Lorenz correction

The crudest approximation to the density matrix for the system is obtained by assuming that there are no statistical correlations between the elementary excitations (perfect fluid), so that can be written as a simple product of molecular density matrices A. A better approximation is obtained if one does a quantum field theory calculation of the local field effects in the system which in a certain approximation gives the Lorentz-Lorenz correction L(TT) in terms of the refractive index n53). One then writes,... 

The other two correction factors account for the effects of induced dipoles in the medium through electronic polarization, and are known as the Lorentz-Lorenz correction factors. The correction for the optical field at frequency 2fti is given by ... 

As mentioned above, the effect of refractive index is more complex than the Lorenz correction can deal with it varies in different ways with different compounds and may reflect the properties of Rydberg transitions. Since the refractive index of many compounds is of the order of (2), we approximate this term as 4/3 and pay it no further attention. A right-handed helix illustrating these terms is shown in Figure 2. For simple four-atom systems, the term LA/D can be calculated from bond lengths (d, d2, d ), bond angles (a and P) and the dihedral angle (0) ... 

The apparent oscillator strength is proportional to the integrated intensity under the molar absorption curve. To derive the formula, Chako followed the elassieal dispersion theory with the Lorentz-Lorenz relation (also known as the Clausius-Mosotti relation), assuming that the solute molecule is located at the center of the spherical cavity in the continuous dielectric medium of the solvent. Hence, the factor derived by Chako is also called the Lorentz-Lorenz correction. Similar derivation was also presented by Kortiim. The same formula was also derived by Polo and Wilson from a viewpoint different from Chako. 

The refractive power is a value which attempts to correct the effects of temperature, pressure, and concentration of the substance, all of which cause the refractive index, n, to vary with the slightest alteration of the conditions. The most accurate expression for the refmctive power is that of Lorenz and Lorentz, which is... 

How does this relate to fluid turbulence The idea is that there exists a critical value of the Reynolds number, TZe, such that intermittent turbulent behavior can appear in the system for TZ > TZe- Moreover, if the behavior of the Lorenz system correctly identifies the underlying mechanism, it may be predicted that, as TZ changes, (1) the duration of the intermittently turbulent behavior will be random, and (2) the mean duration of the laminar phases in between will vary as... 

Hofmann, C., Lorenz, K., and Colca, J. R. (1991). Glucose Transport Deficiency in Diabetic Animals Is Corrected by Treatment with the Oral Antihyperglycemic Agent Pioglitazone. Endocrinology 129, 1915-1925. 

Hofmann C, Lorenz K, Colca JR (1991) Glucose transport deficiency in diabetic animals is corrected by treatment with the oral antihyperglycemic agent pioglitazone. Endocrinol 129 1915-1925... 

If the craze layer extends with complete lateral constraint, the strain in the craze is related to the change in its density. From a relationship between density and refractive index, an equation between strain in the craze and its refractive index can be derived. Although it is usual to start with the Lorenz-Lorentz equation, this may not be the correct relationship for a material having the structure of the craze (9). For the present purposes a linear relationship is assumed. The error introduced is at most 10% and only a few percent for the stretched craze with a high void content. 

If the peak positions are used to determine the unit cell edge lengths, a further correction of the peak position (so far not incorporated in available Rietveld models) is needed for very small crystals the broad peaks of which may show an (apparent) shift A°20 due to inconstancy of the Lorenz-polarization and structure factor over the angular range of the peak. 

Liquid Phase Calculations of the Linear Response. The data in Table 5 for the isotropic polarizability, derived formally via the Lorentz-Lorenz equation (1) from the measured refractive index, shows that the assumption that individual molecular properties are largely retained at high frequency in the liquid is very reasonable. While the specific susceptibilities for the gas and liquid phases differ, once the correction for the polarization of the surface of a spherical cavity, which is the essential feature of the Lorentz-Lorenz equation, has been applied, it is clear that the average molecular polarizabilities in the gas and liquid have values which always agree within 5 or 10%. 

All X-ray intensity data for compound 1 were collected with use of a Broker SMART diffractometer equipped with a CCD area detector using Mo radiation. Intensity data were corrected for Lorenz and polarization effects and were empirically corrected for absorption using... 

It is seen that the effect of the variation of the polarizability is of the same order of magnitude as the effect of statistical fluctuations in the dipole moments / described by the functions S2. For the highest frequencies which may be considered within the approximation introduced into the calculation, the correction to the Lorentz-Lorenz function is about 15 per cent larger than the corresponding correction for the static case, (i.e., to the Clausius-Mossotti function). A similar qualitative behavior may be expected for other noble gases under the same conditions. 

The Lorentz-Lorenz case in which the material is so microscopically inhomogeneous that the spatial distribution of OL is disjoint. The local-field correction is then L P,... 

For this the /-terms are used with the exception of Li, the p-term of which serves for the calculations Rb is omitted on account of its somewhat anomalous Rydberg and Ritz correction. The polaris-abilities of the inert gases arc related to the dielectric constants e or with the refractive indices n for infinitely long waves by the Lorentz-Lorenz formula... 

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