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Atmospheric haze is a leading candidate for opacity and lack of prominent features in expolanetary spectra, as well as in the atmospheres of Solar system planets, satellites, and comets. Exoplanetary transmission spectra, which carry information about how the planetary atmospheres become opaque to stellar light in transit, often show broad absorption in the region of wavelengths corresponding to spectral lines of sodium, potassium, and water. We develop a detailed atomistic model, describing interactions of atomic or molecular radiators with dust and atmospheric haze particulates. This model incorporates a realistic structure of haze particulates from small nano-sized seed particles up to submicron irregularly shaped aggregates and accounting for both pairwise collisions between the radiator and haze perturbers, and quasistatic mean-field shift of atomic levels in haze environments. This formalism can explain large flattening of absorption and emission spectra in hazy atmospheres and shows how the radiator - haze particle interaction affects the absorption spectral shape in the wings of spectral lines and near their centres. The theory can, in principle, account for nearly all realistic structure, density, size, and chemical composition of haze particulates. We illustrate the utility of the method by computing shift and broadening of the emission spectra of the Na I D lines in haze environment, formed by Ar nano-clusters. Argon is used as the illustrative haze constituent only because of the simplicity of closed-shell atoms and their clusters for quantum mechanical calculations of interaction between radiator and nano-sized haze particles. The elegance and generality of the proposed model should make it amenable to a broad community of users in astrophysics and chemistry.