Statistical theory of angular momentum polarization in chemical reactions.
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| 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] |
| Copyright of Molecular Physics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 5743970 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Statistical theory of angular momentum polarization in chemical reactions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Case%2C+D%2E+A%2E%22">Case, D. A.</searchLink><br /><searchLink fieldCode="AR" term="%22Herschbach%2C+D%2E+R%2E%22">Herschbach, D. R.</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Molecular+Physics%22">Molecular Physics</searchLink>. 1/10/2002, Vol. 100 Issue 1, p109-125. 17p. 2 Diagrams, 6 Charts, 7 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Angular+momentum+%28Nuclear+physics%29%22">Angular momentum (Nuclear physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Chemical+reactions%22">Chemical reactions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Molecular Physics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/00268970110088965 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 109 Subjects: – SubjectFull: Angular momentum (Nuclear physics) Type: general – SubjectFull: Chemical reactions Type: general Titles: – TitleFull: Statistical theory of angular momentum polarization in chemical reactions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Case, D. A. – PersonEntity: Name: NameFull: Herschbach, D. R. IsPartOfRelationships: – BibEntity: Dates: – D: 10 M: 01 Text: 1/10/2002 Type: published Y: 2002 Identifiers: – Type: issn-print Value: 00268976 Numbering: – Type: volume Value: 100 – Type: issue Value: 1 Titles: – TitleFull: Molecular Physics Type: main |
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