Answer to Question #13036 Submitted to "Ask the Experts"

Why, for intermediate energies and for different materials, are the best protective materials composed of heavy elements (high atomic number), and with other materials the total mass attenuation coefficients are similar? Why do some of the conventionally best shielding materials, such as lead, at intermediate energies have the lowest mass attenuation coefficient when compared to materials with low atomic numbers where the mass attenuation coefficients are higher? Does it depend on another factor besides the atomic number?

You raise some good points. I shall attempt to address your questions. The major short answer to your question involves recognition of electron density per unit mass as a major factor affecting the values of the mass attenuation coefficients.

Any significant discussion about shielding effectiveness of gamma or x-radiation will inevitably raise the importance of atomic number, Z, as an influencing factor. At low photon energies the photoelectric interaction cross section varies according to the 4^th to 5^th power of Z. At high energies (>1.022 MeV) the pair production cross section varies as the square of Z. It is clear that for these energies the atomic number is important, and high atomic number greatly favors increased photon attenuation. For intermediate energies, the very strong Z-dependence does not prevail, and the Compton scatter interaction dominates the interactions and the cross section for this interaction is proportional to Z. This is a weaker dependence than is observed for the dominant interactions at both low and high energies, but there still remains a direct dependence on Z.

What is not always emphasized in discussions of shielding is that Compton and photoelectric interactions occur with atomic electrons, and the consequence of this, all other factors being equal, is that the material with the highest electron density per unit mass will have the highest mass attenuation coefficient. When we look at a material like lead, perhaps the overall most popular photon shielding material, we see that at low energies, say 50 keV, the mass attenuation coefficient is more than 7 cm² g^-1; for the lowest atomic number material available, hydrogen, however, the mass attenuation coefficient is only about 0.34 g cm^-2. The large difference favoring the lead is associated with the large difference in atomic numbers of the two materials, 82 compared to 1. If we now look at the mass attenuation coefficients at 1 MeV, however, we find the lead value is about 0.07 cm² g^-1, and the hydrogen value is about 0.13 cm²g^-1. At this energy the Compton process will dominate the interactions. While the higher atomic number of lead implies more electrons available per atom compared to hydrogen, on a mass basis the electron density of hydrogen is more than twice that of lead.

The mass of the atom is governed largely by the mass of the nucleons. Hydrogen has only a single proton in the nucleus and a single electron in the neutral atom, thereby having one electron per nucleon. Stable lead has 82 protons plus about 126 neutrons (for the most abundant stable lead isotope); naturally, the neutral lead atom has 82 electrons, implying that there are 82 electrons per 208 nucleons or 1 electron per 2.54 nucleons, an electron density about 40% of hydrogen on a mass basis. Therefore hydrogen, as well as other low atomic number materials for which the electron-to-nucleon ratios are higher than lead, are more effective shielding materials on a mass basis than is lead. Materials with a high atomic number always have a higher ratio of neutrons to protons than do low atomic number materials in order to mitigate some of the repulsive forces between protons. In general, low atomic number materials, especially, have mass densities smaller than high many atomic number materials. It becomes clear why some low Z materials are not used when we look at the practical demands for putting enough material in place to provide the required shielding. For example, water, a relatively low atomic number material, is sometimes a convenient and inexpensive material for some shielding applications. If we consider again 1 MeV photons, we would find it would take about 33 cm of water to reduce the primary fluence of photons incident normally on the water surface by a factor of 10, but only about 3 cm of lead would be required for the same effect.

So, intermediate energy interactions are dominated by Compton scatter; materials with the highest electron density per unit mass are the most effective in shielding such photons, and the highest electron densities are provided by the lowest atomic number materials - but the greater mass densities provided by many of the higher atomic number materials often make for more practical shields because of the reductions in thickness they allow and often the greater ease in handling and implementation—e.g., hydrogen has the highest electron mass density but getting it into a useful physical form for shielding is impractical.

I hope this clarifies the situation for you.

George Chabot, PhD