The interaction of radiation with matter

Transcription

1 Basic Detection Techniques Detection of energetic particles and gamma rays The interaction of radiation with matter Peter Dendooven KVI

2 Contents Interaction of radiation with matter high-energy photons charged particles heavy charged particles electrons neutral particles neutrons neutrinos General radiation detection concepts pulse mode operation energy spectrum detector efficiency timing Radiation detectors semiconductor detectors operation principle examples (silicon, germanium) other materials scintillation detectors principle organic scintillators inorganic scintillators photosensors gas detectors ionisation proportional Geiger 2

3 Radiation categories charged particles heavy charged particles fast electrons neutral particles high-energy photons neutrons neutrinos Coulomb easily stopped transfer 3

4 Nomenclature high-energy photons high-energy photons = energy higher than ionisation energies, so rougly >1 kev (!<1 nm) in principle: X-rays: atomic transitions up to ~115 kev for uranium "-rays: nuclear transitions from few ev to many MeV other sources of high-energy photons bremsstrahlung synchrotron radiation annihilation radiation to keep things simple: "-rays 4

5 High-energy photons: 3 major interactions photo-electric effect Compton scattering pair production Nobel prizes in physics Arthur H. Compton 5

6 Attenuation of gamma rays (1/2) 0 x I 0 I(x) dx all-or-nothing processes: di dx " I di(x) dx = "µ I(x) µ: linear attenuation coefficient I(x) = I 0 e "µ x 6

7 Attenuation of gamma rays (2/2) mean free path mass attenuation coefficient " = $ # 0 $ 0 x e -µx dx # e -µx dx = 1 µ µ " 1 % $ ', ( # cm& µ " # µ " " g % " % $ ' ) µ cm2 # cm 3 ( $ ' & # g & half-thickness I(x) = I 0 e " ln 2 x d 1/2 d 1/ 2 = ln2 " µ cm or g % $ ' # cm 2 & compound or mixture # µ & % ( $ " ' c = ) # w µ & i % $ " ( ' i w i : weight fraction of element i i 7

8 Interaction cross section target, n atoms/cm 3 beam, I t number of interactions proportional with: N [/s] beam intensity I [/s] number of reaction partners encountered n t (#t ) [/cm 2 ] N = $ I t $= cross section [cm 2 ] 1 barn (b) = cm 2 8

9 Photo-electric effect " E e " E " interaction with whole atom K-electron most probable energy deposition: E (E b : electron binding energy) e " = E # " E b % E " > E b electron cloud is rearranged : X-rays Auger electrons photo-electron preferentially emitted in a forward direction 9

10 Photo-electric cross section in lead absorption edges 10

11 Compton scattering (1/2) e - E " E " # = E # 1+ E # 2 ( 1$ cos %) m 0 c E " # m 0 c 2 : electron rest mass (511 kev) & : scattering angle 11

12 Compton scattering (2/2) angular distribution: Klein-Nishina formula d" d# ($) = 1 2 r e ' E % 2 & ) E & ( *, + 2 ' E & + E % * & ) - sin 2 $ ( E % & E, & +. cm / sr 2 d" d# ($) = 1 2 r e ' * ), ( 1+ %(1& cos$) ' 1+ cos 2 $ + %2 (1& cos$) 2 * ), ( 1+ %(1& cos$) + - cm 2 0 / 2. sr 1 " = E # m 0 c 2 r e : classical electron radius = 2.82 x cm 12

13 Compton scattering 13

14 Compton scattering 14

15 Compton scattering 15

16 Pair production nucleus for momentum conservation requires E " > 2 m 0 c 2 = 1022 kev kinetic energy (e + e + ) = E " kev e + annihilates with an electron two 511 kev annihilation photons emitted back-to-back 16

17 Dependence on atomic number and energy type of interaction attenuation coefficient comment photo-electric effect " # Z 4.5 E $ -3.5 dominates for low energies and heavy elements Compton scattering pair production " # Z E $ -1 (0.1 to 10 MeV) " # Z 2 ( E $ %1022 kev) " # Z 2 ln(e $ ) dominates from ~0.5 to 5 MeV (for most elements) E close to 1 MeV E >> 1 MeV dominates for high energies and heavy elements Z : atomic number 17

