No, as in, as the average distance a neutron-hitting nucleus travels before the collision increases, the average energy of the neutron at collision time decreases. Or so I imagine, that's what I'm asking.
The scenario was that the size of the material can increase until you guarantee a sufficiently high rate of collision, and I'm asking whether neutrons really do not lose energy as they travel prior to collision (as the scenario seems to assume).
Why would the average distance a neutron has to travel to strike a nucleus increase?
I suppose it does eventually, as the number of undecayed nuclei falls, but that wouldn’t be a significant effect until the criticality reaction had very significantly progressed. In other words the reaction can’t go on forever.
> Why would the average distance a neutron has to travel to strike a nucleus increase?
Because if the problem is that neutrons are escaping the object before hitting a nucleus, and we are adding more nuclei so the likelihood that they hit something increases, the new collision candidates will be further away than the old ones.
In other words, adding material to the edge of the object does not affect the per distance probability of collision. It only affects the overall probability of collision. Since the per distance probability does not change while the overall probability does, the probability increase must lie outside of the average path length of a neutron through the original object.
In the case we are considering, it doesn’t, but it could with other materials.
Consider that the wavelength of the neutron is a function of its energy, and that the cross sections for interaction between nuclei and neutrons are strong and complex functions of energy.
If the cross section for the interaction of interest gets smaller with decreasing energy, then it would be the case that the neutrons mean free path length would increase as energy decreased.
> In the case we are considering, it doesn’t, but it could with other materials.
Sorry, I said something subtle and easy to miss and also made a confusing typo, writing too fast.
"average distance a [nucleus-hitting neutron]"
As in, as more material is added, the percent of neutrons that successfully collide and don't just fly out increases. But, for the class of nucleus-hitting neutrons, the average distance prior to collision increases.
If the neutron loses energy as it travels, then as the average distance increases I suppose the probability of splitting the collidee nucleus decreases. So as the class increases in size, its rate of nucleus splitting may fall below the threshold, which bounds the useful size increase.
Perhaps this doesn't occur until the object has grown in size way past the point of basically guaranteed criticality, I haven't done the math, just curious since GP's statement sounded as if neutrons do not lose energy across any distance and the object could therefore could be increased to an arbitrary size while maintaining the same qualitative per-iteration behavior, and I find that surprising.
In the regime that's interesting for pure fission devices, the opposite is true. The cross section increases as energy decreases. This is why moderators are a thing in nuclear reactors.
