Neutron Capture and More!

Alrighty, I promised this article way back in my 3rd blog post, the one about neutron radiation. Today I’m going to try and delve into The Black Magic of nuclear energy and hopefully I won’t accidentally pierce the veil and call forth some Horror from Beyond (read: have to use calculus for literally any reason in here)

Of all the things I’ve explained about nuclear energy so far and probably into the future, this is the absolute linchpin. Without understanding how neutrons are absorbed and scattered there would be no nuclear energy and no nuclear medicine.

At its simplest, Neutron Absorption is simply the science of understanding how a neutron interacts with an atom. Specifically, what is the probability of it being scattered, captured, or causing a fission event? And we use what is called the neutron cross-section to describe these probabilities.

But wait, how can we use a cross-section to describe a probability? Think of it like this. You are standing at one end of a football field (Canadian sized football field for Americans, cause it’s longer and our balls are bigger. And Canadian “American-Football” for everyone else in the world. It’s called soccer, fight me.) In your hand you have a dart, that’s the neutron. At the other end of the field strung between the goal posts are three dartboards of different sizes which represent the scattering, absorption, and fission probabilities. Now if you could somehow make that throw, the probability of hitting any of those dartboards is relative to their sizes, cause there’s no way you are aiming that dart over 110 yards.

Fundamentally that’s it. If you stopped reading here you could say that you have a basic grasp of the fact that neutrons interact with different atoms in different ways. But I don’t want to leave you with the bare minimum of understanding. I want to leave you with the ability to understand this topic in, if not scientific discussions, the level of discussions where policy about nuclear energy and nuclear waste is concerned. To be able to constructively contribute to those discussions you Need to know how nuclear energy works and this is the fundamental base of that knowledge. Plus, we already have too many people involved with those discussions that are neither contributing or constructive.

While no copyright infringement is intended, I’m using this image because I’m pretty sure that misrepresenting studies and saying, incorrectly, that Chernobyl has caused a million deaths is not constructive.

Now then to give you the knowledge to contribute to the conversation we have to make things a little more complicated. First of all, most atoms only have two targets, because only fissile isotopes like uranium-235 and plutonium-239 have a third target which corresponds to the probability that the neutron will cause the atom to fission. It’s because of this third target that we can make energy from a nuclear reactor so it’s pretty important.

Secondly, the size of those dartboards changes from atom to atom. A carbon atom has a very different sized set of targets than a Xenon atom. In fact, Wikipedia has a handy sample chart that shows the average values for neutron cross-sectional areas of common atoms in reactors.

There is a reason why they are calling the area a barn. Points for whoever guesses it before I tell you why. No cheating off of the handy Wikipedia link.

Here’s where it gets Real weird. Notice how there are different values in the chart for Thermal and Fast cross sections? Well if you recall a previous post of mine about the difference between Thermal and Fast, you might be able to guess that this means that the size of the targets actually changes with how fast you throw the dart. And sometimes not very smoothly either. There’s no simple step between thermal and fast for absorption cross-sections.

Solid lines are scattering cross sections. Dotted lines are capture cross-sections. Taken from Wikipedia who got it from database NEA N ENDF/B-VII.1 

There is no distinct line separating “Fast” and “Thermal” as you can see. But generally the Fast spectrum is on the right-hand side of the graph with the higher neutron energies and Thermal is on the left with the lower energies. So how do we figure out the probabilities that an atom will scatter or capture a neutron? It’s pretty simple, just divide one cross-sectional area by the other.

For example, Xenon has a capture cross section of 2,000,000 barns and a scattering cross-section of 400,000. This means that Xenon is 5 times more likely to capture a neutron than it is to scatter it, and it is almost 3,000 times more likely to capture a neutron than even the best nuclear fuel.

This little factoid is what earns Xenon and other high capture cross section elements the name of Nuclear Reaction Poisons. Which sounds way more threatening than it actually is, because what it poisons isn’t people or the environment, but the ability of a reactor to generate energy.

Application of this field of science is how we control nuclear reactors using moderators and claddings to maximize power outputs while preventing runaway power spikes and accidents. The science is extremely well known and understood. It’s simple at its core, and it is only the attempt to mix so many different parts in a complicated system that causes the control of a reactor to be non-trivial. Modern designs for GenIV reactors take stock of this fact and work to minimize, not the number of safety features, but the number of interactions between disparate systems that interfere with each other’s abilities to operate at peak efficiency. My personal favourite is the Molten Salt Reactor which I like so much that I plan on doing an entire post about at a later date.

Lastly, you can use the terms you have seen here to ask your own questions about nuclear science and energy. Which is one of the goals of this blog. In complicated fields, it’s hard to even get to the point where you feel you know enough to start asking the right questions about topics, let alone feel confident enough to chime in on discussions yourself. I hope that this post and other before and after it give you enough knowledge to feel confident enough to start asking more questions to further your understanding about how nuclear energy can help our society and improve our lives.

Now, the answer to my earlier question, the reason that the unit that these cross section measurements are called Barns is a mix. One part security from the Manhattan Project so that potential spies wouldn’t know what they were talking about. And one part an anecdotally terrible pun about how the early experiments had such bad luck aiming the neutrons at their targets that they couldn’t hit the broadside of a barn… Yeah, gotta love that physicist sense of humour.

6 thoughts on “Neutron Capture and More!

Add yours

  1. Interesting way of presenting with humour yet conveying the basic concept in terms anyone can easily understand. A few suggestions.

    First, given the growing awareness of Thorium, perhaps you might consider an entry for Th-232 and some discussion of it’s properties compared to Uranium.

    Also, and perhaps this aspect might extend to another lesson, it might be useful to show how Thorium and Uranium fission cross-section changes between thermal and fast neutron ranges, affects the fuel attractiveness for particular reactor designs.

    Finally I’m curious how cross-section affects fission efficiency i.e. waste minimization; essentially how best to “encourage” various isotopes resulting from both fission and absorption, to make their way down the energy well thus maximizing efficiency and minimizing remaining decay emissions. Yet another lesson?


    1. Thanks for the feedback Ike! Don’t worry, I totally have a plan to talk all about thorium in the future. I’m a big fan of it myself. And yeah the idea of comparing the changing cross sections of fissile and fertile materials is definitely something I will want to touch on once I start delving into the more advanced concepts as well. Thanks for reading and feel free to follow me here and on twitter @AlbertaNuclear


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