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Approximation for radiation power of electrons due to inverse-Compton process in the black-body photon field

An approximation for the inverse-Compton radiation power of electrons in the isotropic black-body photon field is presented. The approximation allows one to calculate inverse-Compton emissivity as integral over the energies of incident electrons rather than over the field photon energies. Such an approach allows for accurate modeling of IC emission of electrons with energy spectra being different from power-law, in situation where the CPU resources are limited. High accuracy of this approximation allows one to use it in a wide range of conditions, from Thomson to extreme Klein-Nishina limits. The approach adopted results also in some new analytic expressions representing known results in the Thomson limit.