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<pi/4. An adiabaticity condition valid for all values of theta is also given. We investigate which part of the solar density profile is primarily responsible for matter effects in the quasi-vacuum oscillation regime. 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 a empirical parametrization of these results in terms of elementary functions. Finally, we show 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. We also give an explicit formula for the distribution N_e ~ (coth(x/l)+- 1).Keywords
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