APPENDIX B
BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND RADIATION DOSE DEPOSITION

This appendix provides introductory and reference information for readers who need background on the structure of atoms, radioactive decay, and forms of radiation and their deposition of energy in materials. This is not meant to be a comprehensive treatment, but should, along with the Glossary in Appendix C, provide the information a reader needs to understand scientific discussions in this report.

ATOMIC AND NUCLEAR STRUCTURE

In the Rutherford model of the atom (Figure B-1), nearly all of the mass and positive charge of the atom are concentrated in the nucleus, the size of which is of the order of 1015 m, and the negative charge is distributed in a cloud outside the nucleus, with a radius of the order of 1010 m. The constituent particles forming an atom are protons, neutrons, and electrons. Protons and neutrons are known as nucleons and form the nucleus of the atom. The proton has positive charge and the neutron has no charge. The electron carries a negative charge identical in magnitude to the positive proton charge. The proton and neutron have nearly identical rest masses; the rest mass of the electron is about 2,000 times smaller than that of the proton or neutron.

FIGURE B-1 Schematic diagram of the Rutherford atomic model. SOURCE: With kind permission of Springer Science+Business Media.



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APPENDIX B BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND RADIATION DOSE DEPOSITION This appendix provides introductory and reference information for readers who need background on the structure of atoms, radioactive decay, and forms of radiation and their deposition of energy in materials. This is not meant to be a comprehensive treatment, but should, along with the Glossary in Appendix C, provide the information a reader needs to understand scientific discussions in this report. ATOMIC AND NUCLEAR STRUCTURE In the Rutherford model of the atom (Figure B-1), nearly all of the mass and positive charge of the atom are concentrated in the nucleus, the size of which is of the order of 10−15 m, and the negative charge is distributed in a cloud outside the nucleus, with a radius of the order of 10−10 m. The constituent particles forming an atom are protons, neutrons, and electrons. Protons and neutrons are known as nucleons and form the nucleus of the atom. The proton has positive charge and the neutron has no charge. The electron carries a negative charge identical in magnitude to the positive proton charge. The proton and neutron have nearly identical rest masses; the rest mass of the electron is about 2,000 times smaller than that of the proton or neutron. FIGURE B-1 Schematic diagram of the Rutherford atomic model. SOURCE: With kind permission of Springer Science+Business Media. 193

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194 RADIATION SOURCE USE AND REPLACEMENT When discussing topics that involve atomic and nuclear phenomena, it is useful to know the conventions for referring to features of atoms and nuclei, including the following. • Atomic number Z is the number of protons and number of electrons in an atom. • Atomic mass number A is the number of nucleons in an atom, that is, number of protons Z plus number of neutrons N in an atom; A = Z + N. • Atomic mass M is expressed in atomic mass units u, where 1 u is equal to 1/12th of the mass of the carbon-12 atom. The atomic mass M is smaller than the sum of individual masses of constituent particles because of the intrinsic energy associated with binding the particles (nucleons) within the nucleus. A In nuclear physics, a nucleus X is designated as Z X , where A is the atomic mass number and Z the atomic number. For example, the cobalt-60 nucleus is identified as 60 Co ; the 27 226 Ra. Because both Z and the chemical symbol uniquely identify the radium-226 nucleus as 88 element, Z is commonly omitted leaving 60Co and 226Ra. An element may be composed of atoms that all have the same number of protons, that is, have the same atomic number Z, but have different numbers of neutrons, that is, have different atomic mass numbers A. Such atoms of identical atomic number Z but differing atomic mass numbers A are called isotopes of a given element. The term isotope is often misused to designate nuclear species. For example, cobalt-60, cesium-137, and radium-226 are not isotopes, since they do not belong to the same element. Rather than isotopes, they should be referred to as nuclides. On the other hand, it is correct to state that deuterium (with nucleus called deuteron) and tritium (with nucleus called triton) are heavy isotopes of hydrogen or that cobalt-59 and cobalt-60 are isotopes of cobalt. The term radionuclide should be used to designate radioactive species; however, the term radioisotope is often used for this purpose. If a nucleus exists in an excited state for some time, it is said to be in an isomeric (metastable) state. Isomers thus are nuclear species that have common atomic number Z and atomic mass number A. For example, technetium-99m is an isomeric state of technetium-99 and cobalt-60m is an isomeric state of cobalt-60. RADIOACTIVE DECAY Henri Becquerel discovered natural radioactivity in 1896; Pierre and Marie Curie discovered radium in 1898. These basic discoveries stimulated subsequent discoveries, such as artificial radioactivity by Frédéric and Irène Joliot-Curie in 1934 and neutron-induced fission by Otto Hahn, Fritz Strassmann, Lise Meitner, and Otto Frisch in 1939. All these discoveries are of tremendous importance in science, medicine, and industry. Radioactivity Radioactivity is a process by which an unstable parent nucleus transforms spontaneously into one or several daughter nuclei. These are more stable than the parent nucleus but may still be unstable and will decay further through a chain of radioactive decays until a stable nuclear configuration is reached. Radioactive decay is usually accompanied by emission of energetic particles and/or gamma rays which together form a class of radiation that is referred to as ionizing radiation.

