Particle scattering multipole expansion

For any method of structure reconstruction by ab-initio methods additional assumptions must be made. The multipole expansion method of Harrison, Stuhr-MANN, and SvERGUN ([86], Sect. 5.3 [101], Chap. 6) assumes homogeneous internal density. The shape of the scattering curve is fitted by varying the envelope of the particle. 

For particles not small compared with the wavelength, the interaction properties must be found by solving a complicated boundary-value problem for the electric and magnetic fields. For spherical particles, this theory is well established and the scattering and extinction cross sections are calculated from the multipole expansions. 

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