PHYS 486 Radiation Physics Chapter 2 PDF

PHYS 486 Radiation Physics Chapter 2: Interaction of Radiation with Matter Chapter2: Interaction of Radiation with Matter 2.1 Introduction Radiation includes charged particles like alpha and beta particles, accelerator-generated beams, as well as uncharged particles such as...

PHYS 486 Radiation Physics Chapter 2: Interaction of Radiation with Matter Chapter2: Interaction of Radiation with Matter 2.1 Introduction Radiation includes charged particles like alpha and beta particles, accelerator-generated beams, as well as uncharged particles such as X-rays, gamma rays, and neutrons. alpha 𝛽+ 𝛽− proton 𝛾 𝑥 − 𝑟𝑎𝑦 neutron 2 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.1 Introduction Example 1: Particle Symbol Charge (z) Mass Beta minus 𝛽− -1 0.511 MeV Beta plus 𝛽+ +1 0.511 MeV proton 𝑝 +1 938 MeV Alpha 𝛼 +2 3737 MeV Carbon 6𝐶 +6 ~ 11256 MeV 3 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.1 Introduction The incident radiation interacts with the with the electrons and the nuclei of the absorbing materials. Absorbing material 4 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.1 Introduction How far will the radiation penetrate before it lose all its energy? Radiation Absorbing material 5 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.1 Introduction Penetrating of radiation depends on Radiation type Radiation energy Absorbing materials e.g. e.g. e.g. Alpha keV Atomic number Beta MeV (𝑧) Gamma GeV 6 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles A charged particle interacts with nearly every atom it encounters. charged particles Absorbing material 7 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles For heavy charged particles, the path is typically a straight line. Example 2: Alpha Beta 8 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Case 1: Collisional Coulomb energy loss: When a charged particle interacts via the Coulomb force with an orbital electron in an absorbing material, energy is transferred that can either promote the electron into a higher orbital shell (excitation) or liberate it from the atom (ionization). It should be noted that the incident charged particle only has to approach close to the electron in the absorber material, it does not have to be a direct hit. Since the Coulomb force has infinite range, the incident charged particle can also interact simultaneously with many orbital electrons in the material. This enables true energy transfer to occur. 9 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Excitation of the absorbing atom: In excitation, only a relatively small amount of energy is transferred and so the charged particle does not deviate significantly from its original trajectory. When the electron is promoted into a higher shell, it leaves the atom in an unstable configuration. The electron will therefore subsequently return to its stable position, resulting in the emission of a characteristic x-ray. 1st 2nd 10 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Ionization of the absorbing atom: In ionization interaction, energy is transferred from the incident charged particle to an atomic electron and the atom becomes a positively charged ion. The electron will be emitted with a kinetic energy equal to the difference in transferred energy and the binding energy. The ejected electron may have sufficient energy to induce secondary ionization and excitation, if so, it is named a delta-ray. These secondary ionizations must be included in any calculation of the radiation dose received by a patient and therefore awareness of them is particularly important in radiotherapy treatment planning and verification. 11 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Case 2: Radiative energy loss: The collision of heavy charged particles with the nucleus of the absorbing material primarily results in elastic Coulomb scattering. This is generally true, except for energetic ions that can overcome the repulsive Coulomb barrier and approach the nuclear radius. 12 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Bohr noticed that by elastic Coulomb scattering of light ions from nuclei, the nucleus will recoil but relatively little energy is transferred as a result of the target’s large mass. 13 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles As high energy charged particles pass close to the electric field (the Coulomb field) of the nucleus, they can decelerate and suffer a significant deflection, resulting in the emission of cause an emission a continuous x-rays spectrum called bremsstrahlung radiation. This is known as radiative energy loss. 14 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles The bulk of energy loss is due to ion collisions with atomic electrons. Only for the heaviest projectiles in the lightest targets does energy loss by nuclear collisions exceed that by electronic collisions. 