I want to incorporate an estimate of a matter effect in atmospheric neutrino oscillations into a model including active and sterile neutrinos. Since neutrinos are not only created in the atmosphere directly above the experiment, but also in the atmosphere on the opposite side of the earth, we have to include matter effects with the earths matter in this calculation.
In this paper by J. Linder, the author calculates the effective potential induced by forward-scattering with electrons, protons and neutrons in ordinary matter, leading to the well known MSW effect. These potentials are obviously functions of the density of the above named particles.
My question is: what are the values for the densities $N_e,N_n,N_p$ in earth? Since earth is not homogeneous, is it fair to assume an average density for an estimate?