We discuss the relationship between a symmetry in the neutrino flavour evolution equations and neutrino flavour oscillations in the collective precession mode. This collective precession mode can give rise to spectral swaps (splits) when conditions can be approximated as homogeneous and isotropic. Multi-angle numerical simulations of supernova neutrino flavour transformation show that when this approximation breaks down, non-collective neutrino oscillation modes decohere kinematically, but the collective precession mode is still expected to stand out. We provide a criterion for significant flavour transformation to occur if neutrinos participate in a collective precession mode. This criterion can be used to understand the suppression of collective neutrino oscillations in anisotropic environments in the presence of a high matter density. This criterion is also useful in understanding the breakdown of the collective precession mode when neutrino densities are small. © 2009 IOP Publishing Ltd.

We discuss the effects of resonant spin-flavor precession (RSFP) of Majorana neutrinos on heavy element nucleosynthesis in neutrino-heated supernova ejecta and the dynamics of supernovae. In assessing the effects of RSFP, we explicitly include matter-enhanced (MSW) resonant neutrino flavor conversion effects where appropriate. We point out that for plausible ranges of neutrino magnetic moments and protoneutron star magnetic fields, spin-flavor conversion of [Formula presented] (or [Formula presented]) with a cosmologically significant mass (1–100 eV) into a light [Formula presented] could lead to an enhanced neutron excess in neutrino-heated supernova ejecta. This could be beneficial for models of [Formula presented]-process nucleosynthesis associated with late-time neutrino-heated ejecta from supernovae. Similar spin-flavor conversion of neutrinos at earlier epochs could lead to an increased shock reheating rate and, concomitantly, a larger supernova explosion energy. We show, however, that such increased neutrino heating likely will be accompanied by an enhanced neutron excess which could exacerbate the problem of the overproduction of the neutron number [Formula presented] nuclei in the supernova ejecta from this stage. In all of these scenarios, the average [Formula presented] energy will be increased over those predicted by supernova models with no neutrino mixings. This may allow the SN 1987A data to constrain RSFP-based schemes. © 1997 The American Physical Society.