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In condensed matter physics, the dynamic structure factor (or dynamical structure factor) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the structure factor that considers correlations in both space and time.
From knowledge of elemental structure factors, one can also measure elemental pair correlation functions. See Radial distribution function for further information. Equal-time spin–spin correlation functions are measured with neutron scattering as opposed to x-ray scattering. Neutron scattering can also yield information on pair correlations ...
In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation of scattering patterns ( interference patterns ) obtained in X-ray , electron and neutron ...
Haefliger [1] found necessary and sufficient conditions for the existence of a spin structure on an oriented Riemannian manifold (M,g). The obstruction to having a spin structure is a certain element [k] of H 2 (M, Z 2) . For a spin structure the class [k] is the second Stiefel–Whitney class w 2 (M) ∈ H 2 (M, Z 2) of M.
Results are generally communicated as the dynamic structure factor (also called inelastic scattering law) (,), sometimes also as the dynamic susceptibility ′ ′ (,) where the scattering vector is the difference between incoming and outgoing wave vector, and is the energy change experienced by the sample (negative that of the scattered neutron).
Furthermore, the spin of each electron previously involved in the bond is conserved, [1] [3] which means that the radical-pair now formed is a singlet (each electron has opposite spin, as in the origin bond). As such, the reverse reaction, i.e. the reforming of a bond, called recombination, readily occurs.
Low-spin [Fe(NO 2) 6] 3− crystal field diagram. The Δ splitting of the d orbitals plays an important role in the electron spin state of a coordination complex. Three factors affect Δ: the period (row in periodic table) of the metal ion, the charge of the metal ion, and the field strength of the complex's ligands as described by the spectrochemical series.
The spin magnetic moment of the electron is =, where is the spin (or intrinsic angular-momentum) vector, is the Bohr magneton, and = is the electron-spin g-factor. Here μ {\displaystyle {\boldsymbol {\mu }}} is a negative constant multiplied by the spin , so the spin magnetic moment is antiparallel to the spin.