Radiation Physics Notes PDF

EM Electric Charge Photon 1/137 Weak Weak Charge W+, W- and Z0 10^-6 Gravitational Energy Graviton 10^-39 Classification of Radiation Non-ionizing radiation cannot ionize matter bec...

EM Electric Charge Photon 1/137 Weak Weak Charge W+, W- and Z0 10^-6 Gravitational Energy Graviton 10^-39 Classification of Radiation Non-ionizing radiation cannot ionize matter because its energy is lower than the ionization energy of atoms or molecules of the absorber. (Ultraviolet, visible light infrared, microwaves and radio waves are all examples) Ionizing radiation can ionize matter either directly or indirectly Directly ionizing radiation: Comprises of charged particles that deposit energy in the absorber through a direct one-step process involving Coulomb interactions between the directly ionizing charged particle and orbital electrons of the atoms in the absorber Indirectly ionizing radiation: Comprises neutral particles that deposit energy in the absorber through a two-step process as follows: In the first step a charged particle is released in the absorber (photons release either electrons or electron/positron pairs, neutrons release protons or heavier ions). In the second step, the released charged particles deposit energy to the absorber through direct Coulomb interactions with orbital electrons of the atoms in the absorber. The LET (linear energy transfer) is defined as the mean amount of energy that a given ionizing radiation imparts to absorbing medium per unit path length. Used to specify the quality of the ionizing radiation beam. Ionizing radiation is divided into two categories: Electron therapy with megavoltage electron beams Electron beams are produced relatively inexpensively in clinical linear accelerators (linacs) Hadron therapy with hadron beams Notes 15  Proton beams, on the other hand, are produced in a cyclotron or synchrotron Electrons fall into the following categories based off how they were produced Electrons produced by photoelectric effect are referred to as photoelectrons. Electrons produced from Compton effect are referred to as Compton or recoil electrons. Electrons produced by pair production interactions in the field of the nucleus or in the field of an orbital electron are referred to as pair production electrons Electrons emitted from nuclei during β − decay are referred to as beta particles or beta rays Electrons produced by linacs, betatrons or microtrons for use in radiotherapy with kinetic energies typically in the range from 4 MeV to 30 MeV are referred to as megavoltage electrons. Electrons produced through Auger effect are referred to as Auger electrons, Coster–Kronig electrons, or super Coster–Kronig electrons. Electrons produced through internal conversion are referred to as internal conversion electrons. Electrons produced by charged particle collisions are referred to as delta (δ) rays. Electrons released from metallic surface in thermionic emission are referred to as thermions. There are three ways for generating positrons: Positron emission in beta decay Nuclear pair production and triplet production Heavy Charged Particles: Notes 16  Just before the heavy charged particle has expended all of its kinetic energy, its energy loss per unit distance traveled increases drastically and this results in a high dose deposition at that depth in the absorber. This high dose region appears close to the particle’s range in the absorber and is referred to as the Bragg peak. The depth of the Bragg peak in tissue depends on the mass and incident energy of the charged particle Indirectly ionizing photon radiation falls into 5 categories: Gamma rays: photons resulting from nuclear shell transitions. Annihilation quanta: photons resulting from positron–electron annihilation Characteristic (fluorescence) x-rays: photons resulting from electron transitions between atomic shells Bremsstrahlung x-rays: photons resulting from Coulomb interaction between energetic electrons and positrons with atomic nuclei of absorber Synchrotron radiation (also known as magnetic bremsstrahlung and cyclotron radiation): photons resulting from charged particles moving through a magnetic field Notes 17  Radiations Quantities and Units Exposure X: is related to the ability of photons to ionize air. Its unit roentgen (R) is defined as charge of 2.58×10^−4 C of either sign produced per kilogram of air. Kerma K: (acronym for kinetic energy released in matter) is defined for indirectly ionizing radiations as energy transferred to charged particles per unit mass of the absorber. Dose D: is defined as energy absorbed per unit mass of absorbing medium. Its SI unit gray (Gy) is defined as 1 J of energy absorbed per kilogram of absorbing medium. Equivalent dose H is defined as the dose multiplied by a radiation- weighting factor. The SI unit of equivalent dose is sievert (Sv). Activity A of a radioactive substance is defined as the number of nuclear decays per time. Its SI unit is becquerel (Bq) corresponding to one decay per second. Basic Definitions for Atomic Structure Atomic number Z: number of protons and number of electrons in an atom. Atomic mass number A: number of nucleons in an atom, i.e., number of protons Z plus number of neutrons N in an atom; i.e., A = Z + N. Atomic mass M: expressed in unified atomic mass units u, where 1 u is equal to one twelfth of the mass of the carbon-12 atom Number of atoms Na per mass of an element is given as Na