Abstract
An x-ray image records variations in the passage of x rays through the body because of scattering and absorption. This chapter describes the mechanism by which x-rays and charged particles interact with tissue. Photons interact by several mechanisms, including the photoelectric effect, Compton scattering, and pair production. Other processes can lead to the transfer of energy between photons and electrons, such as the production of Auger electrons, bremsstrahlung radiation, and emission of fluorescence photons. The interaction of tissue with charged particles is described by their range and stopping power, and they often deposit most of their energy near the end of their path in the Bragg peak.
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Notes
- 1.
Since this is one of the few relativistic results we will need, it is not developed here. A discussion can be found in any book on special relativity.
- 2.
The atomic weight is potentially confusing. Sometimes \(A\) has no units (as in labeling an nuclear isotope), sometimes it is in grams per mole, and sometimes it is in kilograms per mole).
- 3.
This distinction between photons and charged particles represents two extremes on a continuum, and we must be careful not to adhere to the distinction too rigidly. A photon may be coherently scattered through a small angle with no loss of energy, while a charged particle may occasionally lose so much energy that it can no longer be followed.
- 4.
A value \(\beta =0.04\) corresponds to a kinetic energy of 400 eV for electrons, 800 keV for protons, and 3.2 MeV for \(\alpha \) particles.
- 5.
Classically, if the electrons go around the nucleus many times while the projectile moves by, the shape of their orbits can change in response to the projectile. Quantum mechanically, the shape of the wave function can change, but the quantum numbers do not change.
- 6.
This difference can be understood classically. In the first approximation, the radiation by a charge is proportional to the product of the charge times its acceleration, \(qa\). For two interacting electrons, \(a_{1}=-a_{2}\), \(q_{1}=q_{2}\), and the sum of these two terms vanishes. For an electron and a positron \(a_{1}=-a_{2}\), \(q_{1}=-q_{2}\), and the two terms add.
- 7.
A plasmon excitation is due to the interaction of the projectile with the entire electron cloud of the atom.
- 8.
The electron density functions are calculated using quantum mechanics. The problem is to find the electron distribution by solving Schrödinger’s equation with the potential distribution due to the nucleus and the potential due to the electron charge distribution for which one is solving. This self-consistent computation is called the Hartree–Fock approximation.
- 9.
\(I\) is not the same as the average ionization energy of Eq. 15.57.
- 10.
The solid line representing the integrand does not fall to zero at 0.12 nm\({}=1.2~\operatorname {\text {\AA }}\) because of the effect of electrons from neighboring atoms. In a solid there are no regions where the electron density is zero.
- 11.
The literature often replaces the \(4\pi \) by \(2\pi \) for electrons and makes \(L\) twice as large.
- 12.
These examples were constructed with a pedagogical simulation program called MacDose (Hobbie 1992). The program is available at the book web site: www.oakland.edu/~roth/hobbie.htm. It runs on a Macintosh using OS-9 or earlier. There is also a 26-min video using MacDose that shows the concepts here in more detail (Hobbie 2009). It is free and available through iTunes. A more realistic but easily understood Monte Carlo simulation is described by Arqueros and Montesinos (2003).
- 13.
- 14.
Neutrinos, which we will discuss in Chap. 17, travel such long distances without interacting that they are not considered in the calculations. Energy carried by neutrinos, which come from nuclear \(\beta \) decay, is assumed to have left the body.
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Hobbie, R., Roth, B. (2015). Interaction of Photons and Charged Particles with Matter. In: Intermediate Physics for Medicine and Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-12682-1_15
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