The diffused gamma halo around our Galaxy recently discovered by EGRET could be produced by annihilations of relic neutrinos N (of fourth generation), whose mass is within a narrow range (Mz /2 < M < Mz). Neutrino annihilations in the halo may lead to either ultrarelativistic electron pairs whose inverse Compton Scattering on infrared or optical galactic photons could be the source of the observed GeV gamma rays, or to prompt 100 MeV- 1 GeV photons (due to neutral pion secondaries) born by N - anti N --> Z--> quark pairs reactions. The consequent gamma flux (10 ^(-7)- 10^(-6) cm ^(-2) s^(-1) sr^(-1)) is well comparable to the EGRET observed one and it is also compatible with the narrow window of neutrino mass : 45 GeV < M < 50 GeV recently required to explain the underground DAMA signals. The presence of heavy neutrinos of fourth generation do not contribute much to solve the dark matter problem of the Universe, but it may be easily detectable by outcoming LEP II data.
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