We analyze the characteristics of the gamma radiation produced by Compton back-scattering of a high brightness electron beam produced by a photoinjector and accelerated in a linac up to energies of 360-720 MeV and a laser operated at about 500 nm, by comparing classical and quantum models and codes. The interaction produces gamma rays in the range 4.9-18.8 MeV. In view of the application to nuclear resonance fluorescence a relative bandwidth of few 10 - 3 is needed. The bandwidth is reduced by taking advantage of the frequency-angular correlation typical of the phenomenon and selecting the radiation in an angle of tens of Am rads . The foreseen spectral density is 20-6 photons per eV in a single shot, a number that can be increased by developing multi-bunch techniques and laser recirculation. In this way a final value of 10 4 photon per eV per second can be achieved.