The GALLEX experiment at the Gran Sasso laboratory measured the ve flux from the Sun by counting

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The GALLEX experiment at the Gran Sasso laboratory measured the ve flux from the Sun by counting the electrons produced in the reaction ve + 71Ga → 71Ge + e. Its energy threshold is Eth = 233 keV. From the solar luminosity one finds the expected neutrino flux Φ = 6 x 1014m-2s-1. For a rough calculation, assume the whole flux to be above threshold and the average cross-section to be σ = 10-48 m2. Assuming the detection efficiency ε = 40%, how many 71Ga nuclei are necessary to have one neutrino interaction per day? What is the corresponding 71Ga mass? What is the natural gallium mass if the abundance of the 71Ga isotope is a = 40%? (The measured flux turned out to be about one half of the expected one. This was a fundamental observation in the process of discovering of neutrino oscillations.)

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