I read this:
These so-called fast neutrons do not cause fission as efficiently as slower-moving ones so they are slowed down in most reactors by the process of moderation.
Why slowly neutrons "thermal" are more efficiently in causing the fission? Is due to their larger cross section? And why the cross section of thermal neutron is larger than the faster ones?
For comparison, I plot below the (total) neutron cross section and the cross section for fission for both 235U and 238U below. These data are readily available at the Evaluated Nuclear Data File site (the linked one is at Brookhaven, look for closer sites if on a different continent). In both plots the blue line is the total cross section (any reaction from a neutron coming in, including elastic and inelastic scattering), while the green line is the cross section solely for the fission reaction.
For 235U one sees:
For 238U you get:
For 235U you see that the thermal (low energy) cross section for fission is quite large (greater than $10^{4}$ barns, and is quite a large fraction of the overall cross section - 235U really wants that neutron to enable it to split apart. The slope of the cross section in that region is quite common, basically going as the inverse of the velocity. In simple terms it is kind of like a transit time of the nucleus. The real question is what the 'size' of the nucleus is, and that depends on just what you are asking it to do.
In contrast, looking at 238U one sees that (1) the overall cross section is down by some 2 orders of magnitude, (2) at low energies the fission cross section is heavily suppressed (by some 7 orders of magnitude), and (3) one needs fairly energetic neutrons to get any reasonable chance of fission at all.
So, the apparent 'size' of the 238U nucleus is smaller than 235U to a neutron, and the nuclear structure of the 2 yields very different energetics of the fission reaction.
