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Finding the Muon decay length reduced by Ionization loss

  1. Dec 9, 2007 #1

    mdj

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    I'm doing a Monte carlo simulation of cosmic ray interactions in the atmosphere, and as part of this I need to calculate how far a decaying particle travels before it decays

    In vacuum it would be simple: [tex]l_D = c \tau \gamma \beta[/tex] with a probability of traveling the distance l before decay: [tex]P_D (l) = \frac{1}{l_D} e^{-l/{l_D}}[/tex]

    But in practice both [tex]\gamma[/tex] and [tex]\beta[/tex] depends on l

    Where [tex]\gamma(l) = \gamma_0 + \frac{dE}{dx}(\gamma_0)[/tex]

    and [tex]\frac{dE}{dx}[/tex] is the Bethe-Bloch formula.

    How do I do this smart? any ideas? I suppose that this happens every day in detectors as well...

    (The above don't take into account the density variation of the atmosphere, but I got that covered - I think... )
     
  2. jcsd
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