15 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Stopping power and charged particle range: The interactions of charged particles with matter are generally expressed in terms of: 𝑑𝐸 1. The energy loss per unit path length (also known as linear stopping power) 𝑆 𝐸 = − 𝑑𝑥 𝑑𝐸 The value of − along a particle track is also called its specific energy loss or, more casually, its "rate" 𝑑𝑥 of energy loss. 2. The total range of the particle. 16 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles The basic expression for the energy loss rate of an ion passing through matter is known as the Bethe–Bloch equation: 17 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles The Bethe–Bloch equation: 18 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Example 3: 19 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Example 4: p 3 MeV Fe p 2 MeV p 1 MeV 26Fe 20 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles A feature of ion stopping power noticed early in the twentieth century is that their stopping power is the greatest, and reaches a local peak, near the end of their range. The peak is called the Bragg peak. The curved is called the Bragg curve. Most of the ionization loss occurs near the end of the path where the speed is smallest, and the curve has a pronounced peak (the Bragg peak) close to the end point before falling rapidly to zero at the end of the particle’s path length. 21 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Example 5: A graph for alpha particles in liquid water shows the stopping power vs. residual range is called the Bragg curve. It is valuable because it is independent of the ion starting energy and displays the maximum in stopping power. 22 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Example 6: The graph bellow shows the Bragg curve for an 8 MeV alpha particle in A-150 tissue-equivalent plastic, a mock up of human tissue. 23 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Example 7: 24 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles When α and β particles interact in materials, their relative mass and velocity result in quite different particle paths. 25 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles Charged particles are also subject to range straggling, defined as the fluctuation in path length for individual particles of the same initial energy. 2 MeV 2 MeV 2 MeV Charged Absorber particle 26 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.1 Alpha particles Alpha particles lose a large fraction of their energy by causing ionization along their paths. The extent of the ionization mused by an 𝛼-particle depends on: 1- The number of molecules it hits along its path. 2- The way in which it hits them. Alpha Absorbing material 27 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.1 Alpha particles Alpha particles travel in a straight line. Alpha Absorbing material 28 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.1 Alpha particles Example 1: 13Al 29Cu 82Pb 29 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.1 Alpha particles To examine 𝜶 transmission intensity and its depth: I(counts I detector detector x (cm) /min) I0 I I0 0 I0 = 30 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.1 Alpha particles 𝐼 The transmission intensity for beams of 𝛼 particles of a given initial energy passing through soft tissue. 𝐼0 It can be seen that the distributions do not follow the exponential attenuation. Since α particles of a given energy will all follow a similar path, the transmission intensity is approximately 1 whilst all the particles have energy remaining to travel through the tissue. There will then be a sharp reduction in intensity to 0, corresponding to when all the α particles have stopped in the tissue. 31 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.1 Alpha particles 𝑅𝑚 In this example, the mean range, 𝑅𝑚 , of the α particles in soft tissue is close to 60 μm, where 𝑅𝑚 is the depth at which the transmission intensity is reduced to 0.5. There is only a small amount of range straggling, in other words nearly all of these α particles stop at the same depth. 32 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.1 Alpha particles The ionization extrapolated range 𝑹𝒆 is defined as the value of the abscissa at which the tangent to the curve at its inflection point crosses the horizontal axis. The mean range 𝑹𝒎 is the thickness at which roughly half the particles are absorbed (lost energy) in the material. The practical range is the thickness at which all the particles are absorbed (lost energy) in the material. 