Abstract
We consider two-family neutrino oscillations in a medium of continuously varying density as a limit of the process in a series of constant-density layers. We find a form for the transition amplitudes that could provide new analytic solutions or could serve as numerical solutions. We test our approach with constructive analytic expressions for the conversion amplitude at high energies within a medium with a density profile that is piecewise linear. We also shed some light on effects that depend on the order of the material traversed by a neutrino beam.
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