Nonadiabatic level crossing in neutrino oscillations for an exponential solar density profile

Abstract

We derive an analytic expression for the conversion probability of neutrinos which propagate in a resonant oscillation region, assuming an exponential solar density profile. We argue that this assumption is a better approximation than the linear Landau-Zener one for large vacuum mixing angles ${\theta }_0$ and that it reduces to it for small ${\theta }_0$, therefore covering the entire ${\sin }^2$2${\mathrm{\theta }}_0$-δ$m^2$/E plane. Our result fails to describe neutrinos produced in the resonance region, while it is still applicable if the resonance occurs close to the core of the Sun, where the density is no longer exponential.