Matter Enhanced Neutrino Oscillations with a Realistic Earth Density Profile

Step function approximations of the Earth matter density profile have been used by several authors, see e.g. Refs. [1,2], for the analysis of matter effects in neutrino oscillation experiments. In order to investigate the quality of this approximation, we have developed methods to numerically calculate the transition probability amplitudes in a realistic matter density profile. Calculations were performed in a two and a three neutrino framework. The neutrino traveling path length L was divided up into several small intervals. In each of these intervals, in which we assumed constant matter density, we computed the effective mixing parameters. Combining the probability amplitudes of each interval leads to the total probability amplitude from which we obtained the transition probabilities. We have used three different matter density profiles, two model-like and one realistic: a constant profile just to show the resonance behavior, a step function describing the mantle-core-mantle structure of the Earth, and a realistic Earth density profile [3]. See Fig. 1 for the different density profiles. For the mantle-core-mantle density profile, we chose ρ = 5 g/cm for the mantle, ρ = 12 g/cm for the core, and a core-width equal to half of the Earth’s diameter. In our study we used the mass squared difference as suggested by atmospheric neutrino data from the SuperKamiokande Collaboration obtained within a two neutrino analysis [4]