# Why neutrons production is falling along beam axis in proton/nucleus collisions?

I'm studying a case where I simulate a protons beam (~70 MeV) on a spherical target composed of light nuclei such as carbon and oxygen. I'm looking for the angular distribution of neutrons produced by nuclear reactions from protons in matter. I noticed that this distribution is falling along beam axis and pass through a maximum around 45° then decrease at higher angles. In other papers, it seems to be also the case but I can't figure out why I have almost no neutrons along beam axis since this is where I would expect to have the most. What is the physics behind this effect ?

• If I'm reading this right your question might be better phrased "Why does my simulated neutron production cross-section show a peak in scattering angle?"" or "Why Isn't my simulation showing any forward neutron production?" – dmckee Jun 8 at 15:57
• But questions about why a simulation is doing something always depend on the code. Are you using a mature framework like Geant or MCNP as the basis? Or if it is something less well known do you know what underlying processes are simulated? If you are absolutely convinced the simulation is a good representation of reality in this case then you can focus the question on the physics of the scattering cross-section, but that does rely on the notion that you are not looking at a software bu^W feature. – dmckee Jun 8 at 16:00
• I'm doing it in Gate so Geant4. I compare different nuclear models. Indeed I have neutrons emitted with a 0 degree angle but just a little. I have a peak at higher angles but almost nothing at angle 0. All nuclear models provide different results, but they all agree on the fact that there are almost no neutrons emitted backward (I can understand this one) but also forward. – Korlek Jun 8 at 16:26
• Nice. You can have some confidence that all but the most exotic physics is pretty well represented. – dmckee Jun 8 at 16:33
• Now, here's a game you can try. Re-run the simulation with beam energies of, say $60$ and $80\,\mathrm{MeV}$ and observe what happens to the angular position of the peak. – dmckee Jun 8 at 16:34

One is geometry. The solid angle corresponding to an interval $$d\theta$$ is $$\sin \theta d \theta$$. So if you have an isotropic production of neutrons and then histogram their values of $$\theta$$ it will fall to zero at 0 and 180 degrees. It is easy (and useful) to avoid this by histogramming the $$\cos \theta$$ values, which will give a flat distribution if production is isotropic.
The second is physics and depends on the size of your target. 70 MeV is not very much, and the protons do not travel very far before they lose energy and stop. Your neutrons are probably mostly produced at the spot where the beam hits the sphere. The target then acts as shielding, absorbing or scattering the neutrons, and this shielding effect is thickest along the $$\theta=0$$ direction.