18 Total "-ray attenuation µ = ' + $ + ( 18

19 Half-thickness 19

20 Relative importance 20

21 Heavy charged particles protons, alpha particles, atomic ions primary interaction through Coulomb forces (only at low energy, nuclear reactions are important for energy loss) Coulomb scattering by atomic electrons maximum energy transfer (head-on collision) "E max # E 4m M m: electron mass M: mass heavy particle for 10 MeV proton: )E max * 20 kev % energy loss in very many small steps Coulomb force has infinite range, so interaction with many electrons simultaneously % continuous, gradual, energy loss 21

22 Heavy charged particles Coulomb interaction leads to: electron capture/loss by projectile exitation projectile exitation and ionisation of target atoms basis for detection kinetic energy is tranferred to +-rays, X-rays, Auger electrons,... many-faceted and complicated process paths are essentially straight because M >> m e % per interaction a small deflection interactions in all directions 22

23 Stopping power 0 x E 0 E(x) dx stopping power # energy loss per unit of amount of material linear stopping power S = " de dx # e.g. MeV & % ( $ cm ' specific stopping power S = " de d(#x) $ & e.g. % MeV ' ) g cm 2 ( 23

24 Bethe-Bloch formula " de dx = % e ' & 4#$ 0 2 ( 4# (ze) 2 n, * ln 2m 0 c ) m 0 c I ( ) " + 2 " ln 1" + 2 / 1 0 incoming particle:,: v/c v: velocity ze: charge absorber material: n: electron density (electrons/cm 3 ) I: average excitation and ionisation potential ~10 Z ev electron: e: charge m 0 : rest mass 24

25 Bethe-Bloch formula " de dx = % e ' & 4#$ 0 2 ( 4# (ze) 2 n, * ln 2m 0 c ) m 0 c I ( ) " + 2 " ln 1" + 2 / 1 0 n " N Z " N A # Z A N: atomic density (atoms/cm 3 ) Z: atomic number N A : Avogadro constant -: density (g/cm 3 ) A: atomic weight " de dx = 0.31 MeV z 2 $ Z % cm2 # 2 A ln 2m 0c 2 # 2 ' & I ( ) " # 2 " ln 1" # 2 ( * ) 25

26 Stopping power dependencies non-relativistic Bethe-Bloch " de dx = % e ' & 4#$ 0 2 ( 4# (ze) 2 n + * ln 2m v ) m 0 v 2, I / [...] changes slowly " de dx # z2 n v 2 different energy different particle (same velocity) different material " de dx # 1 v 2 # 1 E " de dx # z2 " de dx # n 26

27 Bragg-Kleeman rule stopping power per atom of compounds/mixtures is additive 1 N c " $ # de dx % ' & c = ( 1 W i N i i " $ # de dx % ' & i N c, N i : atomic density of compound, component W i : atomic fraction of component i 27

28 Stopping power example #1 protons in aluminum slow-moving ions capture electrons 28

29 Stopping power example #2 about same energy loss minima % minimum ionizing particle ~2 MeV/(g/cm 2 ) in light materials 29

30 The Bragg peak stopping power vs. distance travelled basis for hadron (e.g. proton) therapy 30

31 Electrons electron mass is small % Coulomb interaction causes: large relative energy loss per interaction large deviations in path % large accelerations cause energy loss due to electromagnetic radiation: bremsstrahlung % distance travelled >> projected range % backscattering (low E and high Z) 31

32 Electron energy loss de dx = " de % $ ' # dx & c " + de % $ ' # dx & r c: collisional r: radiative # " de & % ( $ dx ' c # " de & % ( $ dx ' r # e = % $ 4)* 0 # e = % $ 4)* 0 2 & 2) e 2 n, ( ln m v 2 0 E ' m 0 c I 2 (1" + 2 ) " (ln2) # % 2 1" +2 " & ( + (1" + 2 ) + 1 #. % 1" 1" +2 - $ ' 8 $ 2 & e 2 n (Z + 1) E + ( 4 ln 2E ' 137 m 2 0 c 4 m 0 c " , 2 3/ & ( ' 2 / 1 0 (de dx) r " E[ MeV] Z (de dx) c

