Yes, really.
http://www.newscientist.com/article/mg13318055.200-.html "Neutrons can be produced in controlled quantities and at specific energies by nuclear fission in a specially designed nuclear reactor such as that at the Institut Laue-Langevin (ILL) in Grenoble, France . In a typical experiment at ILL, a beam of neutrons, all with more or less the same energies, impinges on a sample. This is called the primary beam. The process is
analogous to firing a series of billiard balls at a collection of moving targets.
I've changed the bolding. What you fail to understand is that analogies aren't perfect. That's why they're only analogies. They tend to have a few aspects in which they are similar, and many aspects in which they are not. The differences get brushed over for non-technical audiences, such as yourself. Conservation of momentum and energy in the interaction is a point of similarity. The neutron as a hard core particle is not. In fact, it is
precisely because neutron scattering is
not well-described that way (but is a wave, and so can create interference patterns) which makes the whole thing so damned useful.
Most of the billiard balls, however, do not hit anything and pass straight through.
As I said. And this applies even when the neutron wavelength is larger than the interatomic spacing. In such a case, the billiard ball model
obviously won't work. Or obviously to anyone who's got a clue about quantum mechanics.
Edit to add: in fact, if the wavelength is long enough compared to interatomic spacing, the wave nature of neutrons can actually end up
precluding any scattering from happening. You can use this property to filter neutrons above certain energies by passing them through a material such as berylium, something which is commonly done to remove higher-order Bragg reflection from your monochromator. This is a quantum effect. A classical billiard-ball picture won't produce this.
The neutron being uncharged continues on its course without suffering any hindrance until it is stopped by direct impact on a nucleus. As the dimensions of the nuclei are extremely small compared with the distances that separates the different parts of the atoms, such impacts are of rare occurrence.
This is again a good way to talk about this for laypeople. But it doesn't actually describe the physics in any real detail. The scattering cross section for electrons to bounce off nuclei is not similarly small, but the it's the same small nucleus. So the physical size of the nucleus really isn't the whole story. Furthermore, when the neutron wavelength is larger than interatomic spacing, does it even make sense to talk about the neutron "avoiding" collisions by zipping between the atoms? No, actually it doesn't. And lastly, why do neutrons get captured by nuclei? Because there's a quantum mechanical energy loss mechanism. Without that, the neutrons might still bounce off, but they can't get captured. There is no appreciable energy loss mechanism for purely gravitational interactions between particles - the rate at which they can radiate away energy in the form of gravitational waves is pretty damned close to zero.
http://www.lightandmatter.com/html_books/6mr/ch05/ch05.html "It can be proved mathematically that the Pauli exclusion principle applies to any type of particle that has half-integer spin.
Thus two neutrons can never occupy the same state,
So? Momentum components are part of the quantum state of a particle. So is spin. Two neutrons can therefore easily occupy the same location without being in the same state. Electrons do it all the bloody time - most of them are doing exactly that in pretty much every atom on earth.
Material objects can't pass through each other,
Not so. Your own link above indicated otherwise for neutrons. Electrons regularly pass through each other - that's how current flows in a wire. Electromagnetic interactions are generally strong enough to preclude such events for anything with
both protons and electrons in most cases, but that's only most cases. Look up Bose-Einstein condensation if you're curious to learn about cases where matter passing through other matter can become quite dramatic.