Neutrino coherent forward scattering and its index of refraction

It is pointed out that, if neutrinos are to maintain coherence over the required distance for the Mikheyev-Smirnov-Wolfenstein solutions to the solar-neutrino problem, effects arising from neutrino multiple scattering must be considered. We give a simple derivation for the neutrino index of refraction that takes into account this effect. The same method is also shown to be useful for situations with varying matter densities and neutrino mixing. We also examine the question whether the coherence of propagating neutrinos in matter will be affected by switching on an external magnetic field, assuming neutrinos have a large magnetic moment