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In this paper the high-order adiabatic approximation method proposed by the author is used to approach the nonadiabatic effects of two-neutrino oscillations in matter. We not only obtain the analytic expressions for high-order approximate solutions of the neutrino-oscillations equation but also give nonadiabatic corrections to the probability of the adiabatic transition between two neutrinos in matter with arbitrarily varying density.
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Chang-Pu Sun (1988) studied this question.