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The related Wikipedia article says:

A breeder reactor is a nuclear reactor that generates more fissile material than it consumes. Breeder reactors achieve this because their neutron economy is high enough to create more fissile fuel than they use, by irradiation of a fertile material, such as uranium-238 or thorium-232 that is loaded into the reactor along with fissile fuel.

Thus, a breeder reactor somehow solves, that the thermal neutrons in it create equal or more $^{239}\rm Pu$ (by the neutron capture of $^{238}\rm U$, which decays to $^{239}\rm Pu$ in two steps), than the fission (of $^{239}\rm Pu$ or $^{235}\rm U$) wastes.

Now my question is, how do they reach this?

In a thermal reactor, the neutrons are thermal (i.e. their kinetical energy is roughly the same, than the medium around them). Thus, also the cross sections for neutron capture are roughly fixed. And these are far smaller, which would be required for breeding (as far I know, roughly half of it).

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  • $\begingroup$ Took lot of time to understand the question because of misleading content. I answered it as per my understanding. $\endgroup$ – SRD Apr 8 '19 at 2:48
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Thermal neutrons get lots of attempts. What you need, which the wiki article doesn't cover, is a picture of the overall "neutron budget" inside the reactor at a given instant. Some reactors run in the 98% neutron efficiency range. With fission averaging about 2.5 neutrons produced per fission event, there is plenty of headroom (at least on paper). You need good moderators and perhaps a hotter fuel load. Plus an external neutron accelerator to help manage both power output and breed ratio simultaneously doesn't hurt. The accelerator gives you a second knob. It's hard to manage two separate variables with just one knob.

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There are two questions asked here.

1. How neutron cross section increased for Thermal neutrons? (As per the title)

Nuclear reaction is just like any other chemical reaction. Just the presence the reactant does not cause reaction. There should be enough time and collisions between reactants. By slowing down the neutrons, other atoms get enough time to capture neutron. In thermal reactor, fast neutrons are slowed down by thousands of times. (When fission happens, released neutrons have around 80% total energy emitted. So Fast neutrons are incredibly fast). This is all just my theory.

2. Few of the neutrons are absorbed by some other atoms which are either don't undergo fission or doesn't emit further neutrons. And even then how more fissile atoms are created in breeder reactors? (As per second paragraph in the content.)

Simple answer - by lot of engineering work. A nuclear reactor is designed around the solution for this problem. For example, Xe is formed as part of fission product. Xe eats lots of neutrons if present in reactor. But in LFTR, Xe comes out of reactor as it forms because Xe is a gas and reactants are in molten state.

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