On the Evolution of the Neutrino State inside the Sun

Abstract

We reexamine the conventional physical description of the neutrino evolution inside the Sun. We point out that the traditional resonance condition has physical meaning only in the limit of small values of the neutrino mixing angle, theta<<1. For large values of theta, the resonance condition specifies neither the point of the maximal violation of adiabaticity in the nonadiabatic case, nor the point where the flavor conversion occurs at the maximal rate in the adiabatic case. The corresponding correct conditions, valid for all values of theta including theta>pi/4, are presented. An adiabaticity condition valid for all values of theta is also described. The results of accurate numerical computations of the level jumping probability in the Sun are presented. These calculations cover a wide range of Delta m^2, from the vacuum oscillation region to the region where the standard exponential approximation is good. A convenient empirical parametrization of these results in terms of elementary functions is given. The matter effects in the so-called &#34;quasi-vacuum oscillation regime&#34; are discussed. Finally, it is shown how the known analytical results for the exponential, 1/x, and linear matter distributions can be simply obtained from the formula for the hyperbolic tangent profile. An explicit formula for the jumping probability for the distribution N_e ~ (coth(x/l) +- 1) is obtained.