33 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles Beta particles 𝛽 are much more penetrating than 𝛼-particles. A Range in Air Particle Kinetic Energy Produces Pairs (penetrating) Alpha 3 MeV 2.8 cm 4000 ion pairs/mm beta 3 MeV 1000 cm 4 ion pairs/mm 34 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles Example 1: 35 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles Beta-particles 𝛽 are also scattered much more easily than are 𝛼-particles, so that their paths are usually not straight. Alpha Beta 36 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles Example 2: A typical trajectory for an electron and alpha particle of 10 MeV in silicon. 37 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles Three paths β particles with the same initial energy are shown. Since the particles undertake different and haphazard paths through the material, the net penetration depth, or range, of these particles will be different. This variation in penetration depth is known as range straggling and has important consequences in dose deposition in radionuclide therapy. 38 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles To examine 𝛽 transmission intensity and its depth: I(counts I detector detector x (cm) /min) I0 I I0 0 I0 = 39 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles 𝐼 The transmission intensity for beams of β particles of a given initial energy passing through soft tissue. 𝐼0 It can be seen that the distributions do not follow the exponential attenuation. The shape of the distribution reflects the haphazard nature of β particle paths. 40 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles 𝑅𝑚 The difference in the mean 𝑅𝑚 and maximum penetration depth for β particles is much larger than for α particles so it becomes necessary to define a new term, the extrapolated range, 𝑅𝑒. 41 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles To examine 𝛽 absorption: detector detector x (𝑐𝑚) I(counts/min) I I0 0 I0 = 42 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles The attenuation of the 𝛽 particles can be described I by a simple exponential law: I(𝑥) = 𝐼0 𝑒 −𝜇𝑥 I0 2 Where: 𝐼0 is the activity without the absorber 𝐼(𝑥) is the activity observed through a thickness 𝑥 𝜇 is the linear absorption coefficient 43 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles The linear attenuation coefficient 𝜇 is obtained by: I 𝑥 ln I 0 μ=− 𝑥 The used thickness 𝑥 of a material expressed in m or cm The reciprocal of μ is called the mean free path 𝜆 or some times the relaxation length: 1 𝜆=𝜇 The mean free path 𝜆 is defined as the average distance traveled in the absorber before an interaction takes place. 44 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles I I0 2 The thickness 𝑥1/2 needed to reduce the intensity of emerging radiation to half of its original value is: 𝑥1/2 = ln(2) /𝜇 45 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles Or: the actual thickness (cm) is multiplied by the density (g/𝑐𝑚3 ), and the resulting quantity, which may be called the superficial density (g/𝑐𝑚2 ), is used as a measure of the thickness. detector detector 𝑥𝑚 (mg/𝑐𝑚2 ) I(counts/min) I I0 0 I0 = 46 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles The mass attenuation coefficient μm (It is the coefficient that is tabulated in most tables ) is obtained by: μ μm = ρ Where ρ is the density of the absorber. The mass attenuation coefficient [cm2. g −1 ] When calculating the attenuation in a material then the thickness 𝑥m should be expressed in kg/m2 or g/cm2. The observed activity through a thickness 𝑥 is given by: I(𝑥) = I0 e−μm 𝑥m 47 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles The activity does not decrease to zero as the absorber becomes very 𝐼0 thick but becomes practically constant at a value which represents the so-called "background”. There is always some radiation present which contributes to the counting rate even though it does not represent beta- particles from the source. I(𝑥) = I0 e−μm𝑥m The range 𝑅𝛽 is the distance traversed by most energetic particles emitted. 48 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles For the majority of beta spectra, the curve happens to have a near-exponential shape and is therefore nearly linear on the semilog plot. Example 3: 49 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.2 Interaction of charged particles 2.2.2 Beta particles The ability of an element to stop ,beta particles depends, therefore, on the ratio of the atomic number to the mass 𝑧 number, i.e., on 𝐴. Although this ratio decreases from the light to the heavy elements, the effect of this variation on the thickness needed to stop beta particles is not large. Absorber material 𝑧 Beta Range of 1 MeV Absorber 𝐴 (𝐠/𝒄𝒎𝟐 ) 13 Aluminum = 0.48 400 27 79 Gold = 0.4 500 197 50 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The gamma-ray has much greater penetrating power and has no definite. 