E γ. Electromagnetic Radiation -- Photons. 2. Mechanisms. a. Photoelectric Effect: photon disappears. b. Compton Scattering: photon scatters

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1 III. letromagneti Radiation -- Photons. Mehanisms a. Photoeletri ffet: γ photon disappears b. Compton Sattering: γ photon satters. Pair Prodution: γ e ± pair produed C. Photoeletri ffet e Sine photon is ompletely absorbed, ejeted eletron (photoeletron) is monoenergeti. where γ ( n ) B (n ) is eletron binding energy B for n orbital

2 D. Compton Sattering: γ > > B (n ) γ The photon energy is too large to be ompletely absorbed by the eletron To understand Compton sattering we need to know the Relativisti Relations. Consider a partile of rest mass m 0 moving with a veloity v. If β v/ where is the veloity of light, then the partile has mass : m momentum : Total nergy : m 0 1 β p total mv m m v 0 1 β m 0 1 β m 0 β 1 β Kineti energy: T 1 m m 1 0 m0 1 β

3 From these relations one an obtain: 0 m p m m p m + This is the Relativisti energy momentum- relation: 4 0 m p + Photons have no rest mass so 0 0 m therefore ω ν γ γ h p

4 From momentum balane: p e p γ p γ ' p e γ + γ ' γ γ ' os ( θ ) nergy balane: γ + me γ ' + e + Sattered photon: 4 ( p m ) 1/ e γ ' + γ 1 me γ ( 1 os( θ )) Reall that h λ so that λ h

5 What is the hange in the wavelength of the sattered photon as ompared to the inident photon? λ' λ h 1 γ ' 1 γ h m e ( 1 osθ ) Notie that when os(θ) 1 that is θ0, there is no differene between the sattered wavelength and the original wavelength. In this ase no momentum is transferred to the eletron. The maximum hange in wavelength ours when os(θ) -1 that is the gamma ray (photon) is sattered to 180 degrees. The quantity h me Is alled the Compton wavelength of the eletron. 1. ffets of Sattering Proess a. Photon energy is degraded, but photon survives b. letron is propagated in medium. Multiple ollisions required to stop photon d. Sattering angle an beome large

6 . nergy spetrum 3. Probability: P P Z/ i.e., P is a funtion of the number of eletrons (Z) in an element (e sea); Again, high Z is best.. Pair Prodution: For γ > 1.0 MeV only Mehanism: Same as in γ-deay, exept photon originates outside nuleus

7 1. Result: e ± is formed ; primary γ disappears. e ± is thermalized in medium e e ation -e pairs e + + e annihilation two, MeV γs 3. Net: photon energy is degraded, but two lower-energy photons are produed (0.511 MeV), these then undergo Compton sattering and photoeletri effet 4. Probability: P pp P pp Z log γ (MeV) ; γ > 1.0 MeV a. High Z best b. Pair prodution is only stopping mehanism that beomes more probable as energy inreases.

8 Aluminum Copper Lead

9 F. Absorbtion of Photons 1. Net effet of mehanisms: Heavy elements are best absorbers Detetors ollet eletrons (or light onverted to eletrons).. Probability of Absorbtion: µ absorbtion oeffiient. Stopping mehanism is random; photon ranges are indeterminate ; e.g., it may take one, or a series of ollisions to make photons disappear due to multiple stopping mehanisms a. µ µ P + µ + µ pp di µ I dx, where I is the photon intensity b. For MONONRGTIC PHOTONS I I 0 e µd, where d is the absorber thikness (Beer-Lambert Law). Half-thikness: d 1/ d 1/ 0.693/µ where the half-thikness is the amount of material required to redue the intensity to one-half of its original value.

10 3. Critial absorbtion of x-rays Bohr atom Quantum #s a. Definitions: K, L, M. Transitions to n 1,, 3 levels b. xample:. x-ray mission nergetis s 1s K α1 4p s L β α, β, γ. n 1,, 3 1,, 3. 0, 1, xray B (n ) B (n ), where n < n and B is eletron binding energy d. Critial absorbtion When µ is very high Critial absorber γ B an atom annot absorb its own x-rays effiiently Approximately equal

11 e. Problem: What is the best absorber for Zn K 1 x-rays? Z Fe Ni Cu Zn B (1s) B (s) Kα ritial absorber kev Z n K α1 x-ray IV. Neutrons A. Soures: Fission, reators, (< n > ~ 0.5 MeV) Aelerators Thermonulear explosions (neutron bombs) B. Interations 1. Properties: Z n 0 M n M H 1u NO LCTROMAGNTIC INTRACTION NGLIGIBL IONIZATION

12 . Collisions: only nulear ollisions are important ; billiard balls σ nuleus 10 8 σ atom C. Stopping Mehanisms Reator Design 1. STP I: Thermalization lasti and inelasti sattering from nulei a. nergy Loss: Light nulei are best materials for reduing energy with fewest ollisions b. Average number of ollisions n Thermal energy: th < th > 3/ kt, where k ev/k at T 300 K < th > 0.04 ev, or ~ 3 km/s THRMAL NUTRONS For H, <n> ~0 U, <n> ~00

13 . STP II: Neutron Capture a. σ f (1/v) i.e., the reation probability inreases as neutron slows down low energy (veloity) neutrons aptured most effetively

14 b. limination of Neutrons Choose materials with large neutron-apture ross setions: e.g., 10 B(n,α) : σ 3838 b ; 113 Cd(n,γ) ; σ 10 4 b; 157 Gd(n,γ): σ b. Preservation of Neutrons Want small σ (n,x) ross setions (reator moderators). Paraffin (~ 100 ollisions for thermalization) 1 n + 1 H H ; σ 0.33 b 1 n + H 3 H ; σ b (synthesis for nulear weapons) 1 n + 1 C 13 C; σ b Water: n + 16 O ; σ b 4 He: σ 0 (a bit expensive)

15 3. Neutron Detetion a. Satter from hydrogenous materials n + 1 H n + H Detet 1 H b. Nulear reations (B or Gd loaded plastis) 1 n + 10 B 7 Li + 4 He Detet harged partiles

16 DTCTORS I. Charged Partile Detetors A. Sintillators B. Gas Detetors 1. Ionization Chambers. Proportional Counters 3. Avalanhe detetors 4. Geiger-Muller ounters 5. Spark detetors C. Solid State Detetors II. III. Gamma ray detetion (Sintillators, Solid State dets.) Neutron detetion

17 Gas detetors nergy required to form and ion-pair (IP) Gases: 0-30 ev/ip Si: 3.6 ev/ip Ge: 3.0 ev/ip Signal amplitude Applied voltage