Two approaches to spatial dispersion in molecular scattering of light

A comparative discussion is given of two approaches to taking spatial dispersion into account in the electrodynamic problem of molecular scattering of light. The first, more traditional approach, may be called the “distributed dipole” approximation (DDA) and is based on the assumption that any given molecule at a given instant of time scatters light as an electric dipole. In this approach spatial dispersion, i.e., the dependence of the spectrum on the variation of the propagation vector $q=k_1-k_2$, is determined by the correlation of the positions of a given molecule (or of different molecules) at different times. Another approach, developed in recent years by Barron and Buckingham for the problem of light scattering by molecules with right-left asymmetry, may be called the “local multipole” approximation (LMA) and is based on taking into account the magnetic dipole and the electric quadrupole as well as the electric dipole interaction of a molecule with the field. A list is given of sets of “complete experiments” for measuring all the independent constants that determine the scattering cross section in both approaches. It is shown that the DDA approach is needed to describe the relatively large ($\sim$1) effects of spatial dispersion in measurements with high spectral resolution ($\delta\omega\lesssim qv$, where $v$ is the velocity of sound in the medium) while the LMA approach is required to describe the small effects ($\sim a/\lambda$, where a is the size of the molecule and $\lambda$ is the wavelength) measured with relatively low spectral resolution $\delta\omega\ll qv$. It is asserted that the right-left asymmetry of the differential (with respect to frequency) cross section for scattering in a gas containing chiral molecules need not involve the smallness parameter $ka$ if $ql\sim$1, where $a$ is the size of the molecule and $l$ is the mean free path. Also new lines are predicted in the rotational Raman scattering in a gas–transitions with $\Delta J=\pm1,\pm3$ in the case of noncentrally-symmetric molecules with a cross section $\sim$10$^{-6}$ of the Rayleigh cross section arising in second order in $a/\lambda$ due to the higher multipoles.