Fourier Analysis of the Parametric Resonance of the Neutrino Oscillation in the Presence of Inhomogeneous Matter

We study the parametric resonance of the neutrino oscillation through the matter whose density varies spatially. The Fourier analysis of the matter effect enables us to clarify the parametric resonance condition, which is summarized in a frequency matching between the neutrino oscillation and the spatial variation of the matter density. As a result, the n-th Fourier mode of a matter density profile modifies the energy spectrum of the νμ →νe appearance probability at around the n-th dip