We consider a relativistically moving blob consisting of an isotropic electron distribution that Compton-scatters photons from an external isotropic radiation field .
We compute the resulting beaming pattern , i.e .
the distribution of the scattered photons , in the blob frame as well as in the observer ’ s frame by using the full Klein-Nishina cross section and the exact incident photon distribution .
In the Thomson regime the comparison of our approach with Dermer ( 4 ) results in concurrent characteristics but different absolute number of the scattered photons by a factor of f _ { corr } = 3.09 .
Additionally , our calculation yields a slightly lower boost factor which varies the more from the corresponding value in Dermer ( 4 ) the higher the spectral index p of the electron distribution gets .