four-pole field, and were analyzed for their final rotational state. The beam originated in an effusive oven source and was chopped to obtain a velocity resolution Avjv of about 7 %. The velocity change due to the inelastic encounters was about 0.3 %. Transition probabilities were calculated using time-dependent perturbation theory and the straight-line trajectory approximation. The interaction potential was taken to be purely attractive ... 

Let us turn now to the corresponding inelastic cross-section. The matrix elements (/, M L + 2S J, M) vanish except for / —/ = 1. Hence, near the forward direction we observe only the dipole-allowed transitions, i.e., the /—> / 1 transitions out of the Hund s rule ground state. Beyond the limit of small K, higher-order transitions contribute to the cross-section, and these are the main subject of the subsequent theory valid for arbitrary values of k. The small-K result we present for inelastic events, / = / 1, is of limited practical value since the minimum value of c is usually quite large owing to the kinematic constraints on the scattering process. Even so, the result is a useful guide to the size of the cross-section, and a welcome check on a complete calculation. 

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