Neutrinos for geophysics

The Mikheyev-Smirnov-Wolfenstein solution to the solar-neutrino deficit provides a range for the acceptable neutrino parameters (Δm² and sin 2θ₀). If the vacuum mixing angle θ₀ is not too small, the resulting neutrino oscillation length in matter is comparable to the radius of the earth. For such appropriate neutrino parameters we study neutrino oscillations inside the earth. The core of the earth is taken as a sphere with constant density 11 g/cm³, while the mantle, surrounding the core, is taken to be a spherically symmetric shell of constant density 4.4 g/cm³. We obtain an exact, analytic expression for the probability that an electron-neutrino after traversing the earth, emerges as an electron-neutrino. Our results indicate that the neutrinos might serve as the ideal tools for earth tomography.