13.1: Show explicitly how you use the results for Coulomb scattering, and how the two coordinate frames are connected.   13.8: It is useful to start in the rest frame of the monopole and transform to the laboratory to get the laboratory fields. Explain the origin of the limits of integration you use, and show whether the classical or quantum limit is appropriate. Give a graph which shows for both the monopole and for a nucleus with equivalent energy loss for for velocities v ~ 1. Describe how you could use the difference for v << 1 to distinguish the particles.

Comments: Take Z/A = ½. The dE/dx curves are important in many areas, for example, radiological physics where one may be interested in shielding with respect to radioactive sources, or in energy deposition in tissue as a hazard or in treatment of cancer using particle beams.   The estimate of the length of shielding made in the second part of the problem is an underestimate. dE/dx is decreased for highly relativistic particles by the density effect.   Radiative energy loss in close collisions also becomes important at the highest energies. While this increases the average dE/dx, so decreases the average range of the particles, the radiative energy loss is subject to significant statistical fluctuations. In particular, the number of close collisions made by a particle in traversing a slab of matter is Poisson-distributed about the mean number. A small fraction of the muons in a monoenergetic beam will therefore have significantly fewer close collisions than the average, lose less than the average amount of energy in radiative processes, and continue to penetrate the shield until their energy is absorbed by ionization. The estimate of the shielding needed, with the density effect taken into account but radiation ignored, is therefore reasonable. See the Review of Paricle Properties, Phys. Rev. D 54, 132 (1996) for a complete discussion of the passage of particles through matter.

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© 1997, 1998, 1999 Loyal Durand