Principal Mechanism of Interaction (Ionization and Excitation). When a charged particle passes through a substance (target), it interacts with the negatively charged electrons and positively charged nuclei of the target atoms or molecules. Through the coulomb forces, it tries to attract or repel the electrons or nuclei near its trajectory. As a result of these pushes and pulls (a sophisticated name for these is inelastic collisions), the charged particle loses some of its energy, which is taken up by the electrons of the target atoms near its trajectory. The absorption of energy by the target atom leads to its ionization or excitation. In this energy range (10 keV to 10 MeV), ionization events predominate over excitation events. For this reason, high-energy radiations are sometimes referred to as ionizing radiations, although excitation events are by no means negligible. The probability of inelastic collisions in general is so high that it does not take a material of much thickness to stop the charged particles completely.

Differences Between Lighter and Heavier Charged Particles. Do all charged particles interact in a similar way? The answer is yes and no. Yes, because inherently the nature of interaction for all charged particles in this energy range is the same (inelastic collisions). No, because the manifestation of these interactions on lighter particles—whose masses are of the order of an electron (e.g., e and e⁺)—and heavier particles—whose masses are equal to or more than that of a proton (e.g., p and α)—is strikingly different. Lighter particles in inelastic collisions with the electrons of the target atoms, besides losing energy, tend to be deflected at larger angles than the heavier particles. This leads to a wide variation in the paths of the two kinds of particles (depicted graphically in Fig. 6.1 for an electron and proton). The path of a heavier particle is more or less a straight line, whereas that of a lighter particle is more tortuous (zig-zag). Whenever a lighter charged particle is deflected at a large angle, the energy transferred to the target electron is also quite large. As a result,
the target electron acquiring this large amount of energy also behaves like a high-energy charged particle, thus creating its own path in the target medium. The paths created by high-energy secondary electrons are known as δ-rays. These are shown by the dotted lines in Figure 6.1. In the case of a proton or other heavier particles, this type of energy transfer is rare.

Range R of a Charged Particle. As a charged particle travels farther and farther in a medium, it loses more and more energy and therefore more and more of the target atoms close to its path become ionized or excited. Eventually, the charged particle loses all its kinetic energy and comes almost to a halt. The average distance traveled by a charged particle in the incident direction is defined as its range R. This definition of range R is strictly valid only for heavy charged particles, such as α particles. For lighter particles, it is difficult to define the range R exactly. For our purpose, it is sufficient to think of the range R of light particles such as electrons or positrons as the minimum thickness of a material that they are just unable to penetrate. The concept of the range of a charged particle is quite useful in radiation protection, design of radiation detectors, and radiation dosimetry.

The range R of the heavier charged particles, because they travel more or less in straight lines, is nearly equal to the average path length of the charged particles in a given medium, whereas the range R for the lighter particles such as electrons, because of their more tortuous paths, is much shorter than the average path length (Fig. 6.1). Table 6.1 lists the ranges of α particles and electrons for various energies and mediums, providing a rough idea of the distances involved.

The concept of range is sometimes used with β-emitting radionuclides in which β particles are emitted with varying amounts of energy up to a maximum, E_βmax. In this case, the range is more or less determined by E_βmax.

Factors That Affect Range, R. The range R of a charged particle depends on various factors. Four of the most important of these are described as follows:

Bremsstrahlung Production. Besides losing energy through inelastic collisions, charged particles can lose energy through the “bremsstrahlung” process. In this case, when a charged particle in the electric field of a nucleus experiences a sudden acceleration or “de-acceleration,” it sometimes emits high-energy photons (x-rays). The probability of such interaction in the energy range of our interest is indeed very small except when electrons and positrons interact with high atomic-number materials (e.g., lead and steel). The fraction of energy, f released as x-rays by electrons of energy E (MeV) in a material with atomic number Z is given approximately by the following equation:

In an x-ray tube with a tungsten target (Z = 74) and electrons with 100-keV (or 0.1 MeV) incident energy, only 0.5% of the total energy of the electrons is converted into x-rays. The same fraction (0.5%) of the total energy of the electrons is converted into x-rays when a 1-MeV electron passes through water (Z = 7.4), except that the x-ray spectrum (energies of emitted x-rays) in this case is quite different from that produced in the first case (x-ray tube). For the purposes of nuclear medicine, because production of high-energy photons by this mechanism is generally very small, it is ignored with one exception. As was explained in Chapter 5, nuclides emitting β particles are used in therapy where large amount of dosage is administered to a patient. Under these circumstances, it is possible, though with challenges, to image the β particle distribution by using bremsstrahlung radiation. An example of this is radioembolization therapy with yttrium-90 (⁹⁰Y), which undergoes β^– emission that can lead to bremsstrahlung radiation.

