chap13 - Chapter Thirteen Charged Particle Collisions,...

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Unformatted text preview: Chapter Thirteen Charged Particle Collisions, Energy Loss, Scattering Niels Henrik David Bohr (1885 - 1962) September 17, 2001 Contents 1 Energy Transfer in Coulomb Collisions 3 1.1 Classical Impulse Approximation . . . . . . . . . . . . . . . . . . . . 3 1.2 Validity of Approximations . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Energy Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Collisions with a Harmonically Bound Charge; Energy Loss 10 3 Density Effect in Energy Loss 17 4 Cherenkov Radiation 26 5 Momentum Transfer 29 5.1 Average Angle of Deflection . . . . . . . . . . . . . . . . . . . . . . . 33 5.1.1 Distribution of Small Angle Scattering . . . . . . . . . . . . . 35 5.1.2 The Distribution of Large Angle Scattering . . . . . . . . . . . 36 1 The topic of interest is a charged particle traversing a material medium. Such a particle looses energy by scattering from the charged particles, electrons and nuclei, in the material. E E ’ E’ < E This is an interesting system from many points of view. Historically it was extremely important in resolving the question of the structure of matter (the Rutherford atom), and at present energy loss is an important phenomenon in particle physics and is also studied in detail by nuclear engineers and by condensed matter physicists in connection with the properties of materials and radiation damage to materials. The problem can be studied as a straightforward application of electromagnetism; charged particles scatter from one another with the result that energy and momentum are transferred. The scattering centers in a material are of two distinct types; there are electrons of charge- e and small mass m ∼ 10- 27 g , and there are nuclei of charge Ze with Z up to about 10 2 and large mass M ∼ 10- 22 g . Thus the nuclear charge is significantly larger than that of an electron, and the nuclear mass is much larger— some 10 5 times larger—than the electronic mass. It is also important to realize that there are Z more electrons than nuclei ( Z is the atomic number of the atoms in the material) in a given volume of target material. Consequently the electrons provide Z times as many scattering centers as the nuclei. 2 e Z e m M M >> m As we shall see, it turns out that electrons soak up most of the energy of an incident particle while nuclei are responsible for most of the momentum transfer in the sense that they are more effective than electrons at deflecting the incident particle from its initial direction of motion. 1 Energy Transfer in Coulomb Collisions The general problem of energy transfer when a charged particle traverses a material is naturally very complicated. We shall approach it a little at a time starting with the classical impulse approximation applied to a pair of particles....
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This note was uploaded on 01/08/2012 for the course PHYSICS 707 taught by Professor Electrodynamics during the Fall '11 term at LSU.

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chap13 - Chapter Thirteen Charged Particle Collisions,...

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