Dipole tensor

The characterisation of the angular dependence of the interaction of two dipole tensors A1 A2 and B B2 is therefore straightforward, namely it depends on the projection angle of the two bonds between A1 and A2 and between B1 and B2. The orientation and magnitude of the chemical shift anisotropy (CSA) tensor, which also can cause cross-correlated relaxation, is not know a priori and therefore needs to be determined experimentally or... 

Dipolar ions like CN and OH can be incorporated into solids like NaCl and KCl. Several small dopant ions like Cu and Li ions get stabilized in off-centre positions (slightly away from the lattice positions) in host lattices like KCl, giving rise to dipoles. These dipoles, which are present in the field of the crystal potential, are both polarizable and orientable in an external field, hence the name paraelectric impurities. Molecular ions like SJ, SeJ, Nf and O J can also be incorporated into alkali halides. Their optical spectra and relaxation behaviour are of diagnostic value in studying the host lattices. These impurities are characterized by an electric dipole vector and an elastic dipole tensor. The dipole moments and the orientation direction of a variety of paraelectric impurities have been studied in recent years. The reorientation movements may be classical or involve quantum-mechanical tunnelling. 

Ordinary Raman scattering is determined by derivatives of the electric dipole-electric dipole tensor ae, and ROA by derivatives of cross-products of this tensor with the imaginary part G,e of the electric dipole-magnetic dipole tensor (the optical activity tensor) and the tensor Ae which results from the double contraction of the third rank electric dipole-electric quadrupole tensor Ae with the third rank antisymmetric unit tensor s of Levi-Civita. The electronic property tensors have the form ... 

This Hamiltonian must be put in the form of equation (Al) (See Appendix A ) for the Redfield theory to be applicable, and depending on the origin, different treatments of the perturbation is necessary. How the direct product is handled is determined by the correlation between the different parts. For simple liquids, the dipole-dipole tensor fluctuates on the picosecond to nanosecond time scale and it is thus not correlated with the nuclear spins. 

In Eqs. (69)-(76) for the electronic observables, the quantities multiplying the electromagnetic fields at the origin are tensors of rank 2, 3 and 4, describing the linear response of the electron distribution. From Eqn. (61) one immediately obtains the equations for those quantities, which are also referred to as second-order properties according to the terminology of perturbation theory. One finds the second-rank dipole tensors ... 

DIELECTRIC CONSTANTS OF FLUID MODELS where I is the unit tensor and r To(r,2) is the dipole tensor... 

In the absence of the Bessel function factor (which arises from the cut-off in the dipole tensor) T(k) would not depend on k and the dominant contributions to the induced moment would come from very large k (as dk = k dkdk). The cut-off diminishes these high k contributions (as density fluctuations cannot have arbitrarily small wavelengths in a fluid of particles of finite size). 

This set of equations can be solved directly, i.e., without proceeding by the pseudo-canonical transformation described in Appendix 3 for the more general case. The only quantities needed are the spherically averaged s and / associated with localized orbitals and the long-range dipole-dipole tensors. The update formula to get the nth approximation to the amplitude matrix element is... 

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