Radiation Interactions

Transcription

1 Raiation Measurement Systems/Lecture. Interactions Raiation Measurement Systems Knoll chap. Raiation Interactions Ho Kyung Kim Pusan National University The operation of any raiation etector epens on the manner (in which the raiation to be etecte) interacts w/ the mat l of the etector itself Unerstan the response of a specific type of etector w/ the funamental mechanisms by which raiations interact an lose their energy in matter Coulomb interactions vs. catastrophic interactions (what they mean? what is the ifference?) Chg particulate raiations HCPs (Char. istance 1 5 m) Fast e (Char. istance 1 3 m) Unchg raiations n s (Char. istance 1 1 m) M (Char. istance 1 1 m)

2 Raiation Measurement Systems/Lecture. Interactions Interaction of heavy charge particles Thru Coulomb forces btwn their positive charge & the negative charge of the orbital electrons (Interactions w/ nuclei rarely occur) lectron feels an impulse from an attractive Coulomb force xcitation Ionization Max. transfer to e = 4m /m (small!) Impact parameter Range A istance beyon which no particles will penetrate Straight because the HCP is not greatly eflecte Atomic raius Nucleus lectron clou Delta rays nergetic electrons, which have sufficient K.. to create further ion pairs, release by the ionization process 3 Proton Alpha Delta rays 4

3 Raiation Measurement Systems/Lecture. Interactions Stopping power S x Along a particle track, its specific energy loss or its rate of energy loss Bethe formula 4 4e z NB x mv m v v v B Z ln ln 1 I c c Varying slowly with particle energy Only the first term is significant for nonrelativistic charge ptl s (v << c) ze = the charge of primary particle N = the atomic ensity I = the average excitation & ionization potential 5 The impulse is largest for a nonrelativistic particle because of greater time in the vicinity of any given electron Air /x as; v z NZ (the electron ensity) ~ Min. ionizing particles ~ MeV per g/cm ~1 MeV for fast electrons Near constant broa min. value at energies where their velocity approaches => Calle "minimum ionizing particle (MIP)" Try to check the of each funamental particle! 6

4 Raiation Measurement Systems/Lecture. Interactions nergy loss characteristics Chg ptl s w/ the greatest # nuclear charges begin to pick up electrons early in their slowing own process Bragg curve A plot of the specific energy loss along the track of a charge particle Near the en of the track, the charge is reuce thru electron pickup (charge exchange) an the curve falls off nergy straggling A sprea in particle energies after passing thru a given thickness of absorber ue to the "stochastic" nature in energy loss 7 Raiation therapy Immobilization Image Acquisition Planning Delivery of Treatment 8

5 Raiation Measurement Systems/Lecture. Interactions Particle therapy 9 Particle range An alpha particle transmission experiment Mean range, R m The absorber thickness reucing the counte number to ½ of its value in the absence of the absorber xtrapolate range, R e A measure obtaine by extrapolating the linear portion of the en of the transmission curve to zero 1

6 Raiation Measurement Systems/Lecture. Interactions Any etector that is to measure the full incient of a chg ptl must have an active thickness that is greater than the range of that ptl in the etector mtl b R a The slope relate parameter is not greatly ifferent for the various ptl s 11 Stopping time Require time to stop a charge particle in an absorber For nonrelativistic particles; v 8 m c 3 1 m mc s (931MeV / amu) m A T R R R mc R 931MeV / amu 8 v Kv Kc K(31 m/s) K =.5 when a ptl is uniformly ecelerate Assuming K =.6 (because ptl s generally lose at a greater rate near the en of range); ma T R m A T [s], R [m], m A [amu], [MeV] a few ps in solis or liquis; a few ns in gases (generally small enough to be neglecte for all but the fastest responing etectors) 1

7 Raiation Measurement Systems/Lecture. Interactions Pop quiz stimate the time require for a 5 MeV alpha particle to stop in Si. Repeat for H gas. Knoll's problem.1 13 nergy loss in thin absorbers x avg t If the energy loss is small; Use the stopping power at the incient ptl The transmitte proton carries off the remainer If the energy loss is not small; Make use of range energy ata = t loss of protons of in a Si etector w/ 4.6 m thickness 14

8 Raiation Measurement Systems/Lecture. Interactions 15 Scaling laws (calle the "Bragg Kleeman" rule) Linear stopping power in compouns or mixtures N = atomic ensity, W = atom fraction Range in compouns n = the number of atoms, A = atomic weight, M = molecular weight 16 i i i i c c x N W x N 1 1 i i i i c c R A n M R A A R R ) ( ) ( v R z m z m v R b a b b a a Range in ifferent materials for the same particle Range in the same material for ifferent particles

9 Raiation Measurement Systems/Lecture. Interactions Other iscussions on HCP interactions Behavior of fission fragments Very large effective charge Higher specific energy loss Very high initial Range ~ ½ of a 5 MeV Seconary electron emission from surfaces Low 's (incl. rays & 's w/ of ~ev) escaping from an absorber (e.g. alkali halies, CsI) Different from those forme in the gammaray interactions 6 1 ev & 9 ev from a carbon surface for & F.F., respectively Can be utilize to etect HCP with an external electron etector (microchannel plate, photomultiplier tube) 17 Interaction of fast electrons Mass is equal to that of the orbital electrons w/ which it is interacting; Losing a much larger fraction of its in a single encounter Losing their energy at a lower rate Following a much more tortuous path Possible in abrupt change of irections ue to electron nucleus interaction Tracks of six 8 kev electrons in water 18

