A general analytical expression is derived for calculating the total scattering cross-section of an aggregate of nanoparticles. The approach is based on the far zone approximation and repeated use of recursive relations for Bessel functions and Legendre polynomials. In comparison with the existing formula for total scattering cross-section, the expression converges faster and makes it easier to analyze the terms that characterize the interactive coupling between nanoparticles during multiple scattering of electromagnetic waves. The expressions are valid for particle aggregates in which no two particles are in direct contact. Calculated results compare well with measurements for a nanoshell dimer. For a linear chain of particles with the chain axis parallel to the polarization direction of the electric field, analysis shows that the red-shift of resonance peaks results primarily from electrons in metal shells of two adjacent particles oscillating out-of-phase to cancel each other’s radiation effects. Multi-scattering in aggregates with more complex arrangements may be explained by combining the effects of linear particle chains.
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