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BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND DOSE 195 • Nuclear decay, also called nuclear disintegration, nuclear transformation, or radioactive decay, is a statistical phenomenon. • The exponential laws that govern nuclear decay and growth of radioactive substances were first formulated by Ernest Rutherford and Frederick Soddy in 1902 and then refined by Harry Bateman in 1910. • A radioactive substance containing atoms of the same structure is referred to as a radioactive nuclide. Radioactive atoms, like any other atomic structure, are characterized by the atomic number Z and atomic mass number A. • Radioactive decay involves a transition from the quantum state of the original nuclide (parent) to a quantum state of the product nuclide (daughter). The energy difference between the two quantum levels involved in a radioactive transition is referred to as the decay energy Q. The decay energy is emitted either in the form of electromagnetic radiation (usually gamma rays) or in the form of kinetic energy of the reaction products. • The mode of radioactive decay depends upon the particular nuclide involved. • Radioactive decay processes are governed by general formalism that is based on the definition of the activity A (t) and on a characteristic parameter for each radioactive decay process: radioactive decay constant λ with dimensions of reciprocal time usually in s −1 . • The radioactive decay constant λ multiplied by a time interval that is much smaller than 1/λ represents the probability that any particular atom of a radioactive substance containing a large number N (t) of identical radioactive atoms will decay (disintegrate) in that time interval. An assumption is made that λ is independent of the physical environment of a given atom. • Activity A (t) of a radioactive substance containing a large number N (t) of identical radioactive atoms represents the total number of decays (disintegrations) per unit time and is defined as a product between N (t) and λ . • The SI unit of activity is the becquerel (Bq), given as 1 Bq = 1 s-1 . The becquerel and hertz both correspond to s−1 , but hertz expresses frequency of periodic motion, while becquerel expresses activity. • The old unit of activity, the curie (Ci), was initially defined as the activity of 1 g of radium-226 and given as 1 Ci = 3.7 × 1010 s-1 . The activity of 1 g of radium-226 was subsequently measured to be 3.665 × 1010 s-1 ; however, the definition of the curie was kept at 3.7 × 1010 s-1 . The current value of the activity of 1 g of radium-226 is thus 0.988 Ci or 3.665 × 1010 Bq . • Bq and Ci are related as follows: 1 Bq = 2.703 × 10 −11 Ci or 1 Ci = 3.7 × 1010 Bq . • The specific activity a is defined as activity A per unit mass M . The specific activity of a radioactive nuclide depends on the decay constant λ and on the atomic mass number A of the radioactive nuclide. The units of specific activity are Bq/kg (SI unit) and Ci/g (old unit). • The half-life of a radioactive substance is that time during which the number of radioactive nuclei of the substance decays to half of the initial value. One may also state that in the time equal to one half-life of a radionuclide the activity of the radionuclide diminishes to one-half of its initial value.

