Space group Clebsch-Gordan coefficients. I. Special solutions of the multiplicity problem and Dirl's criterion
- 21 April 1986
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 19 (6) , 831-840
- https://doi.org/10.1088/0305-4470/19/6/013
Abstract
The wavevector selection rules (WVSR) occurring in the reduction of Kronecker products of space group unirreps are classified, for convenience, into three types. For WVSR of type I, Dirl (1979) has shown that special solutions of the multiplicity problem always exist. For WVSR of type II, Dirl has given a simple criterion for the existence for special solutions of the multiplicity problem and the authors show that, for all 230 (single and double) space groups, the Miller and Love matrix unirreps satisfy this criterion. WVSR of type III will be considered in a subsequent paper.Keywords
This publication has 33 references indexed in Scilit:
- Eigenfunction Method for Space Group Clebsch-Gordan CoefficientsCommunications in Theoretical Physics, 1983
- Clebsch‐Gordan coefficients of symmetry groupsPhysica Status Solidi (b), 1978
- Effective Hamiltonians and Clebsch-Gordan coefficients in crystalsPhysical Review B, 1976
- Clebsch−Gordan coefficients for *X ⊗ *X in diamond O7h−Fd3m and rocksalt O5n−Fm3mJournal of Mathematical Physics, 1975
- Clebsch−Gordan coefficients for crystal space groupsJournal of Mathematical Physics, 1975
- Scattering tensors and Clebsch-Gordan coefficients in crystalsPhysical Review B, 1974
- Scattering tensors for "forbidden" resonance Raman scattering in cubic crystalsPhysical Review B, 1974
- Kronecker Products and Symmetrized Squares of Irreducible Representations of Space GroupsJournal of Mathematical Physics, 1970
- Space Groups and Selection RulesJournal of Mathematical Physics, 1966
- Space Group Selection Rules: Diamond and Zinc BlendePhysical Review B, 1962