What's your current level of understanding of atomic physics? And what more specifically are you wanting to learn about?
There are vast numbers of potential nuclear reactions when two or more particles interact at high (or sometimes, low) energies. For simple two body reactions, they're often presented in the form like MainReactant(InteractsWith, Leaves)FinalProduct" - for example, "4He(t,n)6Li". So in this case, you have helium-4 (the common type, 2 protons and 2 neutrons) interacting with tritium (1 proton and 2 neutrons) yielding lithium-6 (3 protons, 3 neutrons) and a neutron. For short, if the resultant product is considered obvious in the context, it can be omitted, like 4He(t,n) - you can even leave off the initial reactant if it's understood in the context. A particular common type of reaction involved in atomic physics is the (n, γ) reaction - γ (gamma) means just that, gamma radiation and no other resulant particle (these are commonly known as neutron capture, and are particularly noteworthy with "cold" neutrons).
What does temperature have to do with neutrons? Well, the likelyhood that any interaction will occur is known as the "cross section" of that reaction. Picture that you've got a baseball pitcher and you're firing baseballs randomly at a bunch of targets from a distance. If these targets each have a small cross sectional area, then most of your baseballs will pass through without hitting them, only a small percentage will hit their mark. On the other hand, if the targets have a very large cross section, many of the baseballs will hit their mark. With various nuclear reactions, it's the same sort of thing: you can picture the neutrons (or whatever) as if they're traveling through open space with a bunch of targets with varying cross sections in their way, and eventually they'll hit one. It's not the physical size of the atoms (although the figure is scaled to be "roughly" comparable to the size of atomic nuclei), but it's as if the nuclei were that size.
Every different isotope for every different reaction presents a different cross section, and they can vary by many orders of magnitude. There are reactions which take in neutrons and don't yield any neutrons; if an isotope has a good cross section in this regard, then it's considered an absorber. For (n, 2n) reactions (or n, 3n, or so forth), having a good cross section makes you a neutron multiplier. Then there's of course fission cross sections (fission doesn't give a specific this-is-going-to-yield-these-particles list, as that varies - it's just (n, fission)). The balance of all of the different cross sections determines how a particular environment is going to behave.
Back to temperature. Like all particles, neutrons (and other high energy particles undergoing reactions) have a particular energy. They change energy state as they scatter (elastically or inelastically) and undergo various reactions. And a particular energy in electron volts can be mapped to a corresponding temperature. For high energy neutrons, figures in electron volts (keV, MeV) are more useful. But for low energies, presenting it as a temperature is more useful. Why? Because each time a neutron scatters, it's transferring part of its energy to the surrounding environment. So eventually - if it's not consumed in a reaction - its energy will equal the average energy of its environment. It is then considered "thermalized". The further you cool neutrons - aka, thermalizing them in a colder moderator (moderator = substance designed to scatter neutrons but not absorb them) - the lower the temperature (energy) they'll end up.
How does this work out in the real world? Well, as a general rule, (n, γ) reactions (neutron capture) have vastly higher cross sections the lower the neutron temperature. But multiplication reactions, and other more exotic reactions, generally predominate at high temperatures. Fission varies greatly depending on the isotope, with some fissile isotopes having high fission cross sections for thermalized neutrons, while others only having high cross sections for high energy neutrons. Elastic scattering (easy, predictable formula, with energy loss proportional to the atomic mass of the target; light = big energy loss) predominates as the way neutrons lose energy at low temperatures, while inelastic scattering (absorbing a neutron then re-radiating it with lower energy; not as predictable) predominates at high temperatures. Note that all multiplication reactions yield neutrons with significantly lower energies.
Now, all of this is very important for people in the nuclear power world. However, research physicists generally couldn't care less about thermal neutrons - they care about the high energy stuff, because that's the uncharted territory (either that, or the *extremely* cold stuff). As you start to scale up, not only do you start hitting much more varied types of reactions, but high energy particles start causing what's called "spallation". It's like throwing a baseball at a target so hard that it shatters. From the collision of, say, a 1GeV proton with a mercury target you'll get a lot of "evaporation neutrons" (in the low MeV range), like fission, but you also get some more high energy neutrons that can go on to cause their other spallation or other high energy reactions. Overall you may end up with a dozen or so neutrons immediately after the first impact, and with a good multiplication setup, maybe 30 or so when all is said and done. The more energy you throw in, the longer the chain reactions, and the more that other species may end up with enough energy to start causing their own reactions (protons, alphas, light ions, etc). With really
high energy reactions, you end up making something like a highly branched tree, with a single particle hitting off a whole ever-growing shower of weaker reactions, until finally all of the reactions end up as heat. Spallation makes for great non-fission neutron sources, and the target doesn't have to be fissile (it just has to be heavy).
Note that so far I've mainly been talking about the stuff that makes up the nucleus. But there's also other types of radiation. For example, in beta+ and beta- decay, you not only get a high energy electron but also a neutrino, which runs off with a good chunk of your energy and is extremely unlikely to hit anything even remotely near your reactor.
Beta particles (high energy electrons) and gamma often kick off each other, ultimately scattering down as they lose their heat with each reaction into their surrounding medium. While electrons scatter elastically in the same manner as neutrons, they're so light that they lose very little energy per scatter; they lose far more as bremmstrahlung ("braking radiation"), so that's the key cross section to look at when it comes to beta reactions. Note that there are beta and gamma reactions that yield neutrons, but they're generally not an effective source to breed them, the cross sections are too low.
