Inverse Compton Scattering onto BBR in High Energy Physics and Gamma (MeV-Tev) Astrophysics

We considered the Inverse Compton Scattering (ICS) of charged particles onto photons whose distribution is a Black Body Radiation (BBR) deriving the exact energy and angular differential distribution in the general case and in its most useful expansions. These results can be successfully applied in high energy accelerators experiments to evaluate the ICS contribution from the thermal photons in the cavity as well as in astrophysics where the ICS of cosmic rays plays a relevant role in a variety of phenomena. In particular we show how our formulae reproduce the ICS energy spectrum recently measured at LEP, how it could be considered a key tool in explaining the Gamma Ray Bursts (GRB) , SGRs energy spectrum. Finally we predicted the presence of a low gamma flux, nearly detectable at hundred of TeV from SNRs SN1006 as well as, at lower energy (tens TeV, due to gamma ray cascading in cosmic BBR), from relic extragalactic highest cosmic rays sources born by jets in AGN,as blazars 3C279,Mrk421,Mrk 501.