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(adsbygoogle = window.adsbygoogle || []).push({});

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... )

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# Finding the Muon decay length reduced by Ionization loss

Can you offer guidance or do you also need help?

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