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Neutrino Propagation in a Fluctuating Sun

We adapt to neutrino physics a general formulation for particle propagation in fluctuating media, initially developed for applications to electromagnetism and neutron optics. In leading approximation this formalism leads to the usual MSW effective hamiltonian governing neutrino propagation through a medium. Next-to-leading contributions describe deviations from this description, which arise due to neutrino interactions with fluctuations in the medium. We compute these corrections for two types of fluctuations: ($i$) microscopic thermal fluctuations, and ($ii$) macroscopic fluctuations in the medium's density. While the first of these reproduces standard estimates, which are negligible for applications to solar neutrinos, we find the second can be quite large, since it grows in size with the correlation length of the fluctuation. We consider two models in some detail. For fluctuations whose correlations are extend only over a local region in space of length $l$, appreciable effects for MSW oscillations arise if $(δn/n)^2 l\gsim 100$ m or so. Alternatively, a crude model of helioseismic $p$-waves gives appreciable effects only when $(δn/n) \gsim 1%$. In general the dominant effect is to diminish the quality of the resonance, making the suppression of the ${}^7$Be neutrinos a good experimental probe of fluctuations deep within the sun. Fluctuations can also provide a new mechanism for reducing the solar neutrino flux, giving an energy-independent suppression factor of $1/2$, away from the resonant region, even for small vacuum mixing angles.