Ionising Radiation

1. Non-ionising Radiation Directly ionising (charged particles) Electrons, protons, α-particles… Ionising Indirectly ionising (neutral particles) Photons, neutrons… Ionising Radiation There are two types of radiation; ionising and non-ionising. Non-ionising Radiation As its name implies this does not have the ability to give or remove charge from a neutral particle and thus cannot ionise matter. Ionising Radiation This radiation can ionise matter in two ways: • Directly ionising radiation (charged particles) electrons, protons, α-particles and heavy ions, or • Indirectly ionising radiation (neutral particles) photons (x-rays and γ-rays) and neutrons.

2. Directly Ionising Radiation Directly ionising radiation deposits energy in the medium with which it is interacting by Coulomb interaction of the charged particle (radiation) with electrons of atoms in the matter which is being ionised.

3. Indirectly Ionising Radiation Indirectly ionising radiation is not in the form of a charged particle and so cannot interact directly to ionise the medium through Coulomb interactions. It must first react with the matter to release a charged particle which can then go on to interact with the medium and ionise it through Coulomb interactions. E = hν

4. Ionising Photons There are four classifications of ionising photon radiation: • Characteristic x-rays which result from electron transitions from atomic shells • Bremsstrahlung which results from electron-nucleus Coulomb interactions • γ-rays which result from nuclear transitions • Annihilation quanta which result from positron-electron annihilations (511 keV) E = hν E = hν γ e- e+ 180° E = 511 keV

5. Electron Interactions As energetic electrons traverse matter they interact with it through Coulomb interactions and lose energy. There are two possible results of these interactions: • The electron loses energy through collisions or radiative losses • The electron can be deflected from its original path • Energy losses are described by the stopping power • Scattering is described by scattering power

6. Electron Trajectory e- b Nucleus a Electron Cloud Electron Interactions The type of interaction of the incident electron with a particular atom depends on the impact parameter b. b>>a Soft collision between electron and electron. Only a small amount of the incident electron’s kinetic energy will be transferred to the orbital electrons. b≈aThis will result in a hard collision and an appreciable amount of the electrons kinetic energy will be given to the orbital electrons. This can result in ionisation of the atom or excitation. b<<aCoulomb interaction of the electron with the nucleus. This results in x-ray production through Bremsstrahlung and electron scattering

7. Stopping Power Energy losses by an electron moving through a medium of density ρ are described by the total mass-energy stopping power (S/ρ)tot This is a measure of the loss in kinetic energy Ek of the electron per unit path length x. The total stopping power consists of two components – the collision stopping powers (S/ρ)coll (atomic excitations and ionisations) and the radiative stopping powers (S/ρ)rad (Bremsstrahlung production) (S/ρ)tot = (S/ρ)coll + (S/ρ)rad

8. Linear Energy Transfer (LET) The stopping power focuses on the amount of energy lost by an electron traversing a medium. If we focus on how much energy the medium is gaining from the electron we can describe a linear rate of energy absorption. The rate of energy absorption by the material, called the Linear Energy Transfer (LET), is defined as the average energy locally imparted to the absorbing medium by an electron of specified energy traversing a given distance in the medium.

9. Photon Beam Attenuation The intensity of a beam of monoenergetic photons attenuated by an attenuator of thickness x is given by I(x) = I(0) e-μ(hν, Z)x where I(0) is the intensity of the unattenuated beam, and μ(hν, Z) is the linear attenuation coefficient which depends on the energy of the photon hν and the atomic number Z of the attenuator.

10. Half Value Layer (HVL) The Half Value Layer (HVL or x½) is defined as the thickness of the attenuator that will attenuate the photon beam to 50% of it’s original intensity From I(x) = I(0) e-μ(hν, Z)x we have ½ = 1 e-μx½ -ln 2 = -μx½ x½ = (ln 2)/μ

11. Linear Attenuation Coefficient μ The linear attenuation coefficient μ is related to the mass attenuation coefficient μm, atomic attenuation coefficient aμ and electronic attenuation coefficient eμ as follows: μ = ρ μm = (ρ NA aμ)/A = (ρ NA eμ Z)/A The units of the linear, mass, atomic and electronic attenuation coefficients are: cm-1, cm2/g, cm2/atom and cm2/electron. This implies that the thickness given in (–μx) must be quoted in units of: cm, g/cm2, atoms/cm2 andelectrons/cm2 respectively

12. The Photoelectric Effect In the photoelectric effect the photon interacts with an orbital electron and disappears, while the electron is ejected from the atom thus ionising it. The energy of the photoelectron is given by Ek = hν – EB Where Ek is the kinetic energy of the ejected electron, hν the energy of the photon and EB the binding energy of the electron.

13. 1000 100 10 1 0.1 0.01 0.1 1 10 0.01 The Photoelectric Effect The mass attenuation coefficient for the photoelectric effect is proportional to (Z/hν)3 The plot of hν versus mass attenuation shows some sharp discontinuities where hνequals the binding energy of particular electronic shells. These discontinuities, called absorption edges, are caused because for a particular shell, the electrons cannot undergo the photoelectric effect without energy hν greater than or equal to the binding energy of that shell. L edges K edge Mass attenuation coefficient (cm2/g) Photon energy (MeV)

14. Recoil electron Incident photon φ θ Scattered photon Compton Effect The Compton effect represents a photon scattering off an atom and ejecting an orbital electron from that atom. As hν>>EB the electron can be treated as free and stationary when compared to the photon. The energy of the photon dictates the average angle of deflection. For θ = 0, φ = π/2 (no change in photon direction) and for θ = π, φ = 0 (back scattering of the photon). The following is a table of average scattering and recoil values

15. Pair Production In pair production, a photon in the nuclear Coulomb field of an atom converts to an electron-positron pair. e+ E = hν There is a minimum activation energy for this conversion of hν ≥ 2mec2 = 1.02 MeV Any photonic energy above this minimum threshold is shared equally by the electron-positron pair as kinetic energy 180° e- If the pair production occurs in the field of an orbital electron then three particles are created and this process is called triplet production. An electron-positron pair are created and an orbital electron. The minimum energy for this activation is 4mec2 and all particles share this energy.

16. 1000 1000 L edges Photoelectric Effect mass attenuation coefficient 100 100 10 K edge 10 Combined mass attenuation coefficient Mass attenuation coefficient (cm2/g) 1 1 0.1 0.1 Pair Production mass attenuation coefficient Compton Effect mass attenuation coefficient 0.01 0.01 0.1 1 10 0.01 100 Photon energy (MeV) Photonic Attenuation The above graph shows the individual and combined mass attenuation effects upon photons at varying photon energies.

17. Photoelectric Effect Dominant Pair Production Dominant Atomic Number Z Compton Effect Dominant Photon Energy (MeV) Photonic Attenuation