Polarization of x-gamma radiation produced by a Thomson and Compton inverse scattering

A systematic study of the polarization of x-gamma rays produced in Thomson and Compton scattering is presented, in both classical and quantum schemes. Numerical results and analytical considerations let us to establish the polarization level as a function of acceptance, bandwidth and energy. Few sources have been considered: the SPARC_LAB Thomson device, as an example of a x-ray Thomson source, ELI-NP, operating in the gamma range. Then, the typical parameters of a beam produced by a plasma accelerator has been analyzed. In the first case, with bandwidths up to 10%, a contained reduction ($l10%$) in the average polarization occurs. In the last case, for the nominal ELI-NP relative bandwidth of $5\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$, the polarization is always close to 1. For applications requiring larger bandwidth, however, a degradation of the polarization up to 30% must be taken into account. In addition, an all optical gamma source based on a plasma accelerated electron beam cannot guarantee narrow bandwidth and high polarization operational conditions required in nuclear photonics experiments.