51 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The gamma-ray has much greater penetrating power and has no definite. Radiation 𝐄𝐥𝐞𝐜𝐭𝐫𝐢𝐜𝐚𝐥 𝐂𝐡𝐚𝐫𝐠𝐞 Velocity Range in air Range is tissue Alpha +2 Relatively slow 6 mm 0.008 mm “Slightly” less Beta −1 than speed of 3m 4 mm light 3 × 108 𝑚/𝑠 in Gamma 0 > 500 𝑚 > 65 𝑐𝑚 vacuum 52 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray When gamma-rays pass through an absorber; three processes are mainly can be accrued: 1. Photoelectric affect 2. Compton scattering 3. Production of electron-positron pairs 𝛾 Absorbing material 53 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray When gamma-rays pass through an absorber; three processes are mainly can be accrued: 1. Photoelectric affect by the interaction between gamma-rays and the electrons in the atoms. 𝐄𝛄 ≥ 𝟐𝐦𝐞 𝐜 𝟐 2. Compton scattering by the interaction between 𝐄𝛄 < 𝟎. 𝟓 𝐌𝐞𝐕 𝐄𝛄 ≥ 𝟏. 𝟎𝟐 𝐌𝐞𝐕 gamma-rays and the electrons in the atoms. 3. Production of electron-positron pairs as a result of the 𝟎. 𝟏 < 𝐄𝛄 < 𝟓 𝐌𝐞𝐕 interaction between gamma-rays and the electric fields of atomic nuclei. 54 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The relative probability of photoelectric absorption and Compton scattering depends on the atomic number, Z, of the absorbing material and 𝐸𝛾. 55 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 1: absorber absorber The probability of a specific interaction is referred to as the cross section, and its unit is called the barn: 1 barn = 10-24 cm2 56 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray 1. Photoelectric affect by the interaction between gamma-rays and the electrons in the atoms (Dominates at low energy Eγ < 0.5 MeV). In the photoelectric absorption process, a photon undergoes an interaction with an absorber atom in which the photon completely disappears. In its place, an energetic photoelectron is ejected by the atom. Photon’s energy ℎ𝑐 𝐸𝑒 − = 𝐸𝛾 − Φ 𝐸𝛾 = ℎ𝜈 = 𝜆 𝐸𝑒 − = ℎ𝑣 − Φ Φ 57 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Work function (Ionization potential) 58 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray In the photoelectric absorption process, an energetic photoelectron is ejected by the atom from one of its bound shells. For gamma rays of sufficient energy, the most probable origin of the photoelectron is the most tightly bound or K shell of the atom. The photoelectron appears with an energy given by 𝐸𝑒 − = ℎ𝑣 − 𝐸𝑏 𝑒− 𝑒− 𝑒− 𝑒− 𝐸𝑒 − = 𝐸𝛾 − 𝐸𝑏 𝐄𝛄 < 𝟎. 𝟓 𝐌𝐞𝐕 𝑒− 𝑒− 𝐸𝑒 − = ℎ𝑣 − 𝐸𝑏 𝑒− nucleus 𝑒− 𝐸𝑏 is The binding energy of the − 𝑒− 𝑒 𝑒− atomic electron in its original shell 𝑒− 𝑒− 𝑒− 59 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray 𝐸𝑏 60 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray In addition to the photoelectron, the interaction also creates an ionized absorber atom with a vacancy in one of its bound shells. This vacancy is quickly filled through capture of a free electron from the medium and/or rearrangement of electrons from other shells of the atom. Therefore, one or more characteristic x- ray photons may also be generated. 61 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray 2. Compton scattering by the interaction between gamma-rays and the electrons in the atoms, Important between 0.1 and 5 MeV (very important for radiobiology and radiotherapy). The photon is scattered by an electron. The photon energy is divided between the scattered photon and the emitted electron: Eγ = E𝑒 − + E𝛾′ 62 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Eγ E𝑒 − = Eγ - E𝛾′ 63 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The energy of the scattered photon is given by: Eγ E 𝛾′ = Eγ 1+ (1 − cos 𝜃) 𝑚𝑒 𝑐 2 And it can be written as: ℎ𝑣 ℎ𝑣 ′ = Eγ 1+ (1 − cos 𝜃) 𝑚𝑒 𝑐 2 64 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray 𝟎. 𝟏 < 𝐄𝛄 < 𝟓 𝐌𝐞𝐕 Gamma-ray Scattered Gamma-ray E𝑒 − = Eγ - E𝛾′ E𝛾′ < Eγ 65 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The energy of the emitted electron is given by: E𝑒 − = Eγ − E𝛾 ′ Eγ E 𝑒− = Eγ − Eγ 1+ (1 − cos 𝜃) 𝑚𝑒 𝑐 2 Eγ 1+ 1 − cos 𝜃 Eγ − Eγ 𝑚𝑒 𝑐 2 E𝑒 − = Eγ 1+ (1 − cos 𝜃) 𝑚𝑒 𝑐 2 Eγ 2 1−cos 𝜃 𝑚 𝑒 𝑐2 E𝑒 − = Eγ 1+ (1−cos 𝜃) 𝑚 𝑒 𝑐2 66 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The energy of the emitted electron is given by: Eγ 2 1−cos 𝜃 𝑚𝑒 𝑐2 E𝑒 − = Eγ 1+ (1−cos 𝜃) 𝑚𝑒 𝑐2 And it can be written as: ℎ𝑣 2 1 − 𝑐𝑜𝑠 𝜃 𝑚𝑒 𝑐 2 𝐸𝑒 − = ℎ𝑣 1+ (1 − 𝑐𝑜𝑠 𝜃) 𝑚𝑒 𝑐 2 67 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The probability of Compton scattering increases linearly as the number of target electrons, Z, increases. 