Role of dense matter in collective supernova neutrino transformations

For neutrinos streaming from a supernova (SN) core, dense matter suppresses self-induced flavor transformations if the electron density significantly exceeds the neutrino density in the conversion region. If the electron density is comparable to the neutrino density one finds multi-angle decoherence, whereas the standard self-induced transformation behavior requires that in the transformation region the neutrino density is safely above the electron density. This condition need not be satisfied in the early phase after supernova core bounce. Our new multi-angle effect is a subtle consequence of neutrinos traveling on different trajectories when streaming from a source that is not point-like