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Collisional scaling within a multichannel square representation
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25.One alternate approach based on the initial value representation, has been given by S. D. Augustin, J. Chem. Phys. 78, 206 (1983). While in limited application, the approach appeared promising, we are not aware of any attempts to expand on this work.
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27.See R. G. Newton in Ref. 26, pp. 349–350.
28.Clearly the first feature follows from the second. We have chosen to separate these features here in order to facilitate our later discussion of cross section scaling.
29.The same assumption must be made in the ES scaling of cross sections unless the cross sections are rotational degeneracy averaged.
30.One finds a very similar assumption being made in the various ES based scaling schemes.
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37.As noted in Ref. 31, the partial wave expansions for the determination of the integral cross sections were cut off at such that the strongest of the pure rotational transitions are not fully converged. For our scaling analysis, however, it only matters that the expansions have been cut off at the same point for all the transitions (converged and unconverged) and that sufficient terms (in the expansions) have been taken such that in the case of the MS and M‐ES scalings certain assumptions (e.g., vanishing phase coherence and deconvolution of scaling coefficients and S‐matrix elements) prevail.
38.Although there is no free parameter in the ES scaling we have used the quantity to measure the accuracy of ES scaled results and to make comparisons with the corresponding χ values for MS and M‐ES scalings.
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