68 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The scattering angle 𝜃 can be any value between 0° and 180°, which results in a distribution of energies E𝛾′ and E𝑒 − ℎ𝑣 Emitted Photon Energy: ℎ𝑣 ′ = Eγ 1+ (1 − cos 𝜃) 𝑚𝑒 𝑐 2 Electron Kinetic Energy: E𝑒 − = h𝑣 −ℎ𝑣 ′ 0 𝑚𝑒 𝑐 2 ℎ𝑣ൗ 1 + ℎ𝑣 𝑚𝑒 𝑐 2 ℎ𝑣ൗ 1 + 2ℎ𝑣 69 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 2: The figure presents the energies of the scattered photon for a 662 keV γ- ray as a function of scattering angle up to 120°. The most energy that can be imparted to the electron is when back- scattering (180°) occurs. Substituting the incident energy (662 keV) into Eγ equation E𝛾′ = Eγ shows that the minimum energy the 1+ (1−cos 𝜃) 𝑚 𝑒 𝑐2 scattered photon can have is Eγ′ = 184 keV and hence, the maximum electron energy is Ee− = 662 keV − 184 keV = 478 keV. 70 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 3: 131 Calculate the energy transferred to the recoil electron when a 364 keV γ-ray from I interacts by Compton scattering in tissue, if the scattering angle is 45°. 71 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 3: 131 Calculate the energy transferred to the recoil electron when a 364 keV γ-ray from I interacts by Compton scattering in tissue, if the scattering angle is 45°. Eγ 364 E e− = Eγ − = 364 − = 63 keV Eγ 364 1+ (1 − cos θ) 1+ (1 − cos 45) me c 2 511 or Eγ 2 3642 1−cos θ 1−cos 45 me c2 511 Ee− = Eγ = 364 = 63 keV 1+ (1−cos θ) 1+511(1−cos 45) me c2 72 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Key equation: ℎ ∆𝜆 = 𝜆′ − 𝜆 = 1 − cos 𝜃 𝑚𝑒 𝑐 𝜆 𝜆 is initial wavelength 𝜆′ is final wavelength 𝜆′ ℎ is Planck’s const. 𝑚𝑒 is the rest mass energy of e- 𝑐 is the speed of light 𝜃 is the scattering angle 73 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray 3. Production of electron-positron pairs as a result of the interaction between gamma-rays and the electric fields of atomic nuclei: 𝑒− Gamma-ray “photon” 𝐄𝛄 ≥ 𝟐𝐦𝐞 𝐜 𝟐 = 𝟏. 𝟎𝟐 𝐌𝐞𝐕 𝑒− E𝑒 + = 0.511 𝑀𝑒𝑉 𝑒− nucleus 𝑒− 𝑒− E𝑒 − = 0.511 𝑀𝑒𝑉 𝑒− 74 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The kinetic energy of the pair: 𝑇 = ℎ𝜈 − 2𝑚𝑜 𝑐 2 Thus: 𝑇 ℎ𝜈 − 2𝑚𝑜 𝑐 2 𝑇+ = 𝑇− = = 2 2 Where: 𝑇+ , 𝑇− are the kinetic energies of the positron and the electron ℎ𝜈 is the energy of the photon 𝑚𝑜 𝑐 2 is the rest energy of an electron. 75 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray They can be written as: 𝑇 = Eγ − 2𝑚𝑜 𝑐 2 𝑇 Eγ − 2𝑚𝑜 𝑐 2 𝑇+ = 𝑇− = = 2 2 Where: 𝑇+ , 𝑇− are the kinetic energies of the positron and the electron Eγ is the energy of the photon 𝑚𝑜 𝑐 2 is the rest energy of an electron. 76 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray To examine gamma ray absorption: detector detector x (𝑐𝑚) I(counts/min) I I0 0 I0 = 77 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The measured transmitted intensity, I, through a layer of material of thickness 𝑥 can be modelled using an inverse exponential law: I = I0 e−μ𝑥 Where: μ is known as the linear attenuation coefficient [cm-1]. 𝑥 is thickness in the unit of cm 78 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The linear attenuation coefficient 𝜇 is obtained by: I 𝑥 ln I 0 μ=− 𝑥 The used thickness 𝑥 of a material expressed in m or cm The reciprocal of μ is called the mean free path 𝜆 or some times the relaxation length: 1 𝜆=𝜇 The mean free path 𝜆 is defined as the average distance traveled in the absorber before an interaction takes place. 79 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 4: Mean free path λ of photons of energy 𝐸𝛾 in different representative materials: water (body), CsI (detector), and Pb (collimator). 80 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The thickness 𝑥1/2 required to reduce emergent radiation intensity to a half of original intensity: 𝑥1/2 = ln(2) /𝜇 I0 I= 2 81 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 5: Transmission intensity of a beam of 141 keV (red) and 511 keV (blue) γ rays travelling through soft tissue, as a function of depth 82 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The total absorption coefficient 𝜇(𝐸) is the sum of the absorption coefficients for the three different processes: 1. Coefficient of Photoelectric affect 𝜏(𝐸) 2. Coefficient of Compton scattering 𝜎 𝐸 3. Coefficient of Pair Production 𝜅(𝐸) 𝜇(𝐸) 𝜎(𝐸) 𝜇(𝐸) = 𝜏(𝐸) + 𝜎(𝐸) + 𝜅(𝐸) 𝜅(𝐸) 𝜏(𝐸) 83 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 6: Coefficient of Photoelectric affect 𝜏(𝐸) 84 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Or: the actual thickness (cm) is multiplied by the density (g/𝑐𝑚3 ), and the resulting quantity, which may be called the superficial density (g/𝑐𝑚2 ), is used as a measure