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196 RADIATION SOURCE USE AND REPLACEMENT Radionuclides Because they produce ionizing radiation through radioactive decay, radionuclides play an important role in science, industry, and medicine, but are also of concern to humans because, when used unsafely or with malicious intent, they may have significant deleterious effects on human tissues. These effects depend on the type of tissue and the dose absorbed by the tissue. Radionuclides can irradiate humans as a source of external radiation (radionuclide located outside but in the vicinity of the human body) or a source of internal radiation (radionuclide enters the body through various pathways such as ingestion, inhalation, or through skin). Radioactive nuclides (radionuclides) are divided into two categories: naturally occurring and man-made or artificially produced. Aside from their origins, there is no essential physical difference between the two categories of radionuclides and the division is mainly historical. • The man-made (artificial) radionuclides are manufactured by bombarding stable or very-long-lived nuclides with energetic particles produced by machines of various kinds, such as nuclear reactors, cyclotrons, and linear accelerators. The process of radionuclide production is referred to as radioactivation or nucleosynthesis. Currently, the list of known nuclides contains some 275 stable nuclides and over 3,000 radionuclides. • Many of the known radionuclides used in industrial and medical applications are produced artificially through radioactivation; however, there are also radionuclides created through fission (splitting) of heavy nuclei and a few naturally occurring radionuclides, almost exclusively members of one of four natural radioactive series that all begin with very-long-lived parents with half-lives comparable to the age of the Earth. The long-lived parents decay through several radioactive daughter products, eventually to reach a stable lead nuclide or a stable bismuth-203 nuclide. Most notable other examples of naturally occurring radionuclides are carbon-14, produced by cosmic ray protons, and the long-lived potassium-40, which occurs naturally. Radionuclides are unstable and strive to reach more stable nuclear configurations through various processes of spontaneous radioactive decay. General aspects of spontaneous radioactive decay may be discussed using the formalism based on the definitions of activity and decay constant without regard to the actual microscopic processes that underlie the radioactive disintegrations. In each nuclear transformation a number of physical quantities must be conserved. The most important of these quantities are total energy, momentum, charge, atomic number, and atomic mass number. Modes of Radioactive Decay A closer look at radioactive decay processes shows that they are divided into seven main categories: 1. alpha decay producing alpha particles, 2. beta minus decay producing negative beta particles (electrons), 3. beta plus decay producing positive beta particles (positrons), 4. electron capture, 5. gamma decay producing gamma rays, 6. internal conversion producing energetic electrons, 7. spontaneous fission producing neutrons and fission fragments.

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BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND DOSE 197 The seven modes of radioactive decay are characterized by their own decay mechanism and constraints imposed by conservation laws; however, they all follow the same statistical process described by a simple exponential function. The main characteristics of the seven decay modes are as follows: • Alpha decay was the first mode of radioactive decay detected and investigated during the 1890s. It played a very important role in early modern physics experiments that led to the Rutherford atomic model and is characterized by a nuclear transformation in which an unstable parent nucleus attains a more stable nuclear configuration through ejection of an alpha particle (nucleus of helium-4 atom) with kinetic energy of the order of a few million electron volts (MeV). Alpha emitters pose no danger to humans as external sources because the alpha particles have a short range in air (of the order of a few centimeters) and cannot penetrate the superficial dead layer of the skin. However, when ingested or inhaled, alpha emitters are dangerous because they interact with living tissues such as bone marrow or alveoli in the lung, potentially depositing a very high radiation dose to internal human tissues. • Beta minus decay is characterized by a nuclear transformation in which a neutron transforms into a proton, and an electron and anti-neutrino, sharing the available energy, are ejected from the nucleus. Energetic electrons emitted in beta minus decay have a relatively small mass and can penetrate human tissue to a depth of a few centimeters, and so they pose a hazard to humans both as external and internal radiation sources. • Beta plus decay is characterized by a nuclear transformation in which a proton transforms into a neutron, and a positron and neutrino, sharing the available energy, are ejected from the nucleus. Energetic positrons emitted in beta plus decay have a relatively small mass and can penetrate human tissue to a depth of a few centimeters, and so they pose a hazard to humans both as external and internal radiation sources. None of the radionuclides considered in this report decay by beta plus decay. • In electron capture the nucleus captures one of its own atomic shell electrons, a nuclear proton transforms into a neutron, and a neutrino is ejected. The process competes with the beta plus decay. • Gamma decay results from a transition between nuclear excited states or a transition from an excited state to the ground state of a nucleus. The nucleus does not undergo a transformation, but nuclear transitions are typically accompanied by emission of gamma rays with energies of the order of 1 MeV. These gamma rays can penetrate deep into the human body and are thus hazardous to humans both as external or internal sources. The damage that they do to cells and tissue can be used for beneficial purposes, as in the case of radiotherapy to treat malignant tumors. • The energy available for a gamma-ray transition may be transferred to an atomic electron, which is ejected with a relatively large kinetic energy. The process is referred to as internal conversion and competes with gamma decay. • In addition to decaying through alpha and beta decay processes, nuclei with very large atomic mass numbers A may also disintegrate by splitting into two nearly equal fission fragments and concurrently emit two to four neutrons. This decay process, called spontaneous fission, competes with alpha decay and is accompanied by liberation of a significant amount of energy. It is similar to the standard nuclear fission process except that it is not self-sustaining, since it does

