A Simple Parameterization of Matter Effects on Neutrino Oscillations
  We present simple analytical approximations to matter-effect corrected effective neutrino mixing-angles and effective mass-squared-differences. The expressions clarify the dependence of oscillation probabilities in matter to the mixing angles and mass-squared-differences in vacuum, and are useful for analyzing long-baseline neutrino oscillation experiments. 
Minako Honda, Yee Kao, Naotoshi Okamura, and Tatsu Takeuchi