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The fission cross section of $U^{235}$ by slow neutrons is huge, around 584barns = 58400 fm$^2$ according to https://en.wikipedia.org/wiki/Uranium-235, however the geometrical cross section of a $U^{235}$ nucleus is actually small, assuming a radius of $7$fm, it is about 154fm$^2$ which corresponds to 1.5barn.

How is this possible ? I admit comparing a measured cross sections to the geometrical one might be a bit naive, but the nuclear interaction only has a range of several fm. The Broglie wave length certainly is rather large for slow neutrons, however, I consider this as a length scale perpendicular to the cross section. I don't consider it as a scale which tells us something how broad the wave front of the neutron is.

So what is the mechanism which makes the cross section so large (also compared to other nuclear processes)?

Lagrangian
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1 Answers1

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You can indeed directly associate the equivalent wavelength of a neutron with its cross section. In The Los Alamos Primer, Richard Serber uses the analogy of shooting arrows at a target, where slowing down the arrow makes the target's diameter increase greatly.

niels nielsen
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