Multiscale analysis for muon-scattering data

Cosmic rays from deep space are continuously striking the Earth’s atmosphere. The result is a shower of particles of various sorts, travelling in various directions at nearly the speed of light. Some of these particles are so unstable that they decay before reaching the Earth’s surface. Others are less energetic and are absorbed by the atmosphere. Muons, on the other hand, are not so unstable and have only a very weak hadronic interaction. The result is that at the Earth’s surface, there is a shower of muons coming from all directions between the horizon and the zenith. These muons can pass through several feet of lead and many yards of rock. Unlike neutrinos, however, they do not make it through the entire planet, which is why muons only arrive from above. The flux is approximately one per square centimeter per minute. Muons are similar to electrons, and have an electric charge (which may be positive or negative). Their one significant interaction with matter is Coulomb scattering, as they are deflected by electron clouds and nuclei. Their path through matter can be regarded as a form of random walk. The overall deflection angle as a muon of a given energy passes through a given thickness of material is roughly a Gaussian random variable. The standard deviation of the distribution is the number of radiation lengths present in the given thickness of material. The radiation length of a material is a decreasing function of both its density and its atomic number (Z). Since density also tends to go up with increasing Z, the amount that a muon will be scattered by a given thickness of material is strongly related to the atomic number of the material. This is the key to the usefulness of muon radiography, as the danger presented by materials in the context of nuclear smuggling also tends to go up with atomic number. Even non-radioactive materials such as lead or tungsten should be regarded as threatening, due to their ability to act as a radiation shield for the purposes of avoiding detection by conventional means. This is why our problem is framed in terms of detection of high-Z materials, without worrying much about discriminating among high-Z materials. The background muon radiation is perfect for this task.