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Show that the ratio of decay rates

R ≡ Γ(Σ → n + e− + bar νe)/Γ(Σ → Λ + e + bar νe 17

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The difference in the decay rates is due to two reasons (i) the Q - values in the decays are different. For Σ → n + e + bar νe, Q1 = 257 MeV, while for Σ → Λ + e + bar νe, Q2 = 81 MeV, so that by Sargent’s law, the decay rate (ω) will be proportional to Q5. (ii) The first decay involves |ΔS| = 1, so that ω will be proportional to sin2θc, where θc is the Cabibbo angle. The second one involves |ΔS| = 1, so that ω is proportional to cos2θc. In all

where we have used θc = 13. The experimental value for R is 17.8

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