When most people think shielding, they are probably thinking x-rays and gamma rays. However, shielding is much more general than that.
There are a few different kinds of shielding. Shielding is meant to stop something from passing some region, in whole or in part. If the shielding is reflective, there will be momentum imparted to it. If the shielding is absorptive, heat will be generated. If the shielding is transmutive, the incoming radiation is changed to into something else (not heat).
Optical shielding is quite common. Paint applied to wood for use outdoors is an absorptive (or reflective), optical shielding. White paint would be a diffuse, reflective optical shielding. A dark coloured paint would be an absorptive, optical shielding.
A mirror is a reflective, optical shielding; in particular a specular, reflective, optical shielding.
In optics, there are hot mirrors and cold mirrors. A hot mirror is designed to reflect heat (infrared), whereas a cold mirror transmits heat (and reflects visible light).
A fluorescent lamp is an example of a composite shielding that has transmutive and absorptive components. The phosphors seek to transmute the hard UV from the mercury into visible light, and the glass tube is strongly absorptive to whatever UV makes it through the phosphor coating.
Ionising radiation is radiation with sufficient energy, that interactions with matter can result in ionisation. X-rays, gamma rays, alpha and beta particles, and cosmic rays would all be examples of ionising radiation.
How radiation interacts with matter is complicated: it depends on the kind of radiation, the energy of the radiation, and the matter it is interacting with. Some kinds of interactions are outlined below.
If electrons are ejected from atomic shells of atoms, electrons can fill these holes by radiative or non-radiative mechanisms. With inner shell vacancies, the radiative mechanism gives rise to x-rays. With outer shell vacancies, radiative mechanisms can give rise to less energetic forms of electromagnetic radiation (ultraviolet or visible light), or to the ejection of Auger electrons (which creates vacanies again).
Charged particles interact strongly with matter. The charged particle can have its path altered (requiring accelerations), or it can cause electrons or nuclei to alter their movement, again requiring accelerations. Accelerating charges give rise to broadspectrum, electromagnetic radiation.
High energy photons can interact with a nuclear field to produce matter/anti-matter pairs. The lowest energy pair is for electrons, requiring at least 1.022 MeV. Energy in excess of the minimum goes into kinetic energy of the pair. Very high energy photons can excite a nucleus, and cause it to give off particles. Photoneutron production can begin at 1.67 MeV with beryllium and 2.23 MeV with deuterium.
In general, absorbing high energy photons (x-rays and gamma rays) is a matter of mass. A kilogram of water absorbs about as much as a kilogram of lead. At lower energies, certain kinds of shielding are better at absorbing than are others, and/or produce more easily handled secondary radiation.
A commonly seen configuration in gamma spectroscopy labs is a "graded" shield. The outermost layer would be a thick layer of lead (10cm thick would be typical). Some people might even use "old lead", to avoid having radioactive impurities in the lead. Inside of that primary shield, layers of lower atomic number materials would be used.
One of the products of shielding with lead, is the generation of lead x-rays. Employing something of lower atomic number (for example, cadmium) to absorb the lead x-rays, giving rise to cadmium x-rays. Then you would have a layer of of something to absorb the cadmium x-rays and give off an even lower energy x-ray. As the atomic number goes down, there is a tendency to emit electrons instead of x-rays. The electrons at these lower energies are easily absrobed with generating x-rays. One particular graded shield might be: Pb/Cd/Cu/Al/Plastic. Most of the mass is the Pb.
The amount and kind of materials depends on materials and money. Old lead and old steel are a couple of preferred materials. At some time in the future, it might be economically feasible to use enriched stable isotopes for shielding. Until then, most of the concern of what materials to use in shielding depends on what impurities are present and how much things cost.
In some circumstances, an increase in shielding mass leads to an increase in radiation field "behind" the shielding. Cosmic ray interactions are a typical source of this effect.
Charged particles are normally easy to shield, unless they are very high in energy (for example: cosmic rays). Neutral particles like photons and neutrons are typically the harder things to absorb.
Neutron shielding typically uses materials that are very good at absorbing neutrons (usually through nuclear reactions), and that don't generate dangerous radioactivity of their own in absorbing those neutrons.
Lithium and boron are probably the more widely used materials here Li-6 and B-10 in particular. He-3 is a good absorber, but not very abundant. Both He-3 and Li-6 give rise to tritium (radioactive hydrogen) in absorbing neutrons. There are a few other elements that are good at absorbing neutrons, but they typically are only used in contruction of nuclear reactors and such. Eu, Gd, Dy, and Hf would be examples.
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