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 ?
There are two factors that may be responsible.
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.