of the thickness. detector detector 𝑥𝑚 (mg/𝑐𝑚2 ) I(counts/min) I I0 0 I0 = 85 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray The mass attenuation coefficient μm (It is the coefficient that is tabulated in most tables ) is obtained by: μ μm = ρ Where ρ is the density of the absorber. The mass attenuation coefficient [cm2. g −1 ] When calculating the attenuation in a material then the thickness 𝑥m should be expressed in kg/m2 or g/cm2. The observed activity through a thickness 𝑥 is given by: I(𝑥) = I0 e−μm 𝑥m 86 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 7: It can be observed that the coefficient increases significantly with the atomic number (Z) of the material and decreases as the energy of the photon 𝐸𝛾 increases. Absorber 100 keV 200 keV 500 keV Air 0.000195 0.000159 0.000112 Water 0.167 0.136 0.097 Carbon 0.335 0.274 0.196 Aluminium 0.435 0.324 0.227 Iron 2.72 1.09 0.655 Copper 3.8 1.309 0.73 Lead 59.7 10.15 1.64 87 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 8: The 141 keV γ-ray from a sample of 99mTc are collimated intro a beam. Calculate the thickness of lead shielding required to reduce the intensity of the beam by 99%. The linear attenuation coefficient for 141 keV γ-ray in lead is 2.71 cm−1. 88 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.1 Gamma ray Example 8: The 141 keV γ-ray from a sample of 99mTc are collimated intro a beam. Calculate the thickness of lead shielding required to reduce the intensity of the beam by 99%. The linear attenuation coefficient for 141 keV γ-ray in lead is 2.71 cm−1. I = I0 e−μx I = e−μx I0 I ln = −μx I0 I I 1 − 0.99 ln ln 0 ln 0.01 I0 I0 x=− =− =− = 1.7 cm μ μ 2.71 89 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Neutrons have recently been used to serve many aspects of fields, such as industrial applications, fundamental research, and medical treatment and diagnosis. neutrons Neutrons are neutral particles (charge = 0). 90 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Thus, neutrons would not be affected by an electric or magnetic field and their interaction with the nuclei or electrons of the medium would not be Coulomb interactions. They readily penetrate the atomic electron cloud and reach the nucleus. neutrons 91 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Free neutrons have a mean life 𝜏 and half-life 𝑡1/2 : 𝜏 = 885.7 𝑠𝑒𝑐 ≈ 15 𝑚𝑖𝑛 𝑡1/2 = 613.9 𝑠𝑒𝑐 ≈ 10 𝑚𝑖𝑛 They can pass through thick shielding walls that are made of high-atomic number materials. 92 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Neutrons Source: There are no naturally occurring radioisotopes which emit neutrons. (α, n) source Photonuclear sources (𝛾, n) Reactions from accelerated charged particles (Fusion sources) Spontaneous Fission. 93 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons (α, n) source: An alpha emitting nucleus is packaged in a homogeneous mixture with a material which has a low reaction threshold 241 9 for an (α, n) reaction. A very commonly found combination is a so-called AmBe source where Am and Be are packaged together. The choice of 241Am reflects its long half-life of 432 years which also makes it the radioisotope of choice in other applications such as smoke alarms. 4 2He + 49Be → 12 6C + 10n The neutrons produced have a very high energy and are called fast neutrons. 94 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons The actinide-beryllium alloy is usually sealed within two individually welded stainless steel cylinders in the arrangement shown in following figure. Some expansion space must be allowed within the inner cylinder to accommodate the slow evolution of helium gas formed when the alpha particles are stopped and neutralized. 95 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Example 1: 9Be(,n)12C 10B(,n)13N n 11B(,n)14N (,n) 96 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons 97 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons 98 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Photonuclear sources (𝛾, n) : A photonuclear source induces fast neutron emission through a (γ, n) reaction. This is typically achieved by wrapping material such as 9Be around a highly-active gamma source. Example: 99 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons 100 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons 101 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Reactions from Accelerated Charged Particles (Fusion sources) Reactions involving incident protons, deuterons, and so on must rely on artificially accelerated particles. Two of the most common reactions of this type used to produce neutrons are: Because the coulomb barrier between the incident deuteron and the light target nucleus is relatively small, the deuterons need not be accelerated to a very high energy in order to create a significant neutron yield. 