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 Results for DC.creator="A." AND DC.creator="Kirfel" in section 1.11.6 of volume D
Tensor atomic factors (spherical tensor representation)
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.6.6, pp. 279-280 [ doi:10.1107/97809553602060000910 ]
... In order to obtain the scattering amplitude and intensity for a resonant process described by some set of spherical tensor components ... tensor that describes the atomic scattering must be contracted by a tensor of the same rank and inversion/time-reversal symmetry ... the X-ray probe, so that the result would be a scalar. There are well known relations between the components ...

Tensor atomic factors (magnetic case)
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.6.5, pp. 278-279 [ doi:10.1107/97809553602060000910 ]
... possess different densities of states with opposite spin directions. During a multipole transition from the ground state to an excited state ... with time reversal because if and/or (Zeeman splitting in a magnetic field). That the antisymmetric parts of the tensors ... it is parity-even and time-odd, being associated with a magnetic moment (1.11.6.41). This part of the tensor ...

Tensor structure factors
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.6.4, p. 278 [ doi:10.1107/97809553602060000910 ]
... elements), the index u denotes the crystallographically equivalent positions; is a site-occupancy factor, and is the Debye-Waller temperature factor. ... reflections are different for tensor structure factors of different ranks, a circumstance that may be used for experimental separation of different ...

Resonant atomic factors: multipole expansion
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.6, pp. 275-280 [ doi:10.1107/97809553602060000910 ]
... the resonant part of the atomic factor (1.11.4.3) aswhere , is a dimensionless tensor corresponding to the dipole-dipole contribution, is the ... contribution to the resonant atomic factor can be represented as a sum of an isotropic, a symmetric and an antisymmetric part, written as (Blume, 1994) ...

Tensor atomic factors (non-magnetic case)
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.6.2, pp. 276-277 [ doi:10.1107/97809553602060000910 ]
... third-rank tensor describing the dipole-quadrupole term, and denotes a symmetric quadrupole-quadrupole contribution. From the physical point of view ... wavevectors and . Equation (1.11.6.16) is also frequently considered as a phenomenological expression of the tensor atomic factor where each tensor ... instance, the tensor is symmetric, the rank-3 tensor has a symmetric and a antisymmetric part, and the rank-4 ...

Tensor atomic factors: internal symmetry
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.6.1, pp. 275-276 [ doi:10.1107/97809553602060000910 ]
... contribution to the resonant atomic factor can be represented as a sum of an isotropic, a symmetric and an antisymmetric part, written as (Blume, 1994)where ... of the time-reversed state . If, for example, has a magnetic quantum number m, then has a magnetic quantum ...

Hidden internal symmetry of the dipole-quadrupole tensors in resonant atomic factors
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.6.3, pp. 277-278 [ doi:10.1107/97809553602060000910 ]
... versa). Indeed, both of them can be described by a symmetric third-rank tensor resulting from the second-order Born ... symmetry, and have the same number of independent elements (with a maximum 18 for site symmetry 1). Thus, one can ... which the antisymmetric part of the dipole-quadrupole term is a linear function of the symmetric one [however, not vice ...

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