chapter 6 Interaction of Radiation with Matter

The two most important general types of radiation emitted during radioactive decay are charged particles, such as α particles and β particles, and electromagnetic radiation (photons), such as γ rays and x rays. These radiations transfer their energy to matter as they pass through it. The principle mechanisms for energy transfer are ionization and excitation of atoms and molecules. Most of this energy ultimately is degraded into heat (atomic and molecular vibrations); however, the ionization effect has other important consequences. For this reason, the radiations emitted during radioactive decay often are called ionizing radiations. The processes by which ionizing radiations transfer their energy to matter are fundamental to the detection of radiation, discussed in Chapter 7. As well, they are important for radiation dosimetry, discussed in Chapter 22. In this chapter, we discuss those processes in some detail. Because the mechanisms differ, they are discussed separately for particulate versus electromagnetic radiation.

a Interactions of Charged Particles with Matter

1 Charged-Particle Interaction Mechanisms

High-energy charged particles, such as α particles or β particles, lose energy and slow down as they pass through matter, as a result of collisions with atoms and molecules. High-energy electrons, which also are charged particles, are a byproduct of these collisions. In addition, high-energy electrons are generated when γ rays and x rays interact with matter, and they are emitted in internal conversion (see Chapter 3, Section E) and in the Auger effect (see Chapter 2, Section C.3).

For these reasons, this section emphasizes the interactions of electrons with matter. Except for differences in sign, the forces experienced by positive and negative electrons (e.g., β⁺ and β⁻ particles) are identical. There are minor differences between the ionizing interactions of these two types of particles, but they are not of importance to nuclear medicine and are not discussed here. In this chapter, the term electrons is meant to include both the positive and negative types. The annihilation effect, which occurs when a positive electron (positron) has lost all of its kinetic energy and stopped, is discussed in Chapter 3, Section G.

The “collisions” that occur between a charged particle and atoms or molecules involve electrical forces of attraction or repulsion rather than actual mechanical contact. For example, a charged particle passing near an atom exerts electrical forces on the orbital electrons of that atom. In a close encounter, the strength of the forces may be sufficient to cause an orbital electron to be separated from the atom, thus causing ionization (Fig. 6-1A). An ionization interaction looks like a collision between the charged particle and an orbital electron. The charged particle loses energy in the collision. Part of this energy is used to overcome the binding energy of the electron to the atom, and the remainder is given to the ejected secondary electron as kinetic energy. Ionization involving an inner-shell electron eventually leads to the emission of characteristic x rays or Auger electrons; however, these effects generally are very small, because most ionization interactions involve outer-shell electrons. The ejected electron may be sufficiently energetic to cause secondary ionizations on its own. Such an electron is called a delta (δ) ray.

FIGURE 6-1 Interactions of charged particles with atoms. A, Interaction with an orbital electron resulting in ionization. Less-close encounters may result in atomic excitation without ionization. B, Interaction with a nucleus, resulting in bremsstrahlung production.

[Repulsion by orbital electron (A) and attraction toward nucleus (B) indicates incident particles are negatively charged in the examples shown.]

A less-close encounter between a charged particle and an atom may result in an orbital electron being raised to an excited state, thus causing atomic or molecular excitation. These interactions generally result in smaller energy losses than occur in ionization events. The energy transferred to an atom in an excitation interaction is dissipated in molecular vibrations, atomic emission of infrared, visible, ultraviolet radiation, and so forth.

A third type of interaction occurs when the charged particle actually penetrates the orbital electron cloud of an atom and interacts with its nucleus. For a heavy charged particle of sufficiently high energy, such as an α particle or a proton, this may result in nuclear reactions of the types used for the production of radionuclides (see Chapter 5); however, for both heavy charged particles and electrons, a more likely result is that that particle will simply be deflected by the strong electrical forces exerted on it by the nucleus (Fig. 6-1B). The particle is rapidly decelerated and loses energy in the “collision.” The energy appears as a photon of electromagnetic radiation, called bremsstrahlung (German for “braking radiation”).

The energy of bremsstrahlung photons can range anywhere from nearly zero (events in which the particle is only slightly deflected) up to a maximum equal to the full energy of the incident particle (events in which the particle is virtually stopped in the collision). Figure 6-2 shows the energy spectrum for bremsstrahlung photons generated in aluminum by particles from a ⁹⁰Sr-⁹⁰Y source mixture ( = 2.27 MeV) and illustrates that most of the photons are in the lower energy range.

FIGURE 6-2 Bremsstrahlung spectrum for β particles emitted by ⁹⁰Sr + ⁹⁰Y ( = 2.27 MeV) mixture in aluminum.

(Adapted from Mladjenovic M: Radioisotope and Radiation Physics. New York, 1973, Academic Press, p 121.)