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198 RADIATION SOURCE USE AND REPLACEMENT not generate the neutron fluence rate required to sustain a chain reaction. For practical purposes, the most important radionuclide undergoing the spontaneous fission decay is californium-252, used in industry and brachytherapy as an efficient source of fast neutrons. Radioactive Decay of Key Radionuclides Used in industry and Medicine Of the 3,000 known radionuclides, about 200 are used in industry and medicine. For the purposes of this report, four radionuclides are of special interest as a result of their widespread use in industry and medicine. The four radionuclides are cobalt-60, cesium-137, iridium-192, and americium-241; diagrams that illustrate the decay modes and energies of these radionuclides appear in Figures B-2 to B-5, respectively. FIGURE B-2 Decay scheme for the beta minus decay of cobalt-60 into nickel-60 with a half-life of 5.26 years. The cobalt-60 nucleus transforms into a nickel-60 nucleus in the second excited state (99.9% of disintegrations). The excited nickel-60 nucleus decays instantaneously from the second excited state into the first excited state by emitting a 1.17-MeV gamma photon, and from the first excited state to the ground state by emitting a 1.33-MeV gamma photon. Note: the two gamma photons are called cobalt-60 gamma rays, yet they actually originate in nickel-60. The average energy of the two is 1.25 MeV. SOURCE: With kind permission of Springer Science+Business Media.

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BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND DOSE 199 FIGURE B-3 Decay scheme for the beta minus decay of cesium-137 into barium-137 with a half-life of 30 years. The cesium-137 nucleus transforms into a barium-137 nucleus in the first excited state (94.6% of all disintegrations). The excited barium nucleus decays into its ground state by emitting a 0.662-MeV gamma photon (85% of disintegrations). Note: The 0.662-MeV gamma photon is called a cesium-137 gamma photon, yet it is emitted by the barium-137 nucleus. SOURCE: With kind permission of Springer Science+Business Media. FIGURE B-4 Decay scheme for the beta minus decay of iridium-192 into platinum-192 and the electron capture decay of iridium-192 into osmium-192 with a half-life of 74 days. Both platinum-192 and osmium- 192 are produced in various excited states and they both instantaneously attain their ground states through emission of gamma photons. The spectrum of iridium-192 gamma photons thus consists of many gamma photons, and the effective energy of the iridium-192 gamma photons is of the order of 0.34 MeV. Note: The gamma photons emitted by an iridium-192 source are called iridium-192 gamma photons, yet they are emitted by either osmium-192 or platinum-192. SOURCE: With kind permission of Springer Science+Business Media.

