Dielectric response oscillator forms

In Section VILA a strongly idealized picture was described. The dielectric response of an oscillating nonrigid dipole was found in terms of collective vibrations of two charged particles. Now a more specific picture pertinent to an idealized water structure will be considered. Namely, we shall briefly consider thermal motions of a dipole as (i) pure rotations in Fig. 56b and (ii) pure translations in Fig. 58a. Item (i) presents the major interest for us, since we would like to roughly estimate on the basis of a molecular dynamics form of the absorption band stipulated by rotation of a dipole. Of course, even in terms of a simplified scheme, the internal rotations of a molecule should also be accompanied by its translations, so the Figs. 56a and 56b should somehow interfere. However, in Section IX.B.l we for simplicity will neglect this interference. This assumption approximately holds, since, as will be shown in Section IX.B.2, the mean frequencies of these two types of motion substantially differ. 

Any linear dielectric response can be described as the sum (or integral) of damped harmonic oscillators in the form of Eq. (L2.318),... 

It is not so obvious how well Born-Bethe ideas are satisfied in describing excitations in solids with their extended band states. However, the structure of the basic result (eq. (3)) with the partitioning into a Rutherford cross section and a form factor depending on momentum transfer remains intact. All that is required is for the differential oscillator strength to be reinterpreted in terms of a response function for the system e(q,AE), the Fourier transform of the space/time dielectric response e(r,t). 

Simple Spectral Method [23] In the simple spectral method, a model dielectric response function is used. It combines a Debye relaxation term to describe the response at microwave frequencies with a sum of terms of classical form of Lorentz electron dispersion (corresponding to a damped harmonic oscillator model) for the frequencies from IR to UV ... 

In order to investigate solids or polymer systems with free carriers by IR spectroscopy, it is very convenient to measure the reflectivity instead of absorbance or transmittance. Thus, the problems to be discussed in this context are usually described by a linear response formalism. In its simplest form, this means that the response function (dielectric function) s(u ) of a damped harmonic oscillator is used to describe the interaction between light and matter. The complex form of this function is... 

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