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In the paper "The Question of Pure Fusion Explosions under the CTBT" at reference 12, the equation for the neutron dose from the fusion of a small amount of DT gas is given, with a term of $90 kg/m^2$.

It notes that term as "(The neutron mean-free path in water is $90 kg/m2$.)"

I'm quite puzzled by that - I've never seen a free path expressed in that form. Might someone clarify this or perhaps have a reference that might clarify it, or is it a misstatement?

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They're quoting a mean-free-path that's been multiplied by the target mass density.

So to convert to a mean-free-path in units of length, divide by the density. If the target is water, with mass density of 1 g per cc, the mean free path in this case would be 9 cm.

You could also think of the value they quote as the mean particle mass of the target divided by the interaction cross section. So, if the target is one molecule of water with a mass of about 18 proton masses, the corresponding cross section in this case would be about 3 barns, where a barn is 10^(-24) cm^2.

I'm not sure where they got that cross section. It's also possible there's a subtlety involved when thinking about cross sections with water versus cross-sections of the individual nuclei within water.

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  • $\begingroup$ +1, that makes sense, and 9cm fits - I'll wait a bit for any other comments/answers. Thanks for the reply. $\endgroup$
    – rasher
    Commented Dec 25, 2015 at 0:42

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