Scattering tensors and Clebsch-Gordan coefficients in crystals

Birman, Joseph L.; Berenson, Rhoda

doi:10.1103/physrevb.9.4512

Cited by 35 publications

(11 citation statements)

References 10 publications

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“…[see e.g. Birman & Berenson (1974) and Cracknell (1974)]. The essential step of the selection-rules derivations consists in the reduction of Kronecker products of space-group representations into irreducible .…”

Section: Direct Product Of Representations 41 the Problemmentioning

confidence: 99%

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups

Aroyo

Kirov

Capillas

et al. 2006

Acta Crystallogr A Found Crystallogr

902

607

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The Bilbao Crystallographic Server is a web site with crystallographic programs and databases freely available on-line (http://www.cryst.ehu.es). The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones etc.). Apart from the simple tools for retrieving the stored data, there are programs for the analysis of group-subgroup relations between space groups (subgroups and supergroups, Wyckoff-position splitting schemes etc.). There are also software packages studying specific problems of solid-state physics, structural chemistry and crystallography. This article reports on the programs treating representations of point and space groups. There are tools for the construction of irreducible representations, for the study of the correlations between representations of group-subgroup pairs of space groups and for the decompositions of Kronecker products of representations.

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Section: Direct Product Of Representations 41 the Problemmentioning

confidence: 99%

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups

Aroyo

Kirov

Capillas

et al. 2006

Acta Crystallogr A Found Crystallogr

902

607

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“…Raman tensors give the relative intensities of the same phonon in different scattering geometries. It has been shown that the Raman tensors are Clebsch-Gordon coefficients [16].…”

Section: Raman Effect For Ordinary Lightmentioning

confidence: 99%

Raman scattering using vortex light

Birman

2015

Journal of Physics and Chemistry of Solids

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“…We write the first-order Raman scattering tensor according to eq. (A4) of Birman and Berenson [21] as proportional to the CGcs rrz'| ~,z~ with a proportionality factor C(l'l"l) dependent on the representation labels l', l" and l. For the excitation of simmetry specified by representation l and representation row ~ the scattering tensor is…”

Section: -The First-order Raman Scattering Tensor In Hexagonal Icementioning

confidence: 99%

“…Birman and Berenson [21] have shown that elements of the first-order (one-excitation) scattering tensor P~(~) (jr) are appropriate Clebsch-Gordan coefficients or in case of multiplicity greater than one prescribed linear combinations; the elements (2) 9 ., P~ (jz; 3 r') of the second-order (two-excitation) scattering tensor are a particular sum of products of Clebsch-Gordan coefficients for reduction of the symmetrized square of vector representation into irreducible representations of the excitations involved in the scattering process [22,23]. In space group D~h of the uniaxial crystal of h.c.p, structure the vector representation is the direct sum of the unitary irreducible representations/'6-(Elu) and/'2-(A2,~) where we write the representation labels of ML [9] and add those of Herzberg [19] in the brackets:…”

Section: ~2=-~ (Jr) El~l 2 mentioning

confidence: 99%

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Raman scattering tensors for translational vibrations of ice

Ziemczonek

Suffczyński

1991

Il Nuovo Cimento D

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Summary. --Scattering tensors for the first-and the second-order Raman scattering of light on the translational vibrations of hexagonal ice lattice are related to the crystal space-group Clebsch-Gordan coefficients. Scattered intensities are presented for pairs of phonons allowed by the hexagonal close-packed-crystal selection rules and are discussed for the appropriate light polarizations. The results can be of help in analysis of measurements of polarized light scattering on oriented monocrystals of hexagonal ice.PACS 61.50 -Crystalline state (including molecular motions in solids). PACS 78.30 -Infrared and Raman spectra and scattering.

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Scattering tensors and Clebsch-Gordan coefficients in crystals

Cited by 35 publications

References 10 publications

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups

Raman scattering using vortex light

Raman scattering tensors for translational vibrations of ice

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