Neutron Cross Sections

Particle cross sections are one of those things that are all around us, but one never sees. As a matter of fact, the idea of a neutron cross section is exactly what allows us to predict if a neutron will hit some particular material.  

What is a neutron cross section?  If you were to take a baseball and cut it down the middle, what you would have (other than a ruined baseball) is two halves of a baseball-each now with a flat side. The area (pi*r^2) of this flat side is the baseballs “cross-sectional area”.  But, sad to say, a neutron cross section isn’t the area of a neutron cut in half; rather it is the cross-sectional area of the target nucleus that is being hit by a neutron. Its a little funny, but it would be like calling the baseball’s cross-sectional area the “eyeball cross-section” because it is the eyeball that is looking at it. 

So a target nucleus, the thing a neutron is going to hit, has a neutron cross-section. Because it’s still a cross-section, which is a 2-D measurement, the units are often put in square centimeters (think: height and width).  but atoms are small things and the nucleus of an atom much smaller still,  the neutron cross-section of our target is equal( on average) to about 10^-24 square centimeters. This is a very small quantity, so people use the unit of “barn”. 1 barn = 10^-24cm.  Careful though, the neutron cross section is not a probability of it hitting, it’s just related to one.

The neutron cross section is a physical measurement pertaining mainly to 2  things.

  1. The target atom’s nucleus, which has a specific number of neutrons and protons
  2. The incoming energy of the neutron itself, which changes constantly.

These 2 things show us that if the energy is changing constantly then so is the neutron cross-section! Back to the baseball analogy, if you are the catcher (the “target”) the baseball appears to be getting bigger as it moves closer and closer to you. then it must mean that the ball is “seeing” us get bigger as well. As the ball begins to slow down it is easier (more probable) that we can catch it. Likewise, as the neutron slows down (loses energy) the probability of the collision increases.  The probability of interaction and cross section are related, so a simple way to talk about the probability of hitting the target is just to say the neutron cross section is bigger at slow energies. 

As the cross-section is a measurement related to the probability of an interaction occurring, there are different kinds of cross sections because there are different kinds of interactions a neutron could have with a nucleus when they collide. Some of the main interactions include scattering, absorption, and fission. 

If cross section is high, then an interaction is likely to take place. If the cross-section is low, an interaction is less likely to take place.

The way this affects us every day is reflected in a nuclear power plant, space missions, the sun burning bright, and even the more than half of the natural heating of the earths core (which, you know, keeps the iron core flowing, creating the magnetic poles, which stop the solar winds from killing us where we stand…or sit). Anyhow… You see,  the materials with high scattering cross-sections can be used as reflectors or moderators – which is a fancy way of saying the neutron bounces like a pinball and loses a bunch of energy. High absorption cross section materials can be used as a neutron poison (something that just sucks them up for no real gain) or control rod in a reactor-which is part of what allows us to control nuclear reactions.  Of course, materials with high fission neutron cross sections are used for fuel and, when they are hit with a neutron, they split. kicking out a few more neutron to keep it the cycle going and providing us the heat energy that the plant turns into electricity.

So now you know that neutron cross-sections actually affect your everyday life and that it is not just a property of the neutron as well as the target. Oh – and the idea we have explored is more commonly called the “microscopic cross-section” to differentiate it from a similar quantity known as the “macroscopic cross-section”.

Read about the Macroscopic Cross section HERE.

 

Thanks for reading and have a good rest of your day/night.

 

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