Effects and influences on neutrino oscillations due to a thin density layer perturbation added to a matter density profile

In this Letter, we show the effects on the transition probabilities for neutrino oscillations due to a thin constant density layer perturbation added to an arbitrary matter density profile. In the case of two neutrino flavors, we calculate the effects both analytically and numerically, whereas in the case of three neutrino flavors, we perform the studies purely numerically. As an realistic example we consider the effects of the Earthʹs atmosphere when added to the Earthʹs matter density profile on the neutrino oscillation transition probabilities for atmospheric neutrinos.