2 Collisional Versus Radiation Losses

Energy losses incurred by a charged particle in ionization and excitation events are called collisional losses, whereas those incurred in nuclear encounters, resulting in bremsstrahlung production, are called radiation losses. In the nuclear medicine energy range, collisional losses are by far the dominating factor (See Fig. 6-5). Radiation losses increase with increasing particle energy and with increasing atomic number of the absorbing medium. An approximation for percentage radiation losses for β particles having maximum energy (MeV) is

FIGURE 6-5 Collisional (ionization, excitation) and radiation (bremsstrahlung) energy losses versus electron energy in lead and in water.

(Adapted from Johns HE, Cunningham JR: The Physics of Radiology, 3rd ed. Springfield, IL, 1971, Charles C Thomas, p 47.)

(6-1)

where Z is the atomic number of the absorber. This approximation is accurate to within approximately 30%. For a mixture of elements, an “effective” atomic number for bremsstrahlung production should be used

(6-2)

where f₁, f₂, … are the fractions by weight of the elements Z₁, Z₂, … in the mixture.

Example 6-1

Calculate the percentage of radiation losses for ³²P β particles in water and in lead.

Answer

= 1.7 MeV for ³²P. Water comprises parts hydrogen (Z = 1, AW ≈ 1) and parts oxygen (Z = 8, AW ≈ 16); thus its effective atomic number for bremsstrahlung production is (Equation 6-2)

The percentage of radiation losses in water are therefore (Equation 6-1)

and in lead (Z = 82) they are

The remaining 99.6% and 95.4%, respectively, are dissipated as collisional losses.

Example 6-1 demonstrates that high-energy electrons in the nuclear medicine energy range dissipate most of their energy in collisional losses. Bremsstrahlung production accounts for only a small fraction of their energy. Nevertheless, bremsstrahlung can be important in some situations, such as the shielding of relatively large quantities of an energetic β-particle emitter (e.g., hundreds of MBq of ³²P). The β particles themselves are easily stopped by only a few millimeters of plastic, glass, or lead (see Section B.2); however, the bremsstrahlung photons they generate are much more penetrating and may require additional shielding around the primary β-particle shielding. It is helpful in such situations to use a low-Z material, such as plastic, for the primary β-particle shielding, and then to surround this with a higher-Z material, such as lead, for bremsstrahlung shielding (Fig. 6-3). This arrangement minimizes bremsstrahlung production by the β particles in the shielding material.

FIGURE 6-3 Preferred arrangement for shielding energetic β-emitting radioactive solution. Glass or plastic walls of a vial stop the β particles with minimum bremsstrahlung production, and a lead container absorbs the few bremsstrahlung photons produced.

Bremsstrahlung production and radiation losses for α particles and other heavy charged particles are very small because the amount of bremsstrahlung production is inversely proportional to the mass of the incident charged particle. Alpha particles and protons are thousands of times heavier than electrons and therefore dissipate only a few hundredths of 1% or less of their energy as radiation losses. These particles, even at energies up to 100 MeV, dissipate nearly all of their energy as collisional losses.

3 Charged-Particle Tracks

A charged particle passing through matter leaves a track of secondary electrons and ionized atoms in its path. In soft tissue and materials of similar density, the tracks are typically approximately 100 µm wide, with occasionally longer side tracks generated by energetic δ rays. The tracks are studied in nuclear physics using film emulsions, cloud chambers,* and other devices.

When a heavy particle, such as an α particle, collides with an orbital electron, its direction is virtually unchanged and it loses only a small fraction of its energy (rather like a bowling ball colliding with a small lead shot). The maximum fractional energy loss by a heavy particle of mass M colliding with a light particle of mass m is approximately 4 m/M. For an α particle colliding with an electron, this amounts to only approximately 0.05% [4 × (1/1840)/4 ≈ (1/2000)]. Heavy particles also undergo relatively few bremsstrahlung-producing collisions with nuclei. As a result, their tracks tend to be straight lines, and they experience an almost continuous slowing down in which they lose small amounts of energy in a large number of individual collisions.

By contrast, electrons can undergo large-angle deflections in collisions with orbital electrons and can lose a large fraction of their energy in these collisions. These events are more like collisions between billiard balls of equal mass. Electrons also undergo occasional collisions with nuclei in which they are deflected through large angles and bremsstrahlung photons are emitted. For these reasons, electron tracks are tortuous, and their exact shape and length are unpredictable.

An additional difference between electrons and heavy particles is that for a given amount of kinetic energy, an electron travels at a much faster speed. For example, a 4-MeV α particle travels at approximately 10% of the speed of light, whereas a 1-MeV electron travels at 90% of the speed of light. As a result, an electron spends a much briefer time in the vicinity of an atom than does an α particle of similar energy and is therefore less likely to interact with the atom. Also, an electron carries only one unit of electrical charge, versus two for α particles, and thus exerts weaker forces on orbital electrons. For these reasons, electrons experience less frequent interactions and lose their energy more slowly than α particles; they are much less densely ionizing, and they travel farther before they are stopped than α particles or other heavy charged particles of similar energy.

To illustrate these differences, Figure 6-4 shows (in greatly enlarged detail) some possible tracks for β particles and for α particles in water. The actual track lengths are on the order of microns for α particles and fractions of a centimeter for β particles. This is discussed further in Section B.

