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Published byNigel Sparks Modified over 4 years ago

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1 Photon Interactions When a photon beam enters matter, it undergoes an interaction at random and is removed from the beam

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2 Photon Interactions

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3 Notes is the average distance a photon travels before interacting is also the distance where the intensity drops by a factor of 1/e = 37% For medical applications, HVL is frequently used Half Value Layer Thickness needed to reduce the intensity by ½ Gives an indirect measure of the photon energies of a beam (under the conditions of a narrow- beam geometry) In shielding calculations, you will see TVL used a lot

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4 Beam Hardening

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5 Photon Interactions

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6 What is a cross section? What is the relation of to the cross section for the physical process?

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7 Cross Section Consider scattering from a hard sphere What would you expect the cross section to be? b θ α R α α

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8 Cross Section The units of cross section are barns 1 barn (b) = 10 -28 m 2 = 10 -24 cm 2 The units are area. One can think of the cross section as the effective target area for collisions. We sometimes take σ=πr 2

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9 Cross Section One can find the scattering rate by

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10 Cross Section For students working at collider accelerators

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11 Photon Interactions In increasing order of energy the relevant photon interaction processes are Photoelectric effect Rayleigh scattering Compton scattering Photonuclear absorption Pair production

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12 Photon Interactions Relative importance of the photoelectric effect, Compton scattering, and pair production versus energy and atomic number Z

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13 Photoelectric Effect An approximate expression for the photoelectric effect cross section is What’s important is that the photoelectric effect is important For high Z materials At low energies (say < 0.1 MeV)

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14 Photoelectric Effect More detailed calculations show

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15 Photon Interactions Typical photon cross sections

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16 Photoelectric Effect The energy of the (photo)electron is Binding energies for some of the heavier elements are shown on the next page Recall from the Bohr model, the binding energies go as

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17 Photoelectric Effect

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18 Photoelectric Effect The energy spectrum looks like This is because at these photon/electron energies the electron is almost always absorbed in a short distance As are any x-rays emitted from the ionized atom

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Photoelectric Effect and X-rays PE proportionality to Z 5 makes diagnostic x- ray imaging possible Photon attenuation in Air – negligible Bone – significant (Ca) Soft tissue (muscle e.g.) – similar to water Fat – less than water Lungs – weak (density) Organs (soft tissue) can be differentiated by the use of barium (abdomen) and iodine (urography, angiography) 19

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Photoelectric Effect and X-rays Typical diagnostic x-ray spectrum 1 anode, 2 window, 3 additional filters 20

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Photon Interactions Sometimes easy to loose sight of real thickness of material involved

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Photon Interactions X-ray contrast depends on differing attenuation lengths

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23 Photoelectric Effect Related to kerma (Kinetic Energy Released in Mass Absorption) and absorbed dose is the fraction of energy transferred to the photoelectron As we learned in a previous lecture, removal of an inner atomic electron is followed by x-ray fluorescence and/or the ejection of Auger electrons The latter will contribute to kerma and absorbed dose

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24 Photoelectric Effect Thus a better approximation of the energy transferred to the photoelectron is We can then define e.g.

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25 Photoelectric Effect Fluorescence yield Y for K shell

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26 Cross Section dΩ=dA/r 2 =sinθdθdφ

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27 Cross Section

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28 Cross Section If a particle arrives with an impact parameter between b and b+db, it will emerge with a scattering angle between θ and θ+dθ If a particle arrives within an area of dσ, it will emerge into a solid angle dΩ

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29 Cross Section From the figure on slide 7 we see This is the relation between b and θ for hard sphere scattering

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30 Cross Section We have And the proportionality constant dσ/dΩ is called the differential cross section

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31 Cross Section Then we have And for the hard sphere example

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32 Cross Section Finally This is just as we expect The cross section formalism developed here is the same for any type of scattering (Coulomb, nuclear, …) Except in QM, the scattering is not deterministic

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33 Cross Section We have And the proportionality constant dσ/dΩ is called the differential cross section The total cross section σ is just

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