102 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Spontaneous Fission: Spontaneous fission is a type of radioactive decay which is not caused by an incident particle (in contrast to induced fission). The half-lives 𝑡1/2 for spontaneous fission decrease rapidly with increasing z, for example: 238 92U: 𝑡1/2 = 4.5 × 109 𝑦 252 98Cf: 𝑡1/2 = 2.64 𝑦 262 102No: 𝑡1/2 = 5 𝑚𝑠 103 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Other products of the fission process are the heavy fission products prompt fission gamma rays, and the beta and gamma activity of the fission products accumulated within the sample. When used as a neutron source, the isotope is generally encapsulated in a sufficiently thick container so that only the fast neutrons and gamma rays emerge from the source. 104 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Example 2: 105 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Lists some of the common sources of neutrons and their decay modes. 106 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Neutrons Attenuation: When a neutrons beam crossing a space 𝑥, the beam is reduced by an amount proportional to the number of nuclei 𝑁0 per unit volume in the material: 𝐼 𝑥 = 𝐼0 𝑒 −𝜇 𝑥 = 𝐼0 𝑒 −𝜎𝑡 𝐸 𝑁0 𝑥 where 𝜎𝑡 is the total cross section This formula, however, is too simplistic: on one side the cross section 𝜎𝑡 𝐸 depends on the neutron energy. 107 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons If the material contains several isotopes such as silver ( 107Ag and 109Ag ), nickel (five isotopes), or is a compound NaF (one isotope of each element), and so forth, then the effective cross section will be the number weighted cross section: 𝜎𝑎𝑣𝑔 = 𝑓1 𝜎𝑡 (𝐸)1 +𝑓2 𝜎𝑡 (𝐸)2 +𝑓1 𝜎3 (𝐸)3 + ⋯ where the constants, 𝑓𝑖 , are the fraction by number of each isotope in the sample. 108 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons neutrons penetration in matter depends on their energies and atomic number of the medium. neutrons Absorbing material 109 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Neutrons Energies: Neutrons in general classified according to their energies: 110 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Example 3: Calculate the average thermal neutron capture cross section and the mean free path for LiF, a solid crystalline material at room temperature with a density of 2.635 gΤcm3 and a molar mass of 25.94 gΤmol. Lithium has two stable isotopes 6Li (7.5%) and 7Li (92.5%) with thermal neutron capture cross sections of σthermal = 39 mb and 45 mb , respectively. Fluorine is monoisotopic, 9F , with σthermal = 9.6 mb. 111 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Example 3: Calculate the average thermal neutron capture cross section and the mean free path for LiF, a solid crystalline material at room temperature with a density of 2.635 gΤcm3 and a molar mass of 25.94 gΤmol. Lithium has two stable isotopes 6Li (7.5%) and 7Li (92.5%) with thermal neutron capture cross sections of σthermal = 39 mb and 45 mb , respectively. Fluorine is monoisotopic, 9F , with σthermal = 9.6 mb. 𝜎𝑎𝑣𝑔 = 𝑓1 𝜎𝑡 (𝐸)1 +𝑓2 𝜎𝑡 (𝐸)2 +𝑓1 𝜎3 (𝐸)3 Notice that half the atoms are fluorine and half the atoms are lithium, but the lithium atoms are split unevenly between A=6 and A=7. The fractions of each isotope must reflect this distribution. 𝜎𝑎𝑣𝑔 = 0.075 × 0.5 × 39 + 0.925 × 0.5 × 45 + 1 × 0.5 × 9.6 = 27.1 𝑚𝑏 112 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Example 3: Calculate the average thermal neutron capture cross section and the mean free path for LiF, a solid crystalline material at room temperature with a density of 2.635 gΤcm3 and a molar mass of 25.94 gΤmol. Lithium has two stable isotopes 6Li (7.5%) and 7Li (92.5%) with thermal neutron capture cross sections of σthermal = 39 mb and 45 mb , respectively. Fluorine is monoisotopic, 9F , with σthermal = 9.6 mb. 1 1 1 1 𝜆= = = = 𝜇 𝜎𝑎𝑣𝑔 𝑁0 𝜎 𝑁𝐴 𝜌 6.022 × 1023 1 × 2.635 𝑔 2 𝑎𝑣𝑔 𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 27.1 𝑚𝑏 × 10−27 𝑐𝑚 × 𝑚𝑜𝑙 𝑐𝑚3 𝑚𝑏 𝑔 25.94 𝑚𝑜𝑙 𝜆 = 603 cm Thus, the average thermal neutron travels more than 6 m in solid LiF before undergoing a nuclear capture reaction! 113 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Interaction mechanism: There is an enormous variety of possible interactions between a neutron and most nuclei, depending on neutron energy. The interactions differ from one isotope to another of the same element. The neuron interaction with the medium leads to kinetic energy loss that is mainly caused by: Elastic scattering A(n, n)A Inelastic scattering A(n, n′ )A∗ Radiative capture A n, γ A + 1 Neutron capture followed by charged particle or nuclear fission Spallation 114 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Elastic scattering A(n, n)A: Elastic scattering is the principal mode of interaction of neutrons with atomic nuclei. In this process, the target nucleus remains in the same state after interaction. 