Abstract
It is found that a term normally discarded in the standard treatment of the MSW effect might be relevant in the case of non-adiabatic varying matter density, leading to a second order field equation, instead of the usual first order "Schrodinger equation". This leads to dispersion relation that gives rise to the possibility of neutrino trapping in a dense medium as well as the coupling of neutrino oscillation to neutral current interaction. This is found to be in agreement with previous results1. The corresponding conserved probability current is derived for this second order equation, and applied to the case of 2-flavor neutrino oscillation in a dense medium. The results in this work might be applicable to the oscillation of neutrinos in dense astrophysical medium.
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