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That depends on your definition of "capture". Energetic particles will have to slow down (and lose energy) before they "find their place" in the capturing grid. This will typically take some distance. For keV protons interacting with carbon atoms, a single collision is clearly not sufficient to thermalize - so I would say that their mean path definitely ...

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I think its easiest to understand this if one has a minimal understanding of QFT. I'm not sure about your background knowledge but hopefully this isn't gibberish to you. The QCD Lagrangian for massless quarks is given by, {\cal L} = - g \sum_i \bar{\psi} _i A _\mu \gamma ^\mu \psi _i - \frac{1}{4} F _{ \mu \nu } F ^{ \mu \nu } ...

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The distinction between energy and mass is really a matter of semantics here and is not really a fundamental distinction. We tend to call it "mass" when energy is in a bound state, i.e. an object such as a proton or an atomic nucleus that more or less holds together and stays in one place. You can call positron emission "energy to mass conversion" if you ...

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