Vacuum oscillations of quasi degenerate solar neutrinos

The atmospheric neutrino oscillations and the vacuum oscillation solution of the solar neutrino problem can be consistently described by a doubly or triply degenerate neutrino spectrum as long as the high level of degeneracy required is not spoiled by radiative corrections. We show that this is the case for neutrino mass matrices generated by symmetries. This imposes a strong constraint on the mixing angles and requires the mixing should be close to bi-maximal. We briefly discuss the relevance of our results for the measurability of the neutrino spectrum.