Cross Section (sigma = Mu/n)

A handy concept in quantifying the likelihood of electromagnetic or particulate radiation interacting in a particular way with matter is an abstract one referred to as the `cross section` for the event in question. Examples of such interactions are collisions, or specific chemical/nuclear reactions. These involve some combination of beam particles (e.g. nuclei, elementary particles including photons) and target material (e.g. nuclei, atoms, gases, colloids). A real-life event is said to have a cross-section ? (which is conceptual) if its rate of occurrence is equal to the rate of collisions in an analogous and idealised classical scenario of a beam striking a target, where: >> the target particles are thought of as inert, impenetrable discs presenting an area ? (hence the name "cross-section") perpendicular to the beam >> the beam is thought of as a stream of inert point-like particles >> all other experimental variables are kept the same as in the real-life scenario. The cross section values described above are rarely the same as the geometric cross-sectional area of the target nucleus or particle. Why use talk in terms of `cross section` rather than `reaction rate` or `probability`? The answer is that the likelihood of an event depends strongly on variables such as the density of the target material, beam intensity, or area of overlap between beam and target material. The cross section is so useful because it factors out these variables. So, for example, cross section values measured at one accelerator can be directly compared with those obtained at another, irrespective of performance differences in the accelerators.

The SI unit for cross sections is m^2, but in practice smaller units are normal. With visible light beams, the scattering cross-section is expressed in cm^2, whereas with X-rays, Å^2 is used (1Å, one angstrom = 10^10 m). In nuclear and particle physics, the conventional unit is the barn (b), where (1b = 10^28 m^2 = 100 fm^2). Units such as mb and micro-b are also widely used. Cross section values depend on the energy of the bombarding particle and the type of reaction. Boron, when bombarded by neutrons travelling at 10 km/s, has a neutron-capture cross section of about 120 barns for neutrons travelling at one tenth of that speed (1 km/s), the cross section increases by a factor of about ten to roughly 1,200 barns. So-called `slow` neutrons are much more likely to be captured by boron, which is often used as a neutron absorber in nuclear reactors. (Note that boron`s geometric cross-sectional area is only about 0.1 barn.) In the formula sigma=mu/n, n is the number density of the target particles (SI units: m-3) mu is the attenuation coefficient for this event (the fractional reduction in radiant flux per unit distance as the beam passes through a specific material SI units: m^-1).