Lorentz model, application

The latter is determined by the oscillation frequency, decaying coefficient, and vibration lifetime. This nonrigid dipole moment stipulates a Lorentz-like addition to the correlation function. As a result, the form of the calculated R-band substantially changes, if to compare it with this band described in terms of the pure hat-curved model. Application to ordinary and heavy water of the so-corrected hat-curved model is shown to improve description (given in terms of a simple analytical theory) of the far-infra red spectrum comprising superposition of the R- and librational bands. 

From the point of view of theory, the formulae of Table 2.6 are equally applicable to both gas and condensed phase samples, as they include the local field factors, which account for local modifications to the Maxwell fields due to bulk interactions within the Onsager-Lorentz model. 

The Lorentz model becomes more useful and applicable over a wide frequency range if the effect of oscillators of different types is taken into account. In the simplest harmonic approximation, the oscillators representing the lattice... 

Sorana BD, Lorentz J (2011) Predictivity approach for quantitative structure prediction models application for blood barrier permeation for diverse drug like compounds. Int J Mol Sci 12(7) 4348 386... 

The classical theory of the dielectric response in solids is frequently described by the Drude and Lorentz models. The Drude model is applicable to free-eiectron metals its quantum-meehanical analog includes intraband transitions, where intraband transitions are taken to mean all transitions not involving a reciprocal lattice vector. The Lorentz model is applicable to insulators its quantum-mechanieal analog ineludes all direct interband transitions, i.e., all transitions for whieh the final state of an electron lies in a different band but with no change in the k vector in the reduced-zone scheme. In the following discussion, both models will be surveyed and evaluated for real metals. 

The Lorentz-Drude model is largely ad hoc [14,15] but still useful as starting points and for developing feelings for optical properties. Consider an atom with electrons boiuid to the nucleus in the same way as a small mass bound to a large mass by a spring. This is the Lorentz model and is applicable to a wide variety of materials (i.e., metals, semiconductors and insulators). The motion of an electron boiuid to the nnclens is then written as... 

The application of the Lorentz-Lorenz equation gives a convincing demonstration of the general similarity of the linear response in gas and liquid but its application in the liquid introduces an approximation which has not yet been quantified. A more precise objective for the theory would be to calculate the frequency dependent susceptibility or refractive index directly. For a continuum model this may lead to a polarizability rigorously defined through the Lorentz-Lorenz equation as shown in treatments of the Ewald-Oseen theorem (see, for example Born and Wolf, plOO),59 but the polarizability defined in this way need not refer to one molecule and would not be precisely related to the gas parameters. 

The results shown in Table 1 and Fig. 7 prove the applicability of our model - a gradient refractive index layer, where the local refractive index is determined from the volume fraction of the constituents by the Lorentz-Lorenz formula, as the fitted layer thickness corresponded to the particle diameter (Table 1) - and the other results were also consistent with the expectations both about the behavior of the particles and the structure of the interfacial layer. 

It should be noted that the two-electron term in this Dirac—Coulomb equation is based on a classical (i.e., nonrelativistic) picture of the interaction, and it is therefore not Lorentz invariant. In many applications this is a problem of minor importance, and results that are in good agreement with experiment often are obtained with the Dirac-Coulomb equation (Eqs. [71]—[74]) or with theory derived from it through further simplifications. For situations calling for a more accurate model, a relativistic picture of the electron—electron interaction is given by the Breit operator ... 

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