The diffused gamma halo around our Galaxy recently discovered by EGRET coul
d be produced by annihilations of heavy relic neutrinos N (of fourth genera
tion), whose mass is within a narrow range (M-Z/2 < m(N) < M-Z). Neutrino a
nnihilation in the halo may lead to either ultrarelativistic electron pairs
whose Inverse Compton Scattering on infrared and optical galactic photons
could be the source of observed GeV gamma rays, or prompt 100 MeV-1 GeV pho
tons (due to neutral pion secondaries) born by N (N) over bar-->Z-->q (q) o
ver bar 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 compatib
le with the narrow window of neutrino mass 45 GeV < m(N) < 50 GeV, recently
required to explain the underground DAMA signals. The presence of heavy ne
utrinos of fourth generation do not contribute much to solve the dark matte
r problem of the Universe, but may be easily detectable by outcoming LEP II
data. (C) 2000 Elsevier Science B.V. All rights reserved.