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200 RADIATION SOURCE USE AND REPLACEMENT FIGURE B-5 Decay scheme for the alpha decay of americium-241 into neptunium-237 with a half-life of 432 years. A spectrum consisting of five discrete alpha particle energies is emitted and the alpha particles produce neptunium-237 in four excited states in addition to the ground state. All excited states instantaneously decay through various excited states into the ground state of neptunium-237 through emission of gamma photons. SOURCE: Image provided by committee. FORMS OF RADIATION Radiation is referred to as non-ionizing or ionizing (see Figure B-6), depending on its ability to ionize matter. FIGURE B-6 Classification of radiation. SOURCE: With kind permission of Springer Science+Business Media. As the term implies, ionizing radiation, in contrast to non-ionizing radiation, is characterized by its ability to ionize atoms and molecules of matter, thereby producing ions and energetic electrons. These ionizing processes have many useful purposes in medicine and industry, but can also cause serious unwanted biological damage in living tissues when used carelessly or with malicious intent. Energy is transferred from ionizing radiation to an absorbing medium through Coulomb interactions with orbital electrons and nuclei constituting the atoms

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BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND DOSE 201 and molecules of the absorbing medium. Ionizing radiation is split into two main categories: directly ionizing and indirectly ionizing. Directly Ionizing Radiation Directly ionizing radiation consists of charged subatomic particles such as light charged particles (electrons and positrons) and heavy charged particles (protons, alpha particles, and heavier ions) which experience direct Coulomb interactions with orbital electrons and nuclei of the absorbing medium. As the term implies, energy is transferred from the charged particle to atomic orbital electrons in a direct manner. It originates from: • radioactive decay producing alpha particles in alpha decay, beta particles in beta decay, electrons in internal conversion; • a particle accelerator producing energetic electrons in linear accelerator, betatron, microtron, or synchrotron; • a particle accelerator producing energetic protons or heavier ions in cyclotron, synchrocyclotron, or synchrotron. Indirectly Ionizing Radiation Indirectly ionizing radiation consists of energetic neutral “particles” such as x rays, gamma rays, and neutrons. These neutral particles first transfer energy to energetic charged particles and these charged particles, as they move through the absorbing medium, experience Coulomb interactions with orbital electrons and nuclei of the absorbing medium. Energy transfer from neutral particles to absorbing medium is thus a two-step process, hence the term indirect ionization. In the case of x-rays and gamma rays, the energetic charged particles released in the absorbing medium are electrons or positrons produced through photoelectric effect, Compton effect or pair production; in the case of neutrons, these energetic charged particles are protons or heavier nuclei released in the absorbing medium through nuclear reactions. It originates from: • radioactive decay producing gamma rays in gamma decay, neutrons in spontaneous fission; • an electron accelerator producing x-rays in x-ray machine, linear accelerator, betatron, or microtron; • a neutron generator producing neutrons in a charged particle electrostatic accelerator or through bombarding a beryllium target with alpha particles produced through alpha decay (e.g., Am-Be). Indirectly ionizing photon radiation consists of four distinct groups of photons: • characteristic (fluorescent) x rays which result from electron transitions between atomic shells; • bremsstrahlung x rays which result from Coulomb interactions between an electron and atomic nucleus; • gamma rays which result from nuclear transitions; • annihilation quanta which result from positron-electron annihilation.

