International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.11, p. 281

Section 1.11.7. Glossary

V. E. Dmitrienko,a* A. Kirfelb and E. N. Ovchinnikovac

aA. V. Shubnikov Institute of Crystallography, Leninsky pr. 59, Moscow 119333, Russia,bSteinmann Institut der Universität Bonn, Poppelsdorfer Schloss, Bonn, D-53115, Germany, and cFaculty of Physics, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119991, Russia
Correspondence e-mail:  dmitrien@crys.ras.ru

1.11.7. Glossary

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[\chi({\bf r})] local susceptibility tensor in direct space
[\chi({\bf H})] Fourier components of the local susceptibility tensor
[{\bf H}] reciprocal-lattice vector
[{\bf e}] polarization vector of an X-ray wave
[\bf k] wavevector of an X-ray wave
[R_{ij}^g ] matrix corresponding to point-group operator [g]
[{\boldsigma}] polarization vector perpendicular to the scattering plane
[\boldpi ] polarization vector in the scattering plane
[\theta] Bragg angle
[\varphi] azimuthal angle of rotation about a reciprocal-lattice vector
[{\bf A}({\bf r})] vector potential of the electromagnetic wave
[{\bf P}({\bf r})] momentum of an electron
[\omega] frequency of an electromagnetic wave
[\lambda] wavelength of the radiation
[E_i] energy of a discrete atomic level
[\bf s] spin of an electron
[f({\bf k},{\bf e},{\bf k}^{\prime},{\bf e}^{\prime})] scattering amplitude
[\bf G] scattering vector
[\epsilon_{ijk}] Levi-Civita symbol
[\omega_{ca}] transition frequency for states a and c
[\Gamma] energy width of the excited state
[p_a] probability that the state [|a\rangle] of the scatterer is occupied
[f_{jk}] tensor atomic factor
[F_{jk}({\bf H})] structure-factor tensor of rank 2
[I_{{\bf H}}({\bf e}^{\prime},{\bf e})] intensity of the reflection
[EL] notation of the electric multipole transition. [E1]: the dipole; [E2]: the quadrupole
[ML] notation of the magnetic multipole transition
[L] orbital moment of electron
[D_{jk}] dipole–dipole tensor atomic factor
[D_{jk}^+] symmetric part of the dipole–dipole tensor atomic factor
[D_{jk}^-] antisymmetric part of the dipole–dipole tensor atomic factor
[I_{jkl}] third-rank tensor describing the dipole–quadrupole resonant X-ray scattering
[I_{jkl}^{++}] part of the third-rank tensor invariant under time inversion and symmetric under the permutation of j and k
[I_{jkl}^{+-}] part of the third-rank tensor non-invariant under time inversion and symmetric under the permutation of j and k
[I_{jkl}^{-+}] part of the third-rank tensor invariant under time inversion and antisymmetric under the permutation of j and k
[I_{jkl}^{--}] part of the third-rank tensor non-invariant under time inversion and antisymmetric under the permutation of j and k
[Q_{ijkl}] fourth-rank tensor describing the quadrupole–quadrupole resonant X-ray scattering
Tr trace of matrix
[\bf m] magnetic moment of an atom
YLM spherical tensor
[X^{(p)}_q] component of the spherical tensor depending only on the incident and scattered radiation
[F^{(p)}_-q] component of the spherical tensor associated with the tensor properties of the absorbing atom

References

Di Matteo, S., Joly, Y. & Natoli, C. R. (2005). Detection of electromagnetic multipoles by X-ray spectroscopies. Phys. Rev. B, 72, 144406.
Paolasini, L. (2012). Magnetism in condensed matter: resonant and magnetic scattering by synchrotron radiation. In Italian School on Magnetism, Pavia 2012, pp. 1–83. Universita di Pavia.








































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