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The total scattering rate, the optical depth of the universe, and the scattered photon spectrum are derived from gamma-ray photons scattering in an isotropic field of blackbody photons. By solving the kinetic equation describing repeated photon-photon scattering for both monoenergetic and power-law injection of photons, it is shown how the photon spectra resulting from pair-photon cascades are further reprocessed by photon-photon scattering. The power of photons injected at the photon energy epsilon(max), where the pair cascades terminate, is reprocessed into a characteristic spectral jump at epsilon(min). Photon-photon scattering thus reduces the spectral cutoff energy from epsilon(max) to epsilon(min). Photon-photon scattering is likely to be important in consideration of the constraints imposed by the primordial abundances on the properties of exotic unstable particles.
Svensson et al. (Thu,) studied this question.