NA = ​ ​ ​ ​ m A Number of electrons per volume of an element is Z ∗ Na ρ ∗ Z ∗ Na ρ ∗ Z ∗ NA = = ​ ​ ​ ​ ​ ​ V m A Number of electrons per mass of an element is Z N Z N Notes 18  Z ∗ Na Z ∗ Na = ​ ​ ​ ​ m A The term nuclide refers to all atomic forms of all elements. It can be subdivided as follows: Isotopes are atoms with identical Z but differing A Isotopic groups have a common atomic number Z Isobars have a common atomic mass number A Isotones have a common number of neutrons Isomers are nuclear species that have common atomic number Z and atomic mass number A The binding energy is given by the following equation EB = Δmc2 = Zmp c2 + (A − Z)mn c2 − Mc2 ​ ​ ​ M is the nuclear mass in atomic mass units u The larger is the binding energy per nucleon (EB /A) of an atom, the larger is the stability of the atom. Thus the most stable nuclei in nature are the ones with A ≈ 60 Fusion of two nuclei of very small mass will create amore massive nucleus and release a certain amount of energy Fission of elements of large mass will create two lower mass and more stable nuclei and lose some mass in the form of kinetic energy Radioactive decay is a process by which an unstable parent nucleus transforms spontaneously into one or several daughter nuclei that are more stable than the parent nucleus by having larger binding energies per nucleon than the parent nucleus Activity equation: SI unit is the becquerel 1 Bq = 1/s A(t) = λN(t) Radioactive Decay Processes Notes 19  Alpha decay: releases alpha particles Beta decay β − decay releases electron, proton, and antineutrino β + decay releases positron, neutron, and neutrino Electron capture releases a neutron and a neutrino Gamma decay γ decay releases γ rays Internal conversion releases atomic orbital electrons Spontaneous fission releases neutrons Proton emission decay releases protons Neutron emission decay releases neutrons During these processes the following quantities must be conserved Total energy, momentum, charge, atomic number, and atomic mass number Decay energy given as follows Q = [M(P ) − [M(D) + m]]c2 For radioactive decay to be energetically possible the Q value must be greater than zero If a nucleus has a N /Z ratio too high for nuclear stability, it has an excess number of neutrons and is called neutron-rich. It decays through conversion of a neutron into a proton and emits an electron and anti- neutrino. This process is referred to as β − decay. If the N /Z ratio is extremely high, a direct emission of a neutron is possible. If a nucleus has a N /Z ratio that is too low for nuclear stability, it has an excess number of protons and is called proton-rich. It decays through conversion of a proton into a neutron and emits a positron and a neutrino (β + decay). Alternatively, the nucleus may capture an orbital electron, transform a proton into a neutron and emit a neutrino (electron capture). Notes 20  When an α-particle is emitted by the radioactive parent (Z , A) nucleus, the atomic number Z of the parent decreases by 2 and it sheds two orbital electrons from its outermost shell to become a neutral daughter atom (Z − 2, A − 4). The term β decay encompasses modes of radioactive decay in which the atomic number Z of the parent nuclide changes by (±1), while the atomic mass number A remains constant Beta minus (β − ) decay with the following characteristics: Z → Z +1; A = const Beta plus (β + ) decay with the following characteristics: Z → Z -1; A = const Electron capture with the following characteristics: Z → Z − 1; A = const. Typical ratios EC(K shell)/EC(L shell) are of the order of 10:1. Week 2 Photon Interactions with Absorbers Photons experience various interactions grouped into two categories The interactions with nuclei may be direct photon-nucleus interactions (photo-disintegration) or between the photon and the electrostatic field of the nucleus (pair production) The photon-orbital electron interactions are characterized as interactions between the photon and either a loosely bound electron (Thomson scattering, Compton effect, triplet production) or a tightly bound electron (photoelectric effect, Rayleigh scattering) A loosely bound electron is an electron whose binding energy is small in comparison to the photon energy hv (EB 1 the absorber is softening the photon beam Mass attenuation coefficient μm is defined as the linear attenuation coefficient μ divided by the mass per unit volume of the absorber (absorber mass density) ρ Atomic attenuation coefficient a μ is defined as linear attenuation coefficient divided by the number of atoms per volume of the absorber. It can also be defined as the mass attenuation coefficient divided by the number of atoms per mass of the absorber Electronic attenuation coefficient e μ is defined as the linear attenuation coefficient divided by the number of electrons per volume of the absorber. It can also be defined as the mass attenuation coefficient divided by the number of electrons per mass of the absorber. Notes 23  In radiation dosimetry two energy-related coefficients are in use Linear energy transfer coefficient μ_tr: Mean energy transferred from photons to charged particles in a photon–atom interaction with SI unit m^−1 Linear energy absorption coefficient μ_ab: Mean energy absorbed in the medium with units m^−1 Mean energy transferred from photon to secondary charged particles in the absorber, E_tr can be expressed as a sum of two components: E ab defined above and