= Mean-lifetime survival energy estimate
{title2=$p=\exp[-H/(\gamma v\tau_0)]$}
An unstable particle of rest lifetime $\tau_0$ traversing distance $H$ at constant <speed> $v$ has <survival probability> $p=\exp[-H/(\gamma v\tau_0)]$. Requiring a flight time no greater than one dilated <mean lifetime> selects $p\ge e^{-1}$. In the ultrarelativistic approximation $v\simeq c$, this gives $\gamma\gtrsim H/(c\tau_0)$ and $E\gtrsim mc^2H/(c\tau_0)$. It is a specified survival-probability criterion, not a sharp cutoff for individual random decays. Continuous <energy> loss requires integrating the decay probability along the path.
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