The neutrino-nucleus reaction cross sections of 4 He and 12 C are evaluated using new shell model Hamiltonians. Branching ratios of various decay channels are calculated to evaluate the yields of Li, Be, and B produced through the -process in supernova explosions. The new cross sections enhance the yields of

We investigate neutrino oscillations in constant matter within the context of the standard three neutrino scenario. We derive an exact and simple formula for the oscillation probability applicable to all channels. In the standard parametrization, the probability for νe → νµ transition can be written in the form P (νe → νµ) = Aeµ cos δ + Beµ sin δ + Ceµ without any approximation using CP phase δ. For νµ → ντ transition, the linear term of cos 2δ is added and the probability can be written in the form P (νµ → ντ ) = Aµτ cos δ + Bµτ sin δ + Cµτ + Dµτ cos 2δ. We give the CP dependences of the probability for other channels. We show that the probability for each channel in matter has the same form with respect to δ as in vacuum. It means that matter effects just modify the coefficients A, B, C and D. We also give the exact expression of the coefficients for each channel. Furthermore, we show that our results with respect to CP dependences are reproduced from the effective mixing angles and the effective CP phase calculated by Zaglauer and Schwarzer. Through the calculation, a new identity is obtained by dividing the Naumov-Harrison-Scott identity by the Toshev identity.

Within the framework of the standard three neutrino scenario, we derive an exact and simple formula of the oscillation probability P (ν e → ν µ ) in constant matter by using a new method. From this formula, it is found that the matter effects can be separated from the pure CP violation effects. Furthermore, the oscillation probability can be written in the form, P (ν e → ν µ ) = A cos δ + B sin δ + C, in the standard parametrization without any approximation. We also demonstrate that the approximate formula in high-energy can be easily reproduced from this as an example. *

Neutrino oscillations affect light-element synthesis through the -process in supernova explosions. The 7 Li and 11 B yields produced in a supernova explosion of a 16.2 M star model increase by factors of 1.9 and 1.3 in the case of the large mixing angle solution with a normal mass hierarchy and sin 2 2 13 k 2 ; 10 À3 compared with those without the oscillations. In the case of an inverted mass hierarchy or a nonadiabatic 1-3 mixing resonance, the increment of their yields is much smaller. Neutrino oscillations raise the reaction rates of charged-current -process reactions in the region outside oxygen-rich layers. The number ratio of 7 Li/ 11 B could be a tracer of a normal mass hierarchy and a relatively large 13 , still satisfying sin 2 2 13 0:1, through future precise observations in stars having strong supernova components.

Light element synthesis in supernovae through neutrino-nucleus interactions, i.e., the v process, is affected by neutrino oscillations in the supernova environment. There is a resonance of 13-mixing in the O/C layer, which increases the rates of charged-current -process reactions in the outer He-rich layer. The yields of 7Li and 11B increase by about a factor of 1.9 and 1.3, respectively, for a normal mass hierarchy and an adiabatic 13-mixing resonance, compared to those without neutrino oscillations. In the case of an inverted mass hierarchy and a nonadiabatic 13-mixing resonance, the increase in the 7Li and 11B yields is much smaller. Observations of the 7Li/11B ratio in stars showing signs of supernova enrichment could thus provide a unique test of neutrino oscillations and constrain their parameters and the mass hierarchy.

We study the CP dependence of neutrino oscillation probability for all channels in arbitrary matter profile within three generations. We show that an oscillation probability for ν e → ν µ can be written in the form P (ν e → ν µ ) = A eµ cos δ+B eµ sin δ+C eµ without any approximation using the CP phase δ. This result holds not only in constant matter but also in arbitrary matter. Another probability for ν µ → ν τ can be written in the form P (ν µ → ν τ ) = A µτ cos δ + B µτ sin δ + C µτ + D µτ cos 2δ + E µτ sin 2δ. The term which is proportional to sin 2δ disappear, namely E µτ = 0, in symmetric matter. It means that the probability reduces to the same form as in constant matter. As for other channels, probabilities in arbitrary matter are at most the quadratic polynomials of sin δ and cos δ as in the above two channels. In symmetric matter, the oscillation probability for each channel reduces to the same form with respect to δ as that in constant matter. *

We study neutrino oscillation within the framework of three generations in matter. We propose a simple method to approximate the coefficients A, B and C which do not depend on the CP phase δ in the oscillation probability P (νe → νµ) = A cos δ + B sin δ + C. An advantage of our method is that an approximate formula of the coefficients A, B and C in arbitrary matter without the usual first order perturbative calculations of the small parameter ∆m 2 21 /∆m 2 31 or sin θ13 can be derived. Furthermore we show that all the approximate formulas for low, intermediate and high energy regions given by other authors in constant matter can be easily derived from our formula. It means that our formula is applicable over a wide energy region. *

We present a new formulation deriving the neutrino oscillation probabilities relativistically based on not the Schrödinger equation but the Dirac equation. In two generations, we calculate the oscillation probabilities exactly in the case that there exists only the Dirac mass term. We find that two kinds of new terms appear in the oscillation probabilities derived from the Dirac equation. One is the term dependent on the absolute value of neutrino mass. Although it has been considered that the oscillation probabilities depend only on the mass squared differences until now, we could observe the absolute value of mass through neutrino oscillations in principle. The other is the term including a new CP phase. If there are some interactions to distinguish the flavors of right-handed neutrinos beyond the Standard Model, we could also observe this new CP phase in principle even in the framework of two generations. We discuss the possibility to observe the contribution of these terms by the neutrino oscillations of atomic size. On the other hand, it is negligible in the usual short and long-baseline experiments, and there is no contradiction with previous experiments.