Dimensionless scattering intensity

The fundamental scattering mechanism responsible for ROA was discovered by Atkins and Barron (1969), who showed that interference between the waves scattered via the polarizability and optical activity tensors of the molecule yields a dependence of the scattered intensity on the degree of circular polarization of the incident light and to a circular component in the scattered light. Barron and Buckingham (1971) subsequently developed a more definitive version of the theory and introduced a definition of the dimensionless circular intensity difference (CID),... 

Figure 4.11 Intensity of scattered light as a function of the dimensionless scattering vector.

The interparticle structure factor, S(Q), is also a dimensionless function describing the modulation of the scattered intensity by interference effects between radiation scattered from different scattering units in the sample. It therefore gives information on the relative positions of the scattering objects. 

Natural ROA originates in interference between waves scattered via the polarizability and optical activity tensors of the molecule. The relevant experimental quantity is a dimensionless circular intensity difference... 

The interaction of neutrons and matter is extremely weak, for the neutron has no electric charge. It is essentially spin-spin interaction with nuclei, whilst interaction with electron spins is negligible. Nuclei can be treated as dimensionless scattering centres (Fermi potential). The nuclear cross-sections are strictly independent of the electronic surrounding (ionic or neutral, chemical bonding, etc.). Therefore, the scattering cross-section of any sample can be calculated exactly, from the known cross-section of each constituent. Compared to optical techniques, INS intensities can be fully exploited and the spectra can be interpreted with more confidence. They are related to nuclear displacements involved in each vibrational eigenstate. 

Figure 26. Reciprocal partial peak scattering intensities as a function of dimensionless inverse temperature for an asymmetric diblock melt (model C) with N = 2000 and / = 0.5. High-temperature linear (mean-field) extrapolations, shown as dotted lines, converge to a unique apparent spinodal temperature.

Mie Scattering. For systems more complex than very small particles (Rayleigh) or small particles with low refractive indices (Rayleigh-Debye), the scattering from widely separated spherical particles requires solving Maxwells equations. The solution of these boundary-value problems for a plane wave incident upon a particle of arbitrary size, shape, orientation, and index of refraction has not been achieved mathematically, except for spheres via the Mie theory (12,13). Mie obtained a series expression in terms of spherical harmonics for the intensity of scattered light emergent from a sphere of arbitrary size and index of fraction. The coeflBcients of this series are functions of the relative refractive index m and the dimensionless size parameter a = ird/k. 

The complex Mie coefficients an and bn are obtained from matching the boundary conditions at the surface of the sphere. They are expressed in terms of spherical Bessel functions evaluated at a (i.e., a dimensionless size parameter) and ma. The intensity of the scattered light (13.52) may then be seen as a function of the wavelength of light, A, particle size, dp, and the complex refractive index m, of a particle in a medium ... 

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