Astroparticle Physics

94 6 Primary Cosmic RaysFig. 6.16Ratio of fully contained eventsmeasured in theSuper-Kamiokande detector as afunction of the reconstructed valueof distance over energy (L/E ν ).The lower histogram for µ-likeevents corresponds to theexpectation for ν µ ↔ ν τoscillations withδm 2 = 2.2 × 10 −3 eV andsin 2θ = 1{10}fusion reactions in the Suninto a dependence of the rate versus the reconstructed ratioof L/E ν . Figure 6.16 shows the ratio data/Monte Carlo forfully contained events as measured in the Super-Kamiokandeexperiment. The data exhibit a zenith-angle- (i.e., distance-)dependent deficit of muon neutrinos, while the electron neutrinosfollow the expectation for no oscillations. The observedbehaviour is consistent with (ν µ ↔ ν τ ) oscillations,where a best fit is obtained for δm 2 = 2.2 × 10 −3 eV formaximal mixing (sin 2θ = 1).In the Standard Model of elementary particles neutrinoshave zero mass. Therefore, neutrino oscillations representan important extension of the physics of elementary particles.In this example of neutrino oscillations the synthesisbetween astrophysics and particle physics becomes particularlyevident.6.2.2 Solar NeutrinosThe Sun is a nuclear fusion reactor. In its interior hydrogenis burned to helium. The longevity of the Sun is related tothe fact that the initial reactionp + p → d + e + + ν e (6.27)proceeds via the weak interaction. 86% of solar neutrinos areproduced in this proton–proton reaction. Deuterium madeaccording to (6.27) fuses with a further proton to producehelium 3,d + p → 3 He + γ. (6.28)In 3 He– 3 He interactions3 He + 3 He → 4 He + 2p (6.29)‘chemistry’ of nuclear fusionthe isotope helium 4 can be formed. On the other hand, theisotopes 3 He and 4 He could also produce beryllium,3 He + 4 He → 7 Be + γ. (6.30)7 Be is made of four protons and three neutrons. Light elementsprefer symmetry between the number of protons andneutrons. 7 Be can capture an electron yielding 7 Li,7 Be + e − → 7 Li + ν e , (6.31)where a proton has been transformed into a neutron. On theother hand, 7 Be can react with one of the abundant protonsto produce 8 B,