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My book says, in a nuclear reactor, the fast moving neutrons(possessing MeV of energy) will escape if the moderator won't be there(in the core).That's it. It isn't elaborated there. My question is HOW do they escape? what's the escape route?

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The neutrons are just bouncing around, hitting nuclei, bouncing off elastically, being absorbed, or most importantly, causing fission in a fuel nucleus.

But there is nothing confining these neutrons; they are free to carry out their random walk and leave the confines of the reaction zone. They just need to be lucky enough to miss being absorbed or causing fission before finding the edge of the reaction zone.

In the simplest type of uncontrolled nuclear reaction, you start with a hemisphere of, say $U_{235}$. The lump is small enough that the probable number of new neutrons created by one existing neutron as it traverses the lump, and eventually exits, is less than one.

Nothing much happens in this lump, principally because any stray neutron entering into (or appearing in) the lump has a high probability of shooting out of the lump before it has a chance to multiply itself.

Simple physics says half these exiting neutrons will leave through the hemisphere's flat surface.

Now, take that other similar hemisphere over there, and slam the two together into a sphere.

Now, those neutrons that were escaping, "leaking" out of each of the lumps, now finds itself in an identical lump. Those neutrons now have more opportunities to cause fission, and, as long as you can hold the two hemispheres together, the neutron count, and the energy release rate will increase.

Google "twisting the dragon's tail" or "demon core" for some accidents that arose from a different way of "saving" lost neutrons...

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