2001AugQualGEN - Ben Sauerwine Practice for Qualifying...

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Unformatted text preview: Ben Sauerwine Practice for Qualifying Exams Thanks to Yossef for his presentation on this solution. Problem Source: CMU August 2001 Qualifying Exam Pion Photoproduction Consider the Pion photoreaction π γ + = + p p (a) If the initial proton is at rest in the laboratory, find the laboratory threshold gamma ray energy for this reaction to go. Use the energy four-vectors for this reaction. For all four-vectors in all frames, 2 2 2 c m v = v . For the incident gamma ray in the rest frame, assuming that it is moving in the x- direction, I have ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = c E c E γ γ γ v For the proton at rest, then, I have ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = c m p p i v Assuming the minimum-energy interaction, I have for the resulting proton and pion that: ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = = c m c m p p p i f π π v v v Now considering: ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 c m m m m E c m m c m m E p p p p p p p p p p p p p p i f i f i f i π π γ π π γ π π γ π π γ γ π γ π γ + = + = + = + + = + + + = + + = + v v v r v v v v v r v v r v v v r v v v r Solving this (substituting ), I have MeV c m MeV c m p 938 135 2 2 = = π MeV MeV E 7 . 144 135 135...
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2001AugQualGEN - Ben Sauerwine Practice for Qualifying...

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