So, as mentioned, cross sections vary wildly in the nuclear world. Here's some examples of some isotopes off the top of my head.
1H: With a rather high scattering cross section and the lowest possible atomic mass, it's a superb moderator in terms of scattering ability. However, while it's (n, γ) cross section isn't super-high, it's higher than one would prefer in a moderator.
2H: It has a lower scattering cross section and a higher mass, so it's not as effective at moderating. But it has an exceedingly low capture cross section, so overall it works out better.
4He: It has literally zero (n, γ) cross section, so in theory it's a perfect moderator. But its lower scattering cross section and low density make it harder to use effectively.
6Li: Extremely high (n, d+t) cross section for thermal neutrons - so high that it's considered a neutron absorber. Gives off a fairly potent beta in the process. At high neutron energies it tends to undergo 6Li(n,t)4He, and is thus useful as a tritium breeder.
7Li: Despite being more common than 7Li, usually doesn't get a chance to undergo (n, γ) with thermal neutrons because the rarer 6Li takes almost all of them, as per above. But if it does capture a neutron it turns into 8Li, which quickly decays into 8Be with a powerful beta, which almost instantly breaks down into two alphas (helium nuclei). At high neutron energies it tends to undergo 7Li(n,n+t)4He and is thus also useful as a tritium breeder.
9Be: Nothing too special for low energy neutrons, but it's unique among isotopes in having a high (n, 2n) fast neutron cross section that extends to lower energies than other isotopes. With other isotopes, neutron multiplication has to be done at higher energies, generally with heavy isotopes.
10B: Extremely high (n, γ) cross section, making it a powerful neutron absorber. As a bit of historical trivial, the Nazis were convinced that graphite couldn't be used as a moderator because they thought that carbon's absorption cross section was too high; actually, it was the miniscule quantities of boron mixed into the graphite that were ruining it for them.
12C and 16O: Good moderators in general. Carbon is a bit better at scattering, while oxygen has a bit lower absorption.
Zr: Zirconium in general has a surprisingly low neutron absorption cross section (over a wide energy range) for being a metal of its high atomic number, and various isotopes even an order of magnitude less. It's also heat tolerant and chemical resistant, so it's often used as fuel cladding.
135Xe: Xenon-135 is the strongest known neutron absorber, its cross section is truly massive. It came as a surprise to earlier nuclear power plant designers, who found their reactions basically being poisoned as 135Xe was produced during the fission reactions. It's so strong that you basically can't avoid having it capture your neutrons, you have to either burn it off as you go, or - if you're shut down - wait for it to decay before you try to restart (either that or very carefully try to control burn it off as your reactor ramps up, otherwise you risk a runaway criticality incident).
Pb: Lead has a rather low neutron capture rate, but Pb208 an amazingly low one. Being heavy, it's a poor moderator (low transfer of energy in elastic scattering), so it's basically a window to neutrons, making it good for fast breeders
Bi: Similar to lead (sometimes used along with it), also with a fairly low neutron absorption coefficient. Lead-Bismuth eutects are sometimes used instead of pure lead to greatly lower the melting point. The downside is that when bismuth captures a neutron, it breeds polonium, which is very dangerous.
Feel free to browse around at cross sections here: http://www.nndc.bnl.gov/sigma/index.jsp ... .1&nsub=10
. It could keep you busy for weeks
Also the decay and other data here: https://www-nds.iaea.org/relnsd/vcharth ... tHTML.html
Note that all of this sort of stuff imposes additional constraints *on top* of the engineering issues that most fields have to deal with. You know, there's cost/rarity, difficulty of working with it, structural strength, melting points, corrosion/explosion hazards, health risks, and so on down the line, and now you have to <i>also</i> consider how each component is going to react in terms of all of the different cross sections and how the changes over time will change all of the "conventional" properties, as well as having the whole new dimension of being able to choose from different isotopes of the same element For example, aluminum isn't very prone to capturing up to anything that will make it radioactive... but will it melt where you want to use it? Iron is so-so at avoiding becoming too contaminated or absorbing too many neutrons, but will it withstand corrosion? If you alloy it with something to reduce the corrosion, will that "something" have bad results when bombarded with neutrons? If you use graphite somewhere as a moderator, are you running hot enough to prevent the buildup of energy in crystal lattice defects (Wigner energy) that could be released all at once? All together it makes it more complicated and challenging... but also more fun
Back to the high energy stuff: it becomes increasingly important to have some control over what everything is doing when you get to high energy particles. For example, evaporation neutrons from spallation are generally random-directional, but the higher energy particles tend to keep going in roughly the same direction as the original neutron. Neutrons and gamma aren't affected by magnetic fields, but alphas, protons, heavier ions, and beta are. The different particles have different masses, so they have different gyroradii in a magnetic field (charged particles in magnetic fields take spiral paths, it's a result of Lorentz force), which yields some sorting possibilities. Note that a particle won't stay pinned to a field line forever as it's going to eventually run into some other particle, and the two will end up kicked out into different lines; over time there's an outward drift. There's also various kinds of traps one can make. For example, you can't use a simple electric field to trap particles, as electric fields are formed from potential differentials between two objects, so a charged particle will always end up traveling to one potential surface. But you can make RF, or "Penning" traps of various sorts, where you alternate the field in a manner that the charged particles average out to staying roughly in the same place.
There's a million other things I could get into, but hopefully that's a nice primer for now?