Matter Effects on Long Baseline Neutrino Oscillation Experiments

We calculate matter effects on neutrino oscillations relevant for long baseline neutrino oscillation experiments. In particular, we compare the results obtained with simplifying approximations for the density profile in the Earth versus results obtained with actual density profiles. We study the dependence of the oscillation signals on both $E/\Delta m^2_{atm.}$ and on the angles in the leptonic mixing matrix. The results show quantitatively how matter effects can cause significant changes in the oscillation signals, relative to vacuum oscillations and can be useful in amplifying these signals and helping one to obtain measurements of mixing parameters and the magnitude and sign of $\Delta m^2$.