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On the summations involving Wigner rotation matrix elements

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Abstract

Two new methods to evaluate the sums over magnetic quantum numbers, together with Wigner rotation matrix elements, are formulated. The first is the coupling method which makes use of the coupling of Wigner rotation matrix elements. This method gives rise to a closed form for any kind of summation that involves a product of two Wigner rotation matrix elements. The second method is the equivalent operator method, for which a closed form is also obtained and easily implemented on the computer. A few examples are presented, and possible extensions are indicated. The formulae obtained are useful for the study of the angular distribution of the photofragments of diatomic and symmetric-top molecules caused by electric-dipole, electric-quadrupole and two-photon radiative transitions.

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Authors and Affiliations

  1. Vitreous State Laboratory, The Catholic University of America, Washington, DC, 20064, USA

    Shan-Tao Lai

  2. Center for Molecular Dynamics and Energy Transfer, Department of Chemistry, The Catholic University of America, Washington, DC, 20064, USA

    Pancracio Palting & Ying-Nan Chiu

  3. Department of Chemistry, The Johns Hopkins University, Baltimore, MD, 21218, USA

    Harris J. Silverstone

Authors
  1. Shan-Tao Lai
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  2. Pancracio Palting
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  3. Ying-Nan Chiu
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  4. Harris J. Silverstone
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Lai, ST., Palting, P., Chiu, YN. et al. On the summations involving Wigner rotation matrix elements. Journal of Mathematical Chemistry 24, 123–132 (1998). https://doi.org/10.1023/A:1019166518417

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  • DOI: https://doi.org/10.1023/A:1019166518417

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