Stopping Power (S). Quite often, instead of using the range R of a charged particle, another parameter known as stopping power S is used. Stopping power is defined as the ratio of the amount of energy lost dE by a charged particle in traversing a small distance dx in a given medium to the distance dx, or

The range R is related to the stopping power in an approximately inverse relationship (i.e., the
higher the stopping power of a given medium, the shorter will be the range of a given particle in that medium). Because of this relationship, the stopping power S also depends on the same factors (E, M, Q, and d) on which the range R depends, although the relationships are, approximately, inverse of the range R. Stopping power is sometimes referred to as unrestricted linear energy transfer (LET).

Linear Energy Transfer. LET (also referred as restricted LET) is an important parameter in radiation biology. It is defined as the ratio of the amount of energy transferred dE_local by a charged particle to the target atoms in the immediate vicinity of its path in traversing a small distance dx to the distance dx, or

Difference Between LET and Stopping Power, S. In discussing stopping power S one is concerned with the total energy lost by the particle, whereas in discussing LET one is concerned with the local (immediate vicinity of the track) deposition of energy by the charged particle. Because of this, S and LET are almost equal for heavier particles. For lighter particles, however, the two quantities differ significantly because of the energy lost in the δ-rays or through the bremsstrahlung process, which do not deposit energy locally. Both stopping power S and LET are measured in the same units (keV/µm).

Annihilation of Positrons. There is no difference in the way in which an electron or a positron loses energy in a medium. However, a positron, once it has lost its energy, is not stable and is quickly annihilated by combining with an electron. The mass energy of the electron and the positron is converted into two γ-rays of 511 keV that travel in opposite directions as shown in Figure 6.2. Remember that the annihilation of positron occurs only when it has lost almost all of its energy (i.e., near the end of its range in a medium).

Cerenkov Radiation. Charged particles when traveling in matter can also lose energy by emitting visible light, called Cerenkov (or Cherenkov) radiation or luminescence. This phenomenon occurs when charged particles in a medium travel faster than the speed of light in that medium (note that nothing can exceed the speed of light in vacuum). It is analogous to how a sonic boom is generated when an aircraft or another object travels faster than the speed of sound. Cerenkov radiation can for instance occur when very high-energy positrons are emitted from PET radiotracers. It has been used to image β particle distribution in small animals. However, it is not practical for large subjects because the probability of this phenomena is extremely small, and visible light penetrates tissue only a few millimeters.

Although a photon does not have any electrical charge, it nevertheless interacts with electrical charges and therefore with matter that is composed of electric charges. The probability of interaction and the modes of interaction of a photon with matter are strongly dependent on the energy of the photon. Here, we are interested only in the interaction of high-energy photons (x- or γ-rays) with matter.

The probability of interaction of an x-ray or γ-ray with an atom is, in general, very small compared with that of high-energy charged particles. As a consequence, x- or γ-rays have more penetrating power than high-energy charged particles. Because of this high penetrating power of x- or γ-rays, it is not practical to use concepts such as stopping
power or range. Instead, new concepts known as linear attenuation coefficient µ (linear) and the half-value layer (HVL) are commonly used.

Attenuation and Transmission of X- or γ-Rays. Let us consider a simple experiment in which a parallel beam of x- or γ-rays of a given energy E_γ is incident on a thin slab of 1-cm² cross section and x-cm thickness (Fig. 6.3). When a γ-ray passes through this slab, three things may occur: the γ-ray may be completely absorbed by the material, the γ-ray may be deflected (scattered) with some or no loss of energy, or the γ-ray may pass through the slab without any interaction. The first two processes together are known as attenuation; the third is known as transmission. The transmission of γ-rays of a given energy E_γ through a thickness x in the above experiment depends only on the nature of the material (density and atomic number) and the thickness x of the slab. For a given material, the dependence on the thickness x can be experimentally determined by measuring the number of γ-rays (those without any loss of energy or deflection) transmitted through different thicknesses of the slab. The data resulting from such an experiment can be accurately related by the following mathematical expression: