We present laboratory microwave scattering measurements for complex amplitude scattering matrices of three aggregates of 2, 8, and 27 identical spheres and compare them with theoretical predictions. Electromagnetic multiparticle-scattering calculations involve the determination of a large number of vector translation coefficients introduced by the addition theorems for vector spherical harmonics. For one of the two classes of vector translation coefficients there is an overall-sign discrepancy between two groups of formulations that exist in the literature. We compare our experimental data with the theoretical results from scattering calculations using the two different sets of formulas for computation of the translation coefficients. This comparison of experiment with theory reveals that Cruzan's original research on the vector addition theorems [Q. Appl. Math. 20, 33-40 (1962)] is correct, although many authors believe that Cruzan's formulation contains an overall-sign error. # 1997 Optical Society of America
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