Novel matter effects on neutrino oscillations observables

In a recent article (arxiv:1803.06332) we noticed that the electron density in condensed matter exhibits large spikes close to the atomic nuclei. We showed that these spikes in the electron densities, 3-4 orders of magnitude larger than those inside the Sun's core, have no effect on the neutrino emission and absorption probabilities or on the neutrinoless double beta decay probability. However, it was not clear if the effect of these spikes is equivalent to that of an average constant electron density in matter. We investigated these effects by a direct integration of the coupled Dirac equations describing the propagation of flavor neutrinos into, through, and out of the matter. We found little evidence that these spikes affect the standard oscillations probabilities, but found a new fast and efficient algorithm of calculating these probabilities for neutrinos propagating through varying electron densities.