Spectral density light scattering

For a 1 the scattered light spectrum is gaussian with a width determined by the electron temperature, because it is due to the incoherent sum of Thomson scattering from individual, thermally moving electrons. The intensity and spectral linewidth of scattered light therefore yield electron density and temperature. 

Time-dependent correlation functions are now widely used to provide concise statements of the miscroscopic meaning of a variety of experimental results. These connections between microscopically defined time-dependent correlation functions and macroscopic experiments are usually expressed through spectral densities, which are the Fourier transforms of correlation functions. For example, transport coefficients1 of electrical conductivity, diffusion, viscosity, and heat conductivity can be written as spectral densities of appropriate correlation functions. Likewise, spectral line shapes in absorption, Raman light scattering, neutron scattering, and nuclear jmagnetic resonance are related to appropriate microscopic spectral densities.2... 

M. Moraldi. Quantum mechanical spectral moments in collision induced light scattering and collision induced absorption in rare gases at low densities. Chem. Phys., 78 243, 1983. 

M. Zoppi, F. Barocchi, D. Varshneya, M. Neumann, and T. A. Litovitz. Density dependence of the collision induced light scattering spectral moments of argon. Can. J. Phys., 59 1475, 1981. 

The spectral characteristics of the scattered light depend on the time scales characterizing the motions of the scatterers. These relationships are discussed in Chapter 3. The quantities measured in light-scattering experiments are the time-correlation function of either the scattered field or the scattered intensity (or their spectral densities). Consequently, time-correlation functions and their spectral densities are central to an understanding of light scattering. They are, therefore, discussed at the outset in in Chapter 2. 

This quantity plays an important role in much of what follows. In fact, as we shall see, what is sometimes measured in light scattering is the spectral density of the electric field of the scattered light. Let us dwell for a moment on some properties of these functions. Fourier inversion of Eq. (2.4.1) leads to an expression for the time-correlation function in terms of the spectral density. 

Equation (3.2.13) is an expression for the scattered light spectral density in terms of dielectric constant fluctuations. Nowhere in this treatment was it necessary to determine the explicit dependence of these fluctuations on molecular properties. In fact, this theoretical expression is purely phenomenological, ny attempt to write this formula in molecular terms will necessarily involve some degree of approximation. Nevertheless, a molecular formulation will contribute much to our intuitive understanding of light scattering and will also be useful for practical application. 

What are the consequences of these considerations for depolarized light scattering In a dilute gas where reorientation is predominantly inertial, we expect the spectrum to be what is normally called the pure rotational Raman spectrum of the molecule. As higher densities are approached, the discrete spectral lines broaden and overlap to form a continuous band. We show how the band shape can be computed for freely rotating linear molecules and spherical top molecules and then indicate the assumptions that have been used by several authors to include collisions in the theory. 

The depolarized scattering for the Rouse-Zimm dynamical model of flexible polymer chains (cf. Section 8.8) may also be calculated. Ono and Okano (1971) have performed this calculation for q = 0 (zero scattering angle) and find that the scattered light spectral density is a series of Lorentzians each with a relaxation time characteristic of one of the Rouse-Zimm model modes. However the contribution of each mode to the spectrum is equal. This behavior should be contrasted with that of the isotropic spectrum where the scattering spectrum is dominated by contributions from the longest wavelength modes. 

In light-scattering experiments one measures the spectral density of the electric field autocorrelation function of the scattered light wave, given as... 

In 1991, Basche and Moerner included perylene in polyethylene [71]. The small and rigid perylene molecule has good emission and triplet properties, but absorbs in a difficult spectral region, around 445 nm. Because the spectral jumps we discuss here are mainly consequences of matrix dynamics, we must shortly discuss sample preparation. The samples of [71] were made from low-density polyethylene (crystallinity 25%), doped at low concentration with perylene, and were quickly quenched from the melt to liquid nitrogen temperature to reduce light scattering. The thin films thus obtained were 10 to 20 pm thick. The polymer structure is thus expected to be dominantly amorphous. 

The study of inelastic light scattering (the spectral dependence of scattered light) has led to a concept of two kinds of density fluctuations, namely, an adiabatic one and an isobaric one (Landau and Placzek, 1934 Gross, 1940, 1946 Fabelinski, 1965 Kerker, 1969 Vuks, 1977). 

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