Lorentz local field

N Is the number of molecules per unit volume (packing density factor), fv Is a Lorentz local field correction at frequency v(fv= [(nv)2 + 2]/3, v = u) or 2u). Although generally admitted, this type of local field correction Is an approximation vdilch certainly deserves further Investigation. IJK (resp Ijk) are axis denominations of the crystalline (resp. molecular) reference frames, n(g) Is the number of equivalent positions In the unit cell for the crystal point symmetry group g bjjj, crystalline nonlinearity per molecule, has been recently Introduced 0.4) to get general expressions, lndependant of the actual number of molecules within the unit cell (possibly a (sub) multiple of n(g)). 

In this section, a simple description of the dielectric polarization process is provided, and later to describe dielectric relaxation processes, the polarization mechanisms of materials produced by macroscopic static electric fields are analyzed. The relation between the macroscopic electric response and microscopic properties such as electronic, ionic, orientational, and hopping charge polarizabilities is very complex and is out of the scope of this book. This problem was successfully treated by Lorentz. He established that a remarkable improvement of the obtained results can be obtained at all frequencies by proposing the existence of a local field, which diverges from the macroscopic electric field by a correction factor, the Lorentz local-field factor [27],... 

Having established the molecular linear response with the RPA type of screening, as discussed above, we can evaluate a dielectric function, e(u ) of crystalline Ceo from the polarizability by using the Lorentz local field factor defined in the previous section, Eq.(47). The real and imaginary parts of the calculated dielectric function are denoted by cj and C2, respectively and shown in Fig. 23. 

The/functions are the Lorentz local field factors, N is the number of molecules in unit volume and,... 

Figure le (a) The Lorentz local field model (b) the Oneager... 

The dipole strength of an induced electric dipole transition is proportional to the square of the matrix element in the dipole operator and therefore also to the square of the electric field at the lanthanide site. However, in intensity studies, the lanthanide ions are not in a vacuum, but embedded in a dielectric medium. The lanthanide ion in a dielectric medium not only feels the radiation field of the incident light, but also the field from the dipoles in the medium outside a spherical surface. The total field consisting of the electric field E of the incident light (electric field in the vacuum), plus the electric field of the dipoles is called the effective field eff> i e. the field effective in inducing the electric dipole transition. The square of the matrix element in the electric dipole operator has to be multiplied by a factor E fflEf. In a first approximation, ( efr/ = ( + 2) /9. The factor (n + 2fl9 is the Lorentz local field correction and accounts for dipole-dipole corrections. 

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