Mixtures of hard spheres in the Percus–Yevick approximation. Light scattering at finite angles

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Abstract
In a previous paper (I), a new equation for the light scattering (or small angle x‐ray or neutron scattering) of a concentrated p‐component mixture of spherical (colloidal) particles in a low‐molecular weight solvent was derived. Use was made of Baxter’s factorization of the direct correlation matrix. It was found that the light scattering intensity can be formulated in factorized form as well. The formalism was applied to a multicomponent system of hard spheres treated in the Percus–Yevick approximation. For zero scattering angle, a rather simple, exact expression was obtained. In this paper it is proved that a closed expression can also be obtained for finite scattering angles. It contains at most 18 (averaged) functions of the scattering angle for any number of hard sphere components. This makes it possible to apply the equation to a continuous distribution of hard sphere diameters. A series expansion is given for small scattering wave numbers.