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There are many areas of science and technology where the scattering of electromagnetic waves by clusters or merging particles are of interest. The merging particles under study might be inclusions in high-density composites, liquid drops, biological cells, macroscopic ceramic particles, etc. As intersecting particles are bounded by a complex physical surface, the problem of scattering from these particles valid for any degree of merging, including touching, and for arbitrary materials of the constituents, has received limited attention. Here we present solutions which are valid and exact in the long wavelength limit compared with the size of intersecting spherical particles and cardioidal particles of similar dimensions. Both shapes are almost coincident everywhere except in the region of intersection. We treat the case when the waves are polarized along the common axis (longitudinal field). The solutions of Laplace's equation are integrals (spheres) or sums (cardioids) over continuous or discrete eigenvalue spectra respectively. The spectral dependencies of the resulting extinction coefficients and the scattering for the spherical and cardioidal particles are quite distinct. There is an enormous difference in the magnitude of absorption responses. Overall the cardioidal particle behaves as if it is almost invisible in terms of effects on the external field for a very broad band of optical frequencies. THe latter result was checked for a number of dielectric permittivities and seems to be universal. It scatters far more weakly than the isolated sphere. In constrast the intersecting sphere has an extinction band which is broad and is much enhanced at longer wavelegnths relative to the simple sphere. This result has significant implications for the design of surfaces with minimum scattering.
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