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Statistical theory of angular momentum polarization in chemical reactions.

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Bibliographic Details
Title:	Statistical theory of angular momentum polarization in chemical reactions.
Authors:	Case, D. A., Herschbach, D. R.
Source:	Molecular Physics. 1/10/2002, Vol. 100 Issue 1, p109-125. 17p. 2 Diagrams, 6 Charts, 7 Graphs.
Subjects:	Angular momentum (Nuclear physics), Chemical reactions
Abstract:	A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directions k and k′ and the product rotational angular momentum j′ are treated in detail, including both pairwise and triple correlations. Explicit formulae are given for three choices of the quantization axis: along k, along k′, and along k Coefficients for the (kk′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of jpk′ in reactions of alkali atoms with hydrogen halides and with methyl iodide. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directions k and k′ and the product rotational angular momentum j′ are treated in detail, including both pairwise and triple correlations. Explicit formulae are given for three choices of the quantization axis: along k, along k′, and along k Coefficients for the (kk′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of jpk′ in reactions of alkali atoms with hydrogen halides and with methyl iodide. [ABSTRACT FROM AUTHOR]
ISSN:	00268976
DOI:	10.1080/00268970110088965