General expression for the depolarization ratio for first‐order collision‐induced light scattering

Abstract

A general expression that involves only the ranks of the molecular polarizabilties of the two molecules involved in a pair interaction yielding translational and rotational collision-induced light scattering (CILS) is obtained. It may be used to investigate the behaviour of individual interactions that contribute to the incremental collision-induced pair polarizability.When linearly polarized light is incident upon a molecular system, the light scattered may contain a component polarized in a direction perpendicular to that of the incident polarization. The ratio of the intensities of these signals that are polarized perpendicular and parallel to that of the incident beam is known as the depolarization ratio η. This ratio is an important measured quantity in Rayleigh and Raman scattering since it can be correlated with symmetries of the scattering species. It can thereby provide information, for example, on details of molecular structure.Since the scattered light is emitted by a radiating dipole, in the polarizability theory of light scattering the depolarization ratio can be expressed in terms of the isotropic component (α) and the anisotropic component (β) of the dipole-dipole polarizability tensor.If α is zero, then η is 3 4 and the light is said to be completely depolarized. Otherwise, η is less than 3 4 and the light is said to be partially polarized. [1] Collision-induced light scattering (CILS) refers to Rayleigh and Raman spectral features that are forbidden by the symmetry of a free molecule but appear in the scattering from dense media through molecular interactions. [2 -4] The inelastic scattering arises from coupling of the radiation field to the translational and internal degrees of freedom of the molecules through a collision-induced cluster polarizability. The scattering is thus a source of information about the collision-induced polarizability itself and, in principle, intermolecular forces. In the simplest first-order interaction giving rise to the phenomenon, known as the dipole-induced dipole (DID) mechanism, the incident light induces a dipole in a molecule 1. Then the field acting on a neighbouring molecule 2 is that of the light and that of the dipole in 1. The light emitted by the induced dipole in 2 is completely depolarized. This interacting pair of molecules thus behaves like a diatomic molecule whose internuclear separation (here intermolecular separation) is time dependent. The interaction may be extended to higher order wherein the dipole induced in 2 induces a dipole in 1. In another generalization, polarizabilities other than dipole-dipole may be considered. Since the resulting scattered light must be electric dipole radiation, in first order these polarizabilities must be of the type dipole-multipole. It is this latter generalization that is considered in the present paper. The long-range interaction process involves molecular multipole moments and polarizabilities, both of which are expressed through tensors of various ranks. In all cases, the interaction is specified by the mole...

Recent advances in linear and nonlinear Raman spectroscopy. Part VI

“…Senchuk and Tabisz reported a theoretical investigation to describe second‐order collision‐induced light scattering by using a spherical tensor approach . In a second paper, these same two researchers derived a general expression for the depolarization ratio for first‐order collision‐induced light scattering . Shuang and co‐workers described an analysis of stray light in low‐wavenumber Raman spectra and secondary maxima in grating diffraction .…”