Multipole expansion method for supernova neutrino oscillations
  We demonstrate a multipole expansion method to calculate collective neutrino oscillations in supernovae using the neutrino bulb model. We show that it is much more efficient to solve multi-angle neutrino oscillations in multipole basis than in angle basis. The multipole expansion method also provides interesting insights into multi-angle calculations that were accomplished previously in angle basis. 
Huaiyu Duan, Shashank Shalgar
hep-ph astro-ph.HE