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Inelastic light scattering by atomic vibrations

Bernard Hehlen

Published Nov 17, 2019• 0 citations
OpenAlex

Abstract

An introduction to the linear response theory will allow us to define the concepts of susceptibility, fluctuation spectra, autocorrelation function... and to connect these quantities through the fluctuation-dissipation theorem. We will then determine the origin of the scattering of light and calculate the Raman and Brillouin spectra within a (classical) macroscopic theory [1]. These calculations will reveal selection rules that will be applied to few examples taken from crystalline solids, liquids, and glasses [2].

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Introduction and guide to the chapter Linear response functions contain a wealth of information about the physical properties of a many-body system. In the case of the electron liquid, for example, the density–density response function provides a unified framework for the understanding of different phenomena such as static screening, effective interaction, collective modes, electron energy loss spectra (inelastic scattering of electrons), and Raman spectra (inelastic scattering of photons). The spin–spin response function provides the corresponding information for the spin density fluctuations as probed, for example, by cross-polarized Raman scattering experiments, in which the incident and scattered photon have perpendicular polarizations, or by spin-flip electron energy loss spectroscopy, in which the incoming and outgoing electrons have opposite spin orientations. As we have seen, the Hartree–Fock approximation describes each electron as an independent particle moving in a self-consistent field generated by all the other electrons. There is no correlation between this self-consistent field and the instantaneous position of the electron. Reality is however quite different: whenever an electron moves, it acts on the surrounding electrons, causing a collective disturbance which eventually feeds back on its own motion. In order to study these effects we need, first of all, to learn how the electron liquid as a whole responds to disturbances caused by the charge, the spin, and the current of a single electron. The linear response theory of Chapter 3 provides the natural framework for this description. Strictly speaking, the linear response functions describe the readjustments of the electronic density, spin, or current, in response to externally controlled fields.
A review is given of experimental and theoretical achievements in studies of multiphoton spontaneous scattering processes in atomic and molecular media. An analysis is made of integral multiphoton scattering, particularly of scattering in statistically inhomogeneous media with short-range quasiorder. A study of the intensity of the noncoherent multiphoton scattering component provides direct information on the nonlinear polarizability of atoms and molecules whilst the coherent component is associated with various atomic and molecular correlation mechanisms. An analysis of the spectra of elastic and inelastic multiphoton scattering processes yields information on the translational and rotational motion of the molecules. In particular, it is possible to measure the higher-order rotational relaxation times and to verify the adequacy of the various stochastic models of molecular motion. Observations of the spectral lines of three- or more-photon scattering, which obeys new selection rules, yield detail on the fine structure of the molecules and their linear and nonlinear vibrations. Examples are given of the most interesting spectra of three- or more-photon scattering in gases, liquids, and crystals obtained in singleand multichannel systems. The stochastic theory of multiphoton scattering in liquids is discussed, using the spherical tensor concept. The derived general expression reduces to known results for certain cases.
Abstract The doubly differential cross-section for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove. The application of this very general scheme to scattering of neutrons, x-rays and high-energy electrons is discussed briefly. The dynamic structure factor, which is the space and time Fourier transform of the density-density correlation function, is a property of the many-body system independent of the external probe and carries information on the excitation spectrum of the system. The relation of the electronic structure factor to the density-density response function defined in linear-response theory is shown using the fluctuation-dissipation theorem. This is important for calculations, since the response function can be calculated approximately from the independent-particle response function in self-consistent field approximations, such as the random-phase approximation or the local-density approximation of the density functional theory. Since the density-density response function also determines the dielectric function, the dynamic structure can be expressed by the dielectric function.