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## Photon Interactions

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**Photon Interactions**• When a photon beam enters matter, it undergoes an interaction at random and is removed from the beam**Photon Interactions**• Notes • l is the average distance a photon travels before interacting • l 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**Photon Interactions**• What is a cross section? • What is the relation of m to the cross section s for the physical process?**Cross Section**• Consider scattering from a hard sphere • What would you expect the cross section to be? α θ α R b α**Cross Section**• The units of cross section are barns • 1 barn (b) = 10-28m2 = 10-24cm2 • The units are area. One can think of the cross section as the effective target area for collisions. We sometimes take σ=πr2**Cross Section**• One can find the scattering rate by**Cross Section**• For students working at collider accelerators**Photon Interactions**• In increasing order of energy the relevant photon interaction processes are • Photoelectric effect • Rayleigh scattering • Compton scattering • Photonuclear absorption • Pair production**Photon Interactions**• Relative importance of the photoelectric effect, Compton scattering, and pair production versus energy and atomic number Z**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)**Photoelectric Effect**• More detailed calculations show**Photon Interactions**• Typical photon cross sections**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**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**Photoelectric Effect and X-rays**• PE proportionality to Z5 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)**Photoelectric Effect and X-rays**• Typical diagnostic x-ray spectrum • 1 anode, 2 window, 3 additional filters**Photon Interactions**• Sometimes easy to loose sight of real thickness of material involved**Photon Interactions**• X-ray contrast depends on differing attenuation lengths**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**Photoelectric Effect**• Thus a better approximation of the energy transferred to the photoelectron is • We can then define e.g.**Photoelectric Effect**• Fluorescence yield Y for K shell**Cross Section**• dΩ=dA/r2=sinθdθdφ**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**Cross Section**• From the figure on slide 7 we see • This is the relation between b and θ for hard sphere scattering**Cross Section**• We have • And the proportionality constant dσ/dΩ is called the differential cross section**Cross Section**• Then we have • And for the hard sphere example**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**Cross Section**• We have • And the proportionality constant dσ/dΩ is called the differential cross section • The total cross section σ is just