E_rad Mean radiation fraction g ​ Erad g= ​ ​ ​ ​ Etr ​ ​ Build-up factor that accounts for the secondary photons that are scattered from the absorber into the detector factor is defined by IB (x) =B ​ IN (x) ​ ​ Notes 24  Mean effective attenuation coefficient μ_eff lnB μeff = μ − ​ ​ ​ x For medical physics and radiation dosimetry the photon interactions are categorized as follows Interactions of major importance: Photoelectric effect Compton scattering by “free” electron. Pair production in the field of nucleus (including triplet production) Interactions of moderate importance: Rayleigh scattering Notes 25  Interactions of minor importance: Photonuclear reaction (also known as photonuclear effect). Thompson scattering by “free” electron. Negligible interactions: Thomson scattering by the nucleus. Compton scattering by the nucleus. Meson production Delbrück scattering (elastic scattering of photon by nuclear Coulomb field-virtual nuclear pair production) Photoelectric Effect An interaction between a photon and a tightly bound orbital electron of an absorber atom is called photoelectric effect The photoelectric effect occurs between a photon and a “tightly bound” electron EB ≤ hv Notes 26  The extra energy and momentum carried by the photon are transferred to the absorbing atom; however, because of the relatively large nuclear mass, the atomic recoil energy is exceedingly small and may be neglected. When the photon energy hν exceeds the K-shell binding energy of the absorber, about 80% of all photoelectric absorptions occur with the K- shell electrons of the absorber and the remaining 20% occur with less tightly bound higher shell electrons The energy uptake by the photoelectron may be insufficient to bring about its ejection from the atom in a process referred to as atomic ionization but may be sufficient to raise the photoelectron to a higher orbit in a process referred to as atomic excitation The vacancy that results from the emission of the photoelectron from a given shell will be filled by a higher shell electron and the transition energy will be emitted either as a characteristic (fluorescence) photon or as an Auger electron, the probability for each governed by the fluorescence yield ω At low hν of the order of 10 keV photoelectrons tend to be emitted at angles close to 90 degrees to the incident photon direction Atomic Cross section for photoelectric effect The atomic cross section (attenuation coefficient) for the photoelectric effect as a function of the incident photon energy hν exhibits a characteristic saw-tooth structure in which the sharp discontinuities, referred to as absorption edges, arise whenever the photon energy coincides with the binding energy of a particular electron shell The energy dependence is assumed to go as (1/(hν)^3 at low photon energies hν and gradually transforms into 1/(hν) at high hν. The atomic number Z dependence of τ , is Z^n where n ranges from 4 to ∼5 The vacancy that is left behind by the photoelectron is subsequently filled with an electron from a higher-level atomic shell, the resulting vacancy in the higher level shell is filled by another even higher shell electron, and so Notes 27  on until the vacancy migrates (“cascades”) to the outer shell of the atom and is filled by a free electron from the environment to neutralize the ion. The probability P_j for the photoelectric effect, if it occurs, to occur in the j subshell of an absorber atom is determined with the help of the photoelectric mass attenuation coefficient τ /ρ Fluorescence Yield Patterns ω_K ranges from ω_K = 0 for absorbers with atomic number below Z = 10 saturates at ω_K = 0.97 for absorbers with very high atomic number Z ω_L ranges from ω_L = 0 for absorbers with atomic number below Z = 30 and attains a value of ω_L ≈ 0.5 for absorbers with very high atomic number Z ω_M ranges from ω_M = 0 for Z < 60 to ω_M = 0.05 for very high atomic number Z absorbers In general, the macroscopic attenuation coefficient represents a sum of attenuation coefficients for all individual interactions that a photon of energy hν may have with atoms of the absorber. Interactions of interest in medical physics and contributing to the attenuation coefficient are the Notes 28  photoelectric effect, Rayleigh scattering, Compton scattering, and pair production including triplet production. μ = ∑ μi = τ + σR + σc + κ ​ ​ ​ The following conclusions can be made regarding the attenuation coefficients For all absorber materials the photoelectric effect is the predominant mode of photon interaction with the absorber at low photon energies At intermediate photon energies and low atomic numbers Z the Compton effect mass coefficient predominates and makes the largest contribution to the total mass attenuation coefficient The width of the region of Compton scattering predominance depends on the atomic number Z of the absorber; the lower is Z, the broader is the Compton scattering predominance region. For water and tissue this region ranges from∼20 keV up to ∼20 MeV, for most of radiotherapy the most important interaction of photon beams with tissues is the Compton scattering. The pair production dominates at photon energies hν above 10 MeV and at high atomic numbers Z of the absorber. In all energy regions the Rayleigh scattering mass coefficient plays only a secondary role in comparison with the other three coefficients. Week 3 Thomson Scattering The scattering of low energy photons hν