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202 RADIATION SOURCE USE AND REPLACEMENT Indirectly ionizing neutron radiation is classified according to neutron kinetic energy (Ek): ultracold neutrons with Ek < 2 × 10-7eV, • very cold neutrons with 2 x 10-7 eV ≤ Ek ≤ 5 × 10-5 eV, • cold neutrons with 5 × 10-5 eV ≤ Ek ≤ 0.025 eV, • • thermal neutrons with Ek ≈ 0.025 eV, • epithermal neutrons with 1 eV ≤ Ek ≤ 1 keV, • intermediate neutrons with1 keV ≤ Ek ≤ 0.1 MeV, • fast neutrons with Ek > 0.1 MeV. X-rays The importance of ionizing radiation was recognized astonishingly quickly after Wilhelm Roentgen discovered X-rays on November 8, 1895. On December 22 of that year, Dr. Roentgen made a now famous image of his wife Bertha's hand showing her bones and her wedding ring (see Figure B-7). By January 16, 1896, news and understanding of the momentous nature of the discovery was reported in the New York Times, which predicted the “transformation of modern surgery by enabling the surgeon to detect the presence of foreign bodies;” and indeed battlefield physicians began using x rays to find bullets in wounded soldiers and fractures in their bones within months (Asmuss, 1995). The clinical use of x-rays spread rapidly across North America immediately after the discovery of X-rays in 1895 starting in the United States with Yale University on January 27, 1896, and Dartmouth College on February 3, 1896, and in Canada with McGill University on February 5, 1896, and the University of Toronto on February 7, 1896. During the first two decades after 1895, x-rays were produced with low-pressure glass tubes incorporating two electrodes, referred to as the Crookes tube. In the Crookes tube (see Figure B-8a) the potential difference between the two electrodes produces discharge in the rarified gas, causing ionization of gas molecules. Electrons (cathode rays) are accelerated toward the positive electrode, producing x-rays upon striking it. In 1913, William D. Coolidge introduced his invention of ductile tungsten into the x-ray tube and revolutionized x-ray tube design (see Figure B-8b) with the use of a hot-filament cathode for the source of electrons in high-vacuum tubes. Hot cathodes emit electrons through thermionic emission and are still in use today in modern x-ray tubes, now called Coolidge tubes, and in electron guns of linear accelerators. The maximum x-ray energy produced in the x-ray target (anode) equals the kinetic energy of electrons striking the target. X-ray radiographs have advanced to a point where detailed imaging of an entire human body can be carried out in clinical practice. A computed tomography (CT) scanner is a machine that uses an x-ray beam rotating about a specific area of a patient to collect x-ray attenuation data for the patient’s tissues. It then manipulates these data with special mathematical algorithms to display a series of transverse slices through the patient. The transverse CT data can be reconstructed so as to obtain coronal and sagittal section through the patient’s organs or to obtain digitally reconstructed radiographs. The excellent resolution obtained with a modern CT scanner provides an extremely versatile “non-invasive” diagnostic tool. CT scanners have been in clinical and industrial use since the early 1970s and evolved through five generations, each generation increasingly more sophisticated and faster.

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BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND DOSE 203 FIGURE B-7 A radiograph of Bertha Roentgen's hand taken in 1895 as the first example of the potential that Roentgen’s discovery had for clinical use. FIGURE B-8 (a) Photograph of Roentgen’s apparatus for production of x-rays, referred to as Crookes cold cathode tube; (b) schematic diagram of a Coolidge tube, referred to as hot cathode tube. DOSE DEPOSITION IN WATER FOR VARIOUS IONIZING RADIATION BEAMS In benign use of ionizing radiation, the dose deposition in matter is one of the most important characteristics defining the effectiveness of a particular usage. For example, in medical physics the dose deposition properties in water and tissue govern the diagnosis of disease with radiation (imaging physics), treatment of disease with radiation (radiation oncology physics), and the study of deleterious effects of ionizing radiation on humans (health physics). Food irradiation, sterilization of medical equipment with ionizing radiation, and blood irradiation depend heavily on the delivered absorbed dose in the irradiated substances for the successful outcome of the irradiation procedure. In the use of ionizing radiation in industrial imaging, it is the interactions of the radiation with the imaged objects and the dose deposition in the image receptors that govern the image quality as well as the radiation safety requirements. Medical imaging with ionizing radiation is limited to the use of x-ray beams in diagnostic radiology and gamma rays in nuclear medicine (see Figure B-9a), while in radiation oncology

