# Mean number of neutron interactions over distance d

## Main Question or Discussion Point

Let's try something simple and hope this goes better than my last two threads. :( The problem can be stated thusly:

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Given thermal neutrons emitted at a source S interacting with a mean interaction length of L and an evaluation point P distance d away from S, what is the average number of interactions that a neutron measured at P will have experienced before reaching there? Assume that the interaction length does not change during its interactions.
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It's easy in the case where one assumes monoenergetic neutrons emitted directly towards P and leaving each collision on the same path; however, that's not the real world where particles progress with brownian motion and may well end up heading back toward S, off at an angle, etc.

As an alternative: if anyone knows of any good software for simulating neutron interactions so that I don't have to calculate everything by hand...

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mfb
Mentor
I guess Geant 4 can simulate it.

If you want to include changes in the direction (which is probably a good idea for neutrons), then you first need a model of the angular distribution of the scattering results. A completely uniform distribution would be easy to model with Brownian motion (you can directly use those equations), but I'm not sure how good that model is.

I guess Geant 4 can simulate it.

If you want to include changes in the direction (which is probably a good idea for neutrons), then you first need a model of the angular distribution of the scattering results. A completely uniform distribution would be easy to model with Brownian motion (you can directly use those equations), but I'm not sure how good that model is.
Roughly isotropic. And thanks mfb, I'll give Geant 4 a look. :)

(Liking it so far :) If someone had mentioned this earlier this would have completely eliminated a still-ongoing kerfuffle ;) Thanks! )

mfb
Mentor
Geant 4 is the standard program for simulating interactions of particles with matter in particle physics. I don't know any experiment that does not use it.

QuantumPion
Gold Member
Let's try something simple and hope this goes better than my last two threads. :( The problem can be stated thusly:

----
Given thermal neutrons emitted at a source S interacting with a mean interaction length of L and an evaluation point P distance d away from S, what is the average number of interactions that a neutron measured at P will have experienced before reaching there? Assume that the interaction length does not change during its interactions.
----

It's easy in the case where one assumes monoenergetic neutrons emitted directly towards P and leaving each collision on the same path; however, that's not the real world where particles progress with brownian motion and may well end up heading back toward S, off at an angle, etc.

As an alternative: if anyone knows of any good software for simulating neutron interactions so that I don't have to calculate everything by hand...
What is your level of mathematics and nuclear engineering background? Are you familiar with the neutron transport equation and numerical integration techniques?

The most common codes used are SCALE and MCNP. I believe SCALE has student version available and it is a bit easier to get into than MCNP.

Thanks QuantumPion. I have a university-level mathematics and physics with a CS background, but no particular focus on nuclear engineering. However Geant4 seems to be what I need to satisfy my curiosity, it's a lot easier than trying to do everything by hand. A bit of a steep learning curve, but hey...

It's still good to do some of the simpler calculations by hand to know what sort of geometries to try in Geant4, mind you - for example if one wants a certain neutron interaction or doesn't want another, it's rather important to be able to calculate neutron free paths and energy lost to elastic collisions. I already have that down; I'm looking at bremsstrahlung radiation calculations now**, and I'll need to look up EM interactions next to get a very rough sense of how much energy the x-rays will deposit in different geometries. I don't need anything precise, just to be able to get an "orders of magnitude" level handle on the scales / distances of the various interactions.

** Unrelated to the original topic, but if I understand this right, if one had a 16MeV electron moving through 1mm of lithium metal (atomic mass 6.94, 0,534g/cm³, bremsstrahlung cross section 4.3 barns) and wanted to know the amount of bremsstrahlung radiation, then that's the number of atoms per square centimeter (0.1cm * 0.534 g/cm³ / 6.94 g/mol * 6.022e23 atoms/mol = 4.634e21 atoms/cm²) times the cross section in square centimeters (4.3 barns / 1e24 barns/cm²) times the energy (16 MeV), aka 0.32MeV, right? (the cross section changes little over that energy range). Basically like the neutron macroscopic cross section calculation, times the electron energy, correct? And the elastic losses for electron scattering scatter would be presumably 0,5-0,5*((x-1)/(x+1))² where x is A/0.00054858?

Hmm, although that would lead to questions of how energetic are the various bremsstrahlung X-rays emitted... perhaps this would just be easiest to simulate rather than trying to work it out by hand.

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QuantumPion
Gold Member
There aren't any simple hand solutions of the neutron transport equation, it is solved using numerical methods. You can read a good overview here.

You'll have to be more specific with what you are trying to accomplish if you want advice that will point you in the right direction and using the right tool for the job.

QuantumPion: The overall goal? Modeling the multiplication, thermalization, cooling and capture by 7Li targets of spallation neutrons, and tracking the fate of the resultant 8Li beta emission inside an axial magnetic field, in addition to total energy deposited in each component of the target geometry by all sources.

I'm still working with Geant4. Unfortunately based on conversations one of the developers, its low-energy physics handling is a bit lacking (for the CERN people, events below 20 MeV aren't particularly interesting). For example, in most physics usable physics lists, material temperature isn't even taken into consideration. It sounds like it's possible to do low-energy physics with it but it takes extra effort. We'll see how it goes.

QuantumPion