Lorentz theory

With regard to these we may simply quote a remark of Lorentz (Theory of Electrons, Leipzig, 1909, p. 287) The only equation by which the observed phenomena are satisfactorily accounted for is that of Planck, and it seems necessary to imagine that, for short waves, the connecting link between matter and ether is... 

In order to formulate a theory for the evaluation of vibrational intensities within the framework of continuum solvation models, it is necessary to consider that formally the radiation electric field (static, Eloc and optical E[jc) acting on the molecule in the cavity differ from the corresponding Maxwell fields in the medium, E and Em. However, the response of the molecule to the external perturbation depends on the field locally acting on it. This problem, usually referred to as the local field effect, is normally solved by resorting to the Onsager-Lorentz theory of dielectric polarization [21,44], In such an approach the macroscopic quantities are related to the microscopic electric response of... 

Let us first review the basics of the Lorentz theory for polarization. If one assumes that a constant macroscopic field is applied to a homogeneous medium of dielectric constant s, the polarization through the medium will be uniform. However, the polarization of a molecule is not proportional to the macroscopic electric field (created by sources external to the dielectric), but to the local electric field, which contains also the field generated by all the other molecules of the dielectric. To account for the latter, one can separate the medium in a spherical cavity (in which the central molecule and its molecular neighbors reside, see Fig. 1 A) and the rest of the medium, which... 

Now, a small silver particle has a frequency of plasma vibrations with a wavelength X = 2nc/(f>p - 140 nm. To explain the presence of a peak at 650 nm, the classical (Lorentz) theory [111-113] requires the presence in the colloid solution of silver with a volume concentration of p 0.86 (Fig. 37a), whereas the experiment yields p values that are much smaller [115], which agrees with our calculations (Fig. 37b). Thus, the shift of the peak in colloidal solutions toward the region of smaller concentrations of metal can be explained by the formation of fractal structures in these solutions. 

The simple Drude-Lorentz theory described earlier in this chapter pictures the valency electrons in a metal as free to move in a potential well of the form shown in fig. 5.06. Within the metal, from B to C, the potential is uniform, but at the surface a potential difference, V (of the order of 10 V), prevents electron escape. If the electrons are assumed to obey the laws of classical mechanics their energies will correspond to the Boltzmann distribution appropriate to the temperature of the specimen. At room temperatures a quite negligible fraction of the electrons will have energies sufficient to surmount the potential... 

H. A. Lorentz, Theory of Electrons, Teubner, Leipzig, 1909 (reprinted by Dover, New York, 1952). O. F. Mossotti, Bibl. Univ. Modena, 6, 193 (1847) Mem. Math. Fis. Modena, 24 11, 49 (1850). R. Clausius, Die mechanische Warmetheorie Vol. 11, Braunschweig, 1879. In Ann. Phy., 49, 1 (1916), Ewald showed that for a lattice of polarizable atoms of cubic symmetry, the local field is essentially that of the continuum considered by Lorentz. 

Collisions between molecules are the greatest cause of line broadening at the pressures normally employed for MMW spectrometry. In the Lorentz theory (ref 2, p. 338) the lifetime of the rotational state involved in the transition is ended abruptly by collision with another molecule which stops the rotation. When the molecule starts to rotate again, its phase with respect to the other molecules is random. For an assembly of molecules this will give rise to an absorption line profile with a FWHM of Xjlm, where r is the mean time between collisions. This is the linear sum of two terms, one for the upper and one for the lower state, having the shape of the Lorentz function (Figure 1.4) when Av [Pg.12]

Lorenz-Lorentz theory addressed the issue by extending the approach of Clausius-Mossotti to optical frequency fields (12,13). This extension relies on a spherical cavity (compare with the need for a needle-shaped cavity) and takes into account the effect of other charges. The only thorny issue is that a spherical cavity is not the best choice for anisotropic molecules. Nevertheless, the Lorenz-Lorentz approach has been widely used in studying optical properties of polymers (14). The expression of the local field is given by... 

H. A. Lorentz, Theory of Elecrons (translated from the 1909 2nd ed. published in Leiden, The Netherlands), Dover Publications, Inc., Mineola, N.Y., 1915. 

The free thermal of the phenomenon electrons in the interstellar medium behaves classically, and it is straightforward to apply the Lorentz theory to the transfer of polarized radiation through this medium. The index of refraction depends on the sense of polarization because the resonant frequency of the electron is moved to greater or lesser values depending on the sense of helicity of the particles around the local field direction. Thus, if the index of refraction of an electron gas is... 

Indeed, during the early years of the twentieth century, the predictions of the classical Lorentz theory provided a guide to the development of a complete and rigorous quantum theory of the interaction of atoms and radiation. 

---