This is another background post and I am going to explain a bit more about the interaction of neutrons with matter.

Since neutrons do not have a charge we are going ignore their interaction with electrons – they do interact somewhat but going into this now could be confusing. They do interact with atomic nuclei. (you may want to revise the structure of matter at this point).

Scattering

The first thing that they can do is to bounce off the nucleus.

If the size of the nucleus is small (e.g. a hydrogen atom) then the kinetic energy is shared between the neutron and the nucleus. The neutron looses a lot of its kinetic energy.

If the nucleus is much larger than the neutron (e.g. a uranium nucleus) then the nucleus moves only slightly. Most of the kinetic energy remains with the neutron.

In both the above examples, kinetic energy is conserved. This is called elastic scattering.  Light atoms are much better at slowing down neutrons than heavy atoms. This is why hydrogen (in the form of water), deuterium (heavy water) or carbon (graphite) are often used as moderators in nuclear reactors. I shall talk more about moderators below.

There are cases where kinetic energy is not conserved. This happens because some of the energy goes into the nucleus and leaves it in an excited state. This energy is latter released as a gamma ray. This sort of interaction is called inelastic scattering.

Neutron Capture

The neutron can be absorbed by the nucleus. For example, Uranium 238 can absorb a neutron to produce Uranium 239. Capture usually leaves the nucleus in an excited state and therefore results in the emission of one or more gamma rays.

The new isotope formed may not be stable and can decay. For example, Uranium 239 eventually decays into plutonium 239.

 

Where is a beta particle and is a neutrino. The Plutonium 239 itself may undergo neutron capture to form plutonium 240 which itself may undergo neutron capture to produce Plutonium 241. I will talk more about this in a later post.

Many nuclei can undergo neutron capture. For example stable cobalt is converted into highly radioactive Cobalt 60:

This process is sometimes called neutron activation. It is the reason that parts of a nuclear reactor such as the pressure vessel become radioactive.

Fission

If a neutron hits a some nuclei then the nuclei can split to form two smaller nuclei and a number of neutrons and a large amount of energy. This is how a fission reactor works. I have already talked about that here.

Proton, Neutron and Alpha Production

Neutrons can knock out a proton (n,p reaction) or an alpha particle (n,α reaction) from the nucleus. For example Carbon – 14 is produced by the interaction of neutrons in cosmic rays with nitrogen:

The neutron can lead to the production of more two or more neutrons in what are called (n,2n) or (n,3n) reactions.

Neutron Flux

The neutron flux is how many neutrons pass through an area over a given time. So there will be a certain flux of neutrons leaving the reactor core.This is measured in neutrons per second.

We can also talk about the neutron flux density – i.e. the number of neutrons passing through a given area in a given time which will be measured in neutrons per second per meter squared.

Another term that you can come across is the fluence which is the total number of neutrons that have passed through an area.

Cross Sections

Atomic nuclei can behave in more than one way when hit by a neutron. For example, Plutonium 239 can undergo fission or it can undergo neutron capture. The various probabilities of what actually happens depends on the energy of the neutron and the nucleus involved.

It is possible to determine a cross-section for every type of interaction. This means that for a certain neutron flux, you would expect so many nuclei to undergo a certain interaction.

The nucleus has an area of about 1×10^-28m² (1.77×10^-28m² for Uranium). However, the size of the Uranium atom is about 1×10^-19m² since there are electrons orbiting the nucleus. i.e. the nucleus is about half a billion times smaller in terms of area than the atom. I could not represent that as an image on the computer since if the whole computer screen was the atom the nucleus would be one five hundredth of a pixel!

It turns out that often the cross-section when it comes to interactions such as capture or fission are a lot larger than the size of the nucleus (I will not go into the reasons here). Scientists therefore measure cross-sections in barns, since the cross-sections were ‘as large as a barn’ compared to what might be expected. 1 barn is 1×10^-28m².

If you wanted to work out how many times a certain isotope such as Plutonium 239 fissions rather than undergoes neutron capture, then this would simply be the ratio of the fission cross-section ?_f to the capture cross-section ?_c.

The total fission rate would be the number of atoms (N) times the fission cross-section (?_f) times the neutron flux density (?).

Variation of Cross Section With Neutron Energy

Neutrons can travel at various speeds and therefore have different energies. The various cross-sections varies with the energy/speed of the neutrons, as shown in the graph below.

The cross section for fission is about 10,000 times higher for slow neutrons than for fast neutrons. This is why most nuclear reactors use moderators to slow down the neutrons.

Anyway I think this is enough heavy stuff for one post. I shall use this as background information in future posts.

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¹ Monte Carlo criticality analysis of simple geometries containing tungsten–rhenium alloys engrained with uranium dioxide and uranium mononitride, Jonathan A. Webba, Indrajit Charitb, Nuclear Engineering and Design, Volume 241, Issue 8, August 2011, Pages 2968–2973 (http://www.sciencedirect.com/science/article/pii/S0029549311004250)