On the Evolution of the Neutrino State inside the Sun
Abstract
We revisit several aspects of neutrino evolution in the Sun, motivated by our recent study of the so-called quasi-vacuum oscillation region. We point out that the traditional resonance condition can be used to describe the region in the Sun where the neutrino "jumps" between matter mass eigenstates only in the limit of small neutrino mixing angles theta << 1. A modified condition is presented, which correctly gives the center of the "jumping" region for all values of theta, including theta>pi/4. An adiabaticity condition valid for all values of theta is also given. The physical origin of the matter effects in the quasi-vacuum oscillation regime is studied in detail. We present the results of numerical computations of the jumping probability P_c in a wide range of Delta m^2, interpolating between the vacuum oscillation region and the region where the standard exponential approximation is good, and present an empirical parametrization of these results in terms of elementary functions. Finally, it is shown how the known analytical results for the exponential, 1/x, and linear matter distributions can be directly obtained from the formula for the hyperbolic tangent profile. An explicit formula for the jumping probability for the distribution N_e \propto (\coth(x/l)\pm 1) is obtained.Keywords
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