FIGURE 6-4 Representation of α particle and electron tracks in an absorber. Alpha particles leave short, straight, densely ionized tracks, whereas electron paths are tortuous and much longer; δ rays are energetic secondary electrons.

4 Deposition of Energy Along a Charged-Particle Track

The rate at which a charged particle loses energy determines the distance it will travel and the density of ionization along its track. Energy loss rates and ionization densities depend on the type of particle and its energy and on the composition and density of the absorbing medium. Density affects energy loss rates because it determines the density of atoms along the particle path. In the nuclear medicine energy range (10 MeV ), energy loss rates for charged particles increase linearly with the density of the absorbing medium. (At higher energies, density effects are more complicated, as discussed in the sources cited in the references and bibliography at the end of this chapter.)

Figure 6-5 shows collisional and radiation energy loss rates for electrons in the energy range of 0.01-10 MeV in water and in lead. Energy loss rates Δ E /λ x are expressed in MeV/g · cm^–2 to normalize for density effects

(6-3)

Thus for a given density ρ the energy loss rate in MeV/cm is given by

(6-4)

Collisional loss rates Δ E /Δx_coll decrease with increasing electron energy, reflecting the velocity effect mentioned in Section A.3. Also, Δ E/Δx_coll decreases with increasing atomic number of the absorbing medium because in atoms of higher atomic number, inner-shell electrons are “screened” from the incident electron by layers of outer-shell electrons, making interactions with inner-shell electrons less likely in these atoms. Gram for gram, lighter elements are better absorbers of electron energy than are heavier elements.

Radiation loss rates Δ E /Δ x_rad increase with increasing electron energy and increasing atomic number of the absorber. This is discussed in Section A.2.

The total energy loss rate of a charged particle, Δ E /Δ x_total, expressed in MeV/cm, is also called the linear stopping power (S_l). A closely related parameter is the linear energy transfer (LET), L, which refers to energy lost that is deposited “locally” along the track. L differs from S_l in that it does not include radiation losses. These result in the production of bremsstrahlung photons, which may deposit their energy at some distance from the particle track. For both electrons and α particles in the nuclear medicine energy range, however, radiation losses are small, and the two quantities S_l and L are practically identical.

The average value of the linear energy transfer measured along a charged-particle track, , is an important parameter in health physics (see Chapter 23, Section A.1.). usually is expressed in units of keV/µm. For electrons in the energy range of 10 keV to 10 MeV traveling through soft tissue, has values in the range of 0.2-2 keV/µm. Lower-energy electrons, for example, β particles emitted by ³H ( = 5.6 keV), have somewhat higher values of . Alpha particles have values of ≈ 100 keV/µm.

Specific ionization (SI) refers to the total number of ion pairs produced by both primary and secondary ionization events per unit of track length along a charged particle track. The ratio of linear energy transfer divided by specific ionization is W, the average energy expended per ionization event:

(6-5)

This quantity has been measured and found to have a relatively narrow range of values in a variety of gases (25-45 eV per ion pair or, equivalently, per ionization) independent of the type or energy of the incident particle. The value for air is 33.7 eV per ion pair. W is not the same as the ionization potential (I), which is the average energy required to cause an ionization in a material (averaged over all the electron shells). Ionization potentials for gases are in the range 10-15 eV. The difference between W and I is energy dissipated by a charged particle in nonionizing excitation events. Apparently, more than half of the energy of a charged particle is expended in this way. Similar ratios between W and I are found in semiconductor solids, except that in these materials the values of W and I are both approximately a factor of 10 smaller than for gases (see Table 7-1).

Because W does not change appreciably with particle type or energy, specific ionization is proportional to linear energy transfer L along a charged particle track. Figure 6-6 shows specific ionization in air for electrons as a function of their energy. The curve indicates that specific ionization increases with decreasing energy down to an energy of approximately 100 eV. This behavior reflects the fact that energy loss rates and L increase as the electron slows down. Below approximately 100 eV, the electron energy is inadequate to cause ionizations efficiently, and specific ionization decreases rapidly to zero.

FIGURE 6-6 Specific ionization for electrons versus energy in water.

(Adapted from Mladjenovic M: Radioisotope and Radiation Physics. New York, 1973, Academic Press, p 145.)

Specific ionization values for α particles are typically 100 times greater than for electrons of the same energy because of their greater charge and much lower velocities. This leads to greater rates of energy loss, as discussed in previously in Section A.3.

The fact that specific ionization increases as a particle slows down leads to a marked increase in ionization density near the end of its track. This effect is especially pronounced for heavy particles. Figure 6-7 shows a graph of ionization density versus distance traveled for α particles in air. The peak near the end of the α-particle range is called the Bragg ionization peak.* A similar increase in ionization density is seen at the end of an electron track; however, the peak occurs when the electron energy has been reduced to less than approximately 1 keV, and it accounts for only a small fraction of its total energy.