33 Electron collisional vs. radiative energy loss 33

34 Electron stopping power minimum ionizing particle: ~0.5 to ~5 MeV: 1-2 MeV/(g/cm 2 ) 34

35 Range of a charged particle # distance travelled before stopping R = 0 ) E 0 # " de & % ( $ dx ' "1 de range charged particle track projected range of more practical use: projected range (= range ) 35

36 Straggling energy loss is a stochastic process % energy straggling % range straggling % angular straggling range 36

37 Range example: hydrogen, helium ions 37

38 Electron range: examples 38

39 Cherenkov radiation (1/2) a charged particle travelling faster than the speed of light in a medium emits light, so-called Cherenkov radiation v > c n " # v c " n > 1 n: refractive index energy threshold # E th = m 0 c 2 % "1+ 1+ $ & 1 n 2 "1 ( ' m 0 c 2 : electron rest mass 39

40 Cherenkov threshold energy 40

41 Cherenkov radiation (2/2) Cherenkov photons are emitted under a fixed angle cos" = 1 # n yield per unit wavelength. 1/! 2 (breaks down at short! as n%1) electromagnetic shock wave 41

42 Cherenkov light yield d 2 N de dx " 370 z2 sin 2 #(E) 1 ev 1 cm ze: charge of particle 42

43 Cherenkov radiation: example spent nuclear fuel under water at the La Hague reprocessing plant 43

44 Neutrons no Coulomb interaction, only strong interaction short range & atomic nucleus is small: % interaction probability << than charged particles/photons (~10 8 ) as the result of an interaction: neutron disappears, creating secondary radiation mostly heavy charged particles (p,d,t,/) (basis for detection) scattering in which energy and direction are significantly changed can give rise to recoil nuclei (basis for detection) % attenuation of a collimated beam is exponential 44

45 Neutrons type of interaction depends mostly on the neutron energy fast neutrons (> ~0.5 ev) elastic scattering (most effective on light nuclei), gives recoil nuclei inelastic scattering, gives recoil nuclei scattering results in neutron energy loss (neutron is moderated) neutron capture (resulting in the emission of charges particles (p,d,t,/)) resonant slow neutrons elastic scattering small energy loss, so no good for detection, but thermalizes neutrons (~25 mev at room temperature) eventually captured by nucleus followed by gamma ray: (n,") most effectively by B, Cd, In, Gd 45

46 Neutrinos no electromagnetic or strong interaction, only weak interaction % very small interaction probability e.g. " cross section ~ cm 2 e + p # n + e + 1 cm 3 of material contains ~10 24 protons interaction probability ~10-43 x ~ /cm cm (10 light-years) required for a good capture probability neutrino interaction results in secondary radiation, which is then detected interaction possibilities and probabilities are different for the 3 neutrino flavours: electron-, muon-, and tau-neutrino 46

47 Neutrino detection schemes inverse beta-decay " e + Z A X # e + + Z$1 detect e + (annihilation) and/or Y (radiochemical detection) neutrino capture by a nucleus (Homestake experiment) detection of 37 Ar water-cherenkov detection: scattering off electrons A Y " e Cl # e $ Ar all neutrino flavours but with different cross sections detected via Cerenkov radiation from the scattered electrons (E 0 > 5 MeV) Cherenkov cone tells incoming direction and particle type e.g. (Super)-Kamiokande heavy water: 3 options, all 3 neutrino flavours can be detected scattering off electrons (all 3 flavours, different cross sections) 0 e + d % p + p + e detect e via Cherenkov, only 0 e 0 e + d % 0 e + n + p deuteron break-up, detect neutron, all 3 flavors, same cross section e.g. SNO (Sudbury Neutrino Observatory) " + e # $ " + e # 47

48 Super-Kamiokande m underground 41.4 m tall, 39.3 m diameter tonnes ultra-pure water and photomultiplier tubes 48

49 Sudbury Neutrino Observatory 2 km underground tonnes of heavy water 6-metre radius acrylic vessel photomultiplier tubes 49