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Inverse Compton scattering in SR

  1. Sep 23, 2009 #1

    diazona

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    This is actually for a graduate course but it's a basic special relativity problem, i.e. undergraduate-level material, so I'm posting it here...

    1. The problem statement, all variables and given/known data

    2. Relevant equations
    [tex]U^{\mu} = (1, 0, 0, 0)[/tex] (in the observer's rest frame)
    [tex]V^{\mu} = (\gamma, \gamma \vec{v})[/tex]
    [tex]P^{\mu} = (E, \vec{p})[/tex]

    3. The attempt at a solution
    I got parts (a) and (b) easily enough by evaluating 4-vector products in the observer's rest frame,
    (a) [tex]\gamma = -U^{\mu} V_{\mu} \gg 1[/tex]
    (b) [tex]E = U^{\mu}P_{\mu}[/tex]
    The problem is with part (c). We're supposed to express P' in terms of U, V, and P, but it doesn't seem to be possible without knowing the angle at which the scattered photon exits (or the angle at which the charged particle exits). Am I missing something, or is this actually impossible?
     
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  3. Sep 23, 2009 #2

    gabbagabbahey

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    What quantity is conserved during the scattering event?:wink:
     
  4. Sep 23, 2009 #3

    diazona

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    Momentum, I know... P + mV = P' + mV', where V' is the final four-velocity of the charged particle. But I still don't see how that helps... I don't know V'.
     
  5. Sep 23, 2009 #4

    gabbagabbahey

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    Why not just express your answer in terms of V'?
     
  6. Sep 24, 2009 #5

    diazona

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    I thought about that, but it'd be just expressing one unknown in terms of another :/ Anyway, it doesn't matter now, the assignment was due earlier today. In the end even our professor did admit that it was impossible.
     
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