An important reaction producing electron neutrinos in the Sun is e - + 7 Be e + 7 Li In the vast majority

An important reaction producing electron neutrinos in the Sun is e^- + ⁷Be → ν_e +⁷Li In the vast majority of the cases (90%) the Li nucleus is produced in its ground state. Consequently, the ‘Be neutrinos’ energy spectrum is monoenergetic with E_ν = 0.862 MeV. The corresponding total neutrino flux at the Earth is Φ_ν =4.6 x 10¹³ m^-2. The BOREXINO experiment at LNGS detects neutrinos via the reaction ν_e + e^-→ν_e + e^-. Its fiducial volume contains 100 t of liquid scintillator. The liquid is pseudocumene C₉H₁₂. The light produced by the final electron is detected by an array of photo multipliers covering the surface surrounding the volume. Assume σ(νee) = 0.6 x 10^-48 m², σ(νμ, τ^e)≃1/6σ(ν_ee), θ₁₂=34°,δm² =  80 m_eV².

(1) If electron neutrinos did not change flavour, how many events would be expected per day in the 100 t target mass?

(2) Which is the principal mechanism of flavour conversion for Be neutrinos from the Sun, vacuum oscillation or MSW effect?

(3) Under these conditions, calculate the expected number of events per day in BOREXINO of Be neutrinos.