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Obligatory Exercises I 12.03.2012 to be delivered 26.03.2012 @ 12:15 Farid Ould-­‐Saada 3/12/12 1 1. What is the minimum impact parameter needed to deﬂect 7.7 MeV α particles from gold nuclei by at least 1o? What about by at least 30o? What is the ratio of probabilities for deﬂection of θ>1o relative to θ>30o? 2. Calculate the binding energy of the last neutron in 4He and the last proton in 16O. How do these compare with B/A for these nuclei? What does this tell you about the stability of 4He relative to 3He and of 16O relative to 15N? 3. Calculate the approximate density of nuclear matter in g/cm3. What would be the mass of a neutron star that had the diameter of an orange? 4. The Bevatron at Berkeley was built with the idea of producing antiprotons, by the reaction . What is the threshold energy for this reaction? Consider both the laboratory and centre of mass systems. 5. A π0 meson with momentum 135 GeV/c decays into 2 photons. If its mean life is 8.5 10-­‐8 s, calculate to 10% accuracy how far the high-­‐energy π0 will travel prior to decay. What will be the approximate minimum opening angle of its 2-­‐decay photons in the laboratory? 3/12/12 2 1. Which of the following reactions are allowed and which not? -­‐ If allowed, draw the Feynman graph and state which interac8on is at work. -­‐ If forbidden, give the reasons. 1. K − + p →K + + Ξ − 2. π 0 → γ + γ + γ 3. K + + p →K + + Σ + + K 0 4. ρ 0 → γ + γ 5. n → p + π − 6. e + + e − → γ + γ + γ 7. e + + e − →ν e + ν e 8. Λ0 → p + e − + ν e 9. ν µ + n → µ − + p 10. e + + n → p + ν e 11. µ + →e + + ν e + ν µ + e + + e − 12. p →n + e + + ν e 13. 147 N + n→146 C + p 14. 146 C→147 N + e + + ν e 2. Using isospin decomposition for the decays of the ρ meson (I=1, JP=1-­‐) ρ + → π +π 0 ; ρ − → π −π 0 ; ρ 0 → π +π − ; ρ 0 → π 0π 0 prove that the last decay is f€ orbidden. 3. What are the charge conjugate reac8ons to reac8ons (a) and (b) below? Can a system be an eigenstate of the charge conjuga8on operator? € (a) K − + p →K 0 + n ; 3/12/12 (b) p + p → π + + π − 3 1. 2. 3. How are solar neutrinos produced and detected? What is the solar neutrino problem and how is it solved? How are atmospheric neutrinos produced and detected? What is the atmospheric neutrino anomaly and how is it explained? Derive the probability for an electron neutrino to oscillate into a muon neutrino. 3/12/12 4