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204 RADIATION SOURCE USE AND REPLACEMENT (see Figure B-9b) the use of ionizing radiation is broader and covers essentially all ionizing radiation types ranging from x rays and gamma rays through electrons to neutrons, protons, and heavier charged particles. In diagnostic radiology and industrial radiography, one is interested in the radiation beam that propagates through the patient or imaged object, respectively, while in nuclear medicine, one is interested in the radiation that emanates from the patient. In radiation oncology, on the other hand, one is interested in the energy deposited in the patient (radiation dose) by a radiation source that is located outside the patient (external beam radiotherapy) or placed directly inside the tumor (brachytherapy). When considering the dose deposition in tissue by radiation beams, four beam categories are usually defined: two categories (photons and neutrons) for indirectly ionizing radiation and two categories (electrons and heavy charged particles) for directly ionizing radiation. Since water is the main constituent of human tissue, it is for practical reasons often used as tissue substitute in the determination of the interaction of ionizing radiation with human tissue and the absorbed dose in tissue. Figure B-10 displays depth doses in water or patient normalized to 100 percent at the depth of dose maximum (percent depth doses) for various ionizing radiation types and energies: for indirectly ionizing radiation (in [a] for photons and in [b] for neutrons) and for directly ionizing radiation (in [c] for electrons and in [d] for protons). It is evident that the depth dose characteristics of radiation beams depend strongly upon beam type and energy. However, they also depend in a complex fashion on other beam parameters, such as field size and source- patient distance. In general, indirectly ionizing radiation exhibits exponential-like attenuation in absorbing media, whereas directly ionizing radiation exhibits a defined range in absorbing media. Although all four radiation categories are used in radiotherapy, routine radiotherapy is generally done with x-rays, gamma rays, or electrons, the beam choice depending on the location of the treated tumor and availability of equipment. Dose Distributions for Photon Beams in Water A photon beam propagating through air or vacuum is governed by the inverse-square law which results in the diminution of the beam’s intensity as the inverse square of the distance from the radiation source. A photon beam propagating through water or a patient, on the other hand, is not only affected by the inverse-square law, but also by attenuation and scattering of the photon beam inside the patient. These three effects make the dose deposition in a patient a complicated process and its determination a complex task. FIGURE B-9 Schematic diagram of ionizing radiation use in medicine for (a) diagnosis of disease (diagnostic radiology and nuclear medicine) and (b) treatment of disease (external-beam radiotherapy and brachytherapy). SOURCE: Provided by the committee.

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BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND DOSE 205 Typical dose distributions in water for several photon beams in the energy range from 100 kVp to 22 MV are shown in Figure B-10a). Several important points and regions of the absorbed dose curves may be identified. The beam enters the patient on the surface, where it delivers a certain surface dose Ds. Beneath the surface the dose first rises rapidly with depth, reaches a maximum value at a depth zmax, and then decreases almost exponentially until it reaches an exit dose value at the patient’s exit point. The depth of dose maximum is proportional to the beam energy and typically amounts to 0 for superficial (50–100 kVp) and orthovoltage (100–300 kVp) beams; 0.5 cm for cobalt-60 gamma rays; 1.5 cm for 6-MV beams; 2.5 cm for 10-MV beams; and 4 cm for 22-MV beams. The relatively low surface dose for high-energy photon beams (referred to as the skin sparing effect) is of great importance in radiotherapy for treatment of deep-seated lesions without involvement of the skin. The tumor dose can be concentrated at large depths in the patient concurrently with delivering a low dose to patient’s skin that is highly sensitive to radiation and must be spared as much as possible when it is not involved in the disease. FIGURE B-10 Absorbed dose against depth in water for ionizing radiation beams of various types and energies. Parts (a) and (b) are for indirectly ionizing radiation: in (a) for photon beams in the range from 100 kVp to 22 MV and in (b) for neutron beams. Parts (c) and (d) are for directly ionizing radiation: in (c) for megavoltage electron beams in the range from 9 to 32 MeV and in (d) for heavy charged particle beams (187-MeV protons, 190-MeV deuterons, and 308-MeV carbon ions). SOURCE: With kind permission of Springer Science+Business Media.

