Three neutrino oscillations in matter

Following similar approaches in the past, the Schrodinger equationfor three neutrino propagation in matter of constant density is solved analytically by two successive diagonalizations of 2 x2 matrices. The final result for the oscillation probabilities is obtained directly in the conventional parametric form as in the vacuum but with explicit simple modification of two mixing angles (theta(12) and theta(13)) and mass eigenvalues. In this form, the analytical results provide excellent approximation to numerical calculations and allow for simple qualitative understanding of the matter effects. (C) 2018 The Authors. Published by Elsevier B.V.