Charged Particle Interactions with Matter

Abstract

In nuclear medicine, moving charged particles are released in tissue through either the radioactive decay processes of Chap. 4 or as a result of the photon–matter interactions of Chap. 6. Being charged, these particles interact signi- ficantly with the medium, transferring their kinetic energy resulting in an absorbed dose to the medium as they slow down to thermal energies. Hence, the study of charged particle interactions with matter is the fundamental core of ionizing radiation dosimetry. In this chapter, the two mechanisms of energy loss are presented. Colli- sion energy losses between the particle and atomic electrons are derived through the Bohr classical and the Bethe quantum-mechanical means; hard collisions losses are derived independently from various quantum-mechanical results. Radiative energy losses resulting from bremsstrahlung are initially derived from classical theory which then progresses to the Bethe–Heitler quantum-mechanical theory. The polari- zation effects of a charged particle upon the medium will limit the collision energy losses and are derived. As energy loss is inherently stochastic, energy straggling models are also presented. In particular, the Vavilov theory of energy straggling is derived as are the Gaussian and Landau results which are treated limiting conditions to that theory. Multiple scatter strongly affects electrons and positrons and the Fermi–Eyges theory is derived as a means of justifying the Gaussian model. The Goudsmit–Saunderson and Molie ´re theories of multiple scattering are derived. Finally, the mechanisms through which a positron can annihilate on an electron are derived.