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206 RADIATION SOURCE USE AND REPLACEMENT The dose region between the surface and the depth of dose maximum zmax is called the dose buildup region and represents the region in the patient in which the dose deposition rises with depth as a result of the range of secondary electrons released in tissue by photon interactions with the atoms of tissue. It is these secondary electrons released by photons that deposit energy in tissue (indirect ionization). The larger is the photon energy, the larger is the range of secondary electrons and, consequently, the larger is the depth of dose maximum. Dose Distributions for Neutron Beams in Water Neutron beams belong to the group of indirectly ionizing radiation, but rather than releasing electrons like photons do, they release protons or heavier nuclei which then deposit their energy in absorbing media through Coulomb interactions with the electrons and nuclei of the absorber. As shown in Figure B-10b, the dose deposition characteristics of neutrons in water are similar to those of photon beams. Neutron beams exhibit a relatively low surface dose, although the skin sparing effect is less pronounced than that for energetic photon beams. They also exhibit a dose maximum beneath the skin surface and an almost exponential decrease in dose beyond the depth of dose maximum. The dose buildup region depends on neutron beam energy; the larger is the energy, the larger is the depth of dose maximum. For comparison, we may state that a 14-MeV neutron beam has depth dose characteristics that are comparable to a cobalt-60 gamma-ray beam; a 65-MeV neutron beam is comparable to a 10-MV x-ray beam. Dose Distributions for Electron Beams in Water Electrons are directly ionizing radiation that deposits the energy in tissue through Coulomb interactions with orbital electrons and nuclei of the absorber atoms. Megavoltage electron beams represent an important treatment modality in modern radiotherapy, often providing a unique option for treatment of superficial tumors that are less than 5 cm deep. Electrons have been used in radiotherapy since the early 1950s, first produced by betatrons and then by linear accelerators. Modern high-energy linear accelerators typically provide, in addition to two megavoltage x-ray beams, several electron beams with energies from 4 to 25 MeV. As shown in Figure B-10c, the electron-beam dose distribution with depth in patient exhibits a relatively high surface dose and then builds up to a maximum dose at a certain depth, referred to as the electron-beam depth dose maximum zmax. Beyond zmax the dose drops off rapidly, and levels off at a small low-level dose component referred to as the bremsstrahlung tail. Several parameters are used to describe clinical electron beams, such as the most probable energy on the patient’s skin surface, the mean electron energy on the patient’s skin surface, or the depth at which the absorbed dose falls to 50 percent of the maximum dose. Unlike the case for photon beams, the depth of dose maximum for electron beams does not depend on beam energy; rather it is a function of machine design. On the other hand, the beam penetration into tissue clearly depends on beam energy; the higher is the electron beam energy, the more penetrating is the electron beam, as is evident from Figure B-10c. The bremsstrahlung component of the electron beam is the photon contamination that results from radiation losses experienced by the incident electrons as they penetrate the various machine components, air, and the patient. The higher is the energy of the incident electrons, the higher is the bremsstrahlung contamination of the electron beam.

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BACKGROUND ON THE ATOM, RADIOACTIVE DECAY, RADIATION, AND DOSE 207 Dose Distributions for Heavy Charged Particle Beams in Water Heavy charged particle beams fall into the category of directly ionizing radiation and deposit their energy in tissue through Coulomb interactions with orbital electrons of the absorber. As they penetrate into tissue, heavy charged particles lose energy but, in contrast to electrons, do not diverge appreciably from their direction of motion and therefore exhibit a distinct range in tissue. This range depends on the incident particle’s kinetic energy and mass. Just before the heavy charged particle expends all of its kinetic energy, its energy loss per unit distance traveled increases drastically and this results in a high dose deposition at that point in tissue. As shown in Figure B-10d, this high-dose region appears close to the particle’s range, is very narrow, and defines the maximum dose deposited in tissue. This peak dose is referred to as the Bragg peak, and it characterizes all heavy charged particle dose distributions. Because of their large mass compared to the electron mass, heavy charged particles lose their kinetic energy, only interacting with orbital electrons of the absorber. Since they do not lose any appreciable amount of energy through bremsstrahlung interactions with absorber nuclei, their depth dose curves do not exhibit a bremsstrahlung contamination tail.

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