Statistical theory of angular momentum polarization in chemical reactions

D. A. Case, D. R. Herschbach

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 [kcirc] and [kcirc]′ 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 [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.

Original languageEnglish (US)
Pages (from-to)109-125
Number of pages17
JournalMolecular Physics
Volume100
Issue number1
DOIs
StatePublished - Jan 2002

Fingerprint

Angular momentum
Chemical reactions
chemical reactions
angular momentum
Polarization
Alkalies
polarization
Hydrogen
angular correlation
Legendre functions
Correlation theory
Polynomials
coefficients
Direction compound
correlation coefficients
iodides
halides
alkalies
Scattering
Atoms

All Science Journal Classification (ASJC) codes

  • Biophysics
  • Molecular Biology
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

Cite this

@article{accea421a4b742358803569cfa26c043,
title = "Statistical theory of angular momentum polarization in 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 [kcirc] and [kcirc]′ 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 [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.",
author = "Case, {D. A.} and Herschbach, {D. R.}",
year = "2002",
month = "1",
doi = "10.1080/00268970110088965",
language = "English (US)",
volume = "100",
pages = "109--125",
journal = "Molecular Physics",
issn = "0026-8976",
publisher = "Taylor and Francis Ltd.",
number = "1",

}

Statistical theory of angular momentum polarization in chemical reactions. / Case, D. A.; Herschbach, D. R.

In: Molecular Physics, Vol. 100, No. 1, 01.2002, p. 109-125.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Statistical theory of angular momentum polarization in chemical reactions

AU - Case, D. A.

AU - Herschbach, D. R.

PY - 2002/1

Y1 - 2002/1

N2 - 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 [kcirc] and [kcirc]′ 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 [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.

AB - 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 [kcirc] and [kcirc]′ 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 [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.

UR - http://www.scopus.com/inward/record.url?scp=70349657218&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349657218&partnerID=8YFLogxK

U2 - 10.1080/00268970110088965

DO - 10.1080/00268970110088965

M3 - Article

AN - SCOPUS:70349657218

VL - 100

SP - 109

EP - 125

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 1

ER -