Answer to Question #8536 Submitted to "Ask the Experts"

For photons, over a very wide range of energy and for almost all elements, it is possible to find data for the attenuation coefficients and for the absorption coefficients. However, is it possible to find data for the attenuation coefficients and the absorption coefficients for neutrons? If the answer is yes, please let me know where.

Many sources provide neutron cross-section information. The data are usually presented as atomic cross sections for specific isotopes of selected elements, with units of cm². Photon attenuation coefficients and absorption coefficients are most often presented as macroscopic cross sections, usually the mass attenuation or mass absorption coefficient, with common dimensions of cm² g^-1, or the volume cross section, with common units of cm^-1 (i.e., cm² cm^-3), also referred to as the linear attenuation coefficient. If you are given the neutron atomic cross section for a specific isotope, you can obtain the mass macroscopic cross section for a given material by multiplying the atomic cross section for the isotope by the isotope atom density, in atoms per gram, of the material.

As an example, consider the absorption of thermal neutrons by ¹⁰B to produce the well-known (n,a) reaction. Assume that the material being irradiated is pure borax, Na₂B₄O₇, which contains boron of natural composition. Natural boron contains 19.9 atom percent ¹⁰B and 80.1 atom percent ¹¹B, and the density of anhydrous borax is 2.37 g cm^-3. The molecular weight of borax is 201.2, and the atomic weight of natural boron is 10.81. The thermal neutron (n,a) cross section of ¹⁰B is 3,840 barns. Making use of Avogadro's number, we can calculate the mass macroscopic absorption cross section (for the (n,a) reaction) of the borax as: 

S_m = (6.022 x 10²³ molecules borax/201.2 g borax)(4 atoms B/molecule borax)

        (0.199 atoms ¹⁰B/atom B)(3,840 x 10^-24 cm²/atom ¹⁰B) = 9.15 cm² g^-1.

If we preferred the volume macroscopic cross section, we would simply multiply the above value by the mass density of the borax.

A convenient source of neutron cross section information is the Brookhaven National Laboratory's National Nuclear Data Center. The "Library" box above the periodic table should say "ENDF/B-VII.0 (USA, 2006)," and the "Sublibrary" box should say "Neutron reactions." Simply click on the element of interest in the periodic table, then select the isotope of interest from the mass numbers that will be displayed to the right of the table. A pop-up window will appear, and you can select to display the data for the reaction of interest; the "Plot" option for display is very convenient. If you select it you will see the cross-section data plotted as a function of neutron energy, and when you position the cursor on the curve you will see the exact energy (in eV) and the cross section at that energy (in barns).

If you are a member of the Health Physics Society, you may access the Members Only section of the HPS site and activate the HP Toolbox, which is the last item shown in the list of available materials. Once you open this you will see the major topic areas listed, and you may click on "Neutrons" to obtain other cross-section information.

I hope you find what you need. Good luck.

George Chabot, PhD, CHP