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solutions 09

# Introductory Nuclear Physics

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PHY431 Homework Set 9 Reading: Lecture Notes Homework: See below: Due date: Wednesday May 3 Hints and Solutions Problem IX.1 Show that the SU(2) group of continuous operators exp{ i ½ σ · α ( x )}: is unitary . has determinant 1 b. Hints: see the lecture notes Solution: no solution yet Problem IX.2 Show that the Pauli matrices have the group structure defined by [ σ i , σ j ] = 2 i ε ijk σ k . Hints: the tensor ε ijk is the fully anti-symmetric tensor under any permutation of the indices ijk . Solution: no solution yet Problem IX.3 Draw the Feynman diagram of Λ→ n + π 0 . Show all quark lines, and indicate how it differs from the figure next to equation (13.18) in the notes. . Using the Cabibbo mixing matrix, estimate the ratio of the decay amplitudes (the Feynman factors) of the processes Λ→ p + e - + f8e5ν e and n p + e - + f8e5ν e b. Hints: The ratio will be a ratio of Cabibbo mixing factors: express the quark states in their

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