115 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Elastic scattering of neutrons with nuclei can occur in two different modes: 1. Potential elastic scattering refers to the process in which the neutron is acted on by the short-range nuclear forces of the nucleus and as a result scatters off of it without touching the particles inside. 2. Resonance mode, a neutron with the right amount of energy is absorbed by the nucleus with the subsequent emission of another neutron such that kinetic energy is conserved. 116 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Example 4: 117 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Inelastic scattering A n, n′ A∗ : Inelastic scattering leaves the target nucleus A in an excited state A∗. To undergo inelastic scattering, the incident neutron must have sufficient energy to excite the product nucleus, generally about 1 MeV or more. 118 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons In this process, the incoming neutron is absorbed by the nucleus, forming a compound and unstable nucleus, which quickly emits a neutron of lower kinetic energy in an effort to regain stability. Since the nucleus may still have some excess energy left after neutron emission, it may go through one or more γ- decays to return to the ground state. 119 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Radiative capture A n, γ A + 1: Neutron capture followed by gamma emission. This process is important for low-energy neutrons. 120 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons In radiative capture, a nucleus absorbs the neutron and goes into an excited state. To return to the stable state, the nucleus emits γ-rays. However, the isotopic form of the element changes due to the increase in the number of neutrons. 60 Radiative capture is generally used to produce radioisotopes, such as Co: 121 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Neutron capture followed by charged particle (know as transmutation) or fission: - Transmutation: This is a reaction in which one element changes into another. Neutrons of all energies are capable of producing transmutations. 10 7 For example, when a B nucleus captures a slow neutron, it transforms into Li and emits an α-particle ( 4He): 122 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons - Nuclear fission A(n, f): 235 In this process a slow neutron is captured by a heavy nucleus, such as U, taking it into an excited state. The nucleus then splits up into fragments after a brief delay. Several neutrons and γ-ray photons are also emitted during this process. 235 Fission of U can be written as: 123 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons It should be pointed out that although iodine and yttrium are the most probable elements produced during this fission process, other elements are also produced during fission of a sample. 124 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Two typical examples of fission reaction triggered by thermal neutron bombarding a uranium-235 nucleus are as follows: 125 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Example 5: Fission cross section of 235U and 239Pu as a function of energy. Both cross sections become very large at thermal energies. The cross sections show characteristic resonance peaks at certain energies. 126 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Spallation: Spallation refers to the fragmentation of a nucleus into several parts when a high energy neutron collides with it. This process is important only with neutrons having energy greater than about 100 MeV. As an example: 127 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons The total neutron interaction cross section, 𝜎𝑡𝑜𝑡𝑎𝑙 (𝐸), is the sum of the various reaction cross sections: 𝜎𝑡𝑜𝑡𝑎𝑙 𝐸 = 𝜎𝑒𝑙𝑎𝑠𝑡𝑖𝑐 + 𝜎𝑖𝑛𝑒𝑙𝑎𝑠𝑡𝑖𝑐 + 𝜎𝑐𝑎𝑝𝑡𝑢𝑟𝑒 + ⋯ 128 PHYS486 - Dr. Tahani Almusidi Chapter2: Interaction of Radiation with Matter 2.3 Interaction of uncharged particles 2.3.2 Neutrons Example of using neutrons: Thermal neutrons are used for medical purposes, for example BNCT treatment (Boron Neutron Capture Therapy), where a tumor is injected with 10B solution before being irradiated by a neutron beam. The interaction between the neutrons and 10B in the tumor leads to the emission of alpha particles. These highly ionizing particles destroy the tumor cells. 129 PHYS486 - Dr. Tahani Almusidi