10 Raiation Measurement Systems/Lecture. Interactions Specific energy loss Collisional losses Raiative losses (bremsstrahlung) Negligible in HCP interactions (note the m term) Important for e w/ high (note the term) & large Z (note the Z them) Total linear stopping power: Note: ( [MeV]) ) (1 1 1 (ln ) ) (1 ln I m v m v NZ e x c 3 4 4ln 137 1) ( 4 4 m c c m e Z NZ x r r c x x x 7 ) ( ) ( Z x x c r lectron range Absorption of monoenergetic electrons As a very crue estimate; ~ mm per MeV in low materials ~1 mm per MeV in moerate materials To a fair egree of approximation, R (in g/cm ) of the absorber is a constant for ifferent materials for electrons of equal initial

11 Raiation Measurement Systems/Lecture. Interactions Pop quiz stimate the range of 1 MeV electrons in Al referring to the following graph. Knoll's problem.4 1 Range base on the continuous slowing own approximation =

12 Raiation Measurement Systems/Lecture. Interactions Absorption of beta particles (w/ continuous spectrum) Backscattering Large-angle eflections Most pronounce for electrons w/ low & absorbers w/ high Z I I e nt Al Beta ptl absorption coeff. npoint =.5( m + av ) Avg. 3 Positron interactions The behaviors in tracks, specific energy loss & range are similar to those in normal negative electrons The only ifference is that the annihilation raiation is generate at the en of the positron track 4

13 Raiation Measurement Systems/Lecture. Interactions Interaction of gamma rays Among a larger number of possible interaction mechanisms, photoelectric absorption, Compton scattering, an pair prouction are only consiere Contrast to the charge particles, which slow own graually thru continuous, simultaneous interactions w/ many absorber atoms, photons result in suen & abrupt changes in the history, in that the photon either isappears entirely or is scattere thru a significant angle Coulomb vs. catastrophic interactions 5 Photoelectric absorption Interaction w/ an absorber atom (tightly boun electrons) Photon isappears; an energetic photoelectron is ejecte leaving a vacancy in the orbital shell hv e b Competition btwn char. x rays & Auger electrons xample: A 3 kev photon interaction w/ Xenon 86% K shell interaction 87.5% K & K x rays 1.5% Auger electrons 14% L or M shell interaction Much lower char. x rays or Auger electrons 6

14 Raiation Measurement Systems/Lecture. Interactions Prob. of P per atom Z n constant 3.5 n = 4 5 Preominant interaction for low & high Z mat l Absorption eges 7 Compton scattering Interaction w/ an electron (free or loosely boun electrons) Incoherent scattering Deflection (or scattering, ) of an incient photon hv hv hv 1 (1 cos ) mc hv hv hv hv 1 hv m c mc Recoil electron () e hv hv 8

15 Raiation Measurement Systems/Lecture. Interactions Prob. of Compton scattering per atom Increasing linearly w/ Z Klein Nishina formula 1 1 cos (1 cos ) Zr 1 1 (1 cos ) (1 cos )[1 (1 cos )] r = the classical electron raius 9 Pair prouction Interaction w/ the Coulomb fiel of a nucleus Possible when m c = 1. MeV Photon isappears, generating an electron positron pair xcess energy are share into K.. of the positron & the electron Two annihilation photons as seconary proucts Prob. of pair prouction per nucleus Approximately ~ Z Sharply increasing w/ 3

16 Raiation Measurement Systems/Lecture. Interactions Pop quiz Inicate which of the interaction process is ominant in the following situations? 1 MeV gamma rays in Al (13) 1 kev gamma rays in H (1) 1 kev gamma rays in Fe (6) 1 MeV gamma rays in C (6) 1 MeV gamma rays in Pb (8) Knoll's problem.7 31 Coherent scattering Interaction w/ electrons Rayleigh scattering Neither exciting nor ionizing the atom (hv = hv ) Prob. of coherent scattering Significant only for low Most prominent in high Z Deflection angle ecreases w/ increasing 3

17 Raiation Measurement Systems/Lecture. Interactions Attenuation coefficients A transmission experiment ach of the interaction processes removes the photon from the beam either by absorption or by scattering away from the etector irection Characterize by a fixe prob. of occurrence per unit path length Linear attenuation coefficient ( photoelectric) (Compton) (pair) The fraction number of transmitte photons I I e t 33 Mean free path The avg. istance travele in the absorber before an interaction take place x xe x e x x 1 Mass attenuation coefficient, / To avoi the epenency on the ensity of the absorber (even for the same absorber material) Compouns or mixtures c i wi w = the weight fraction i 34

18 Raiation Measurement Systems/Lecture. Interactions Absorber mass thickness, t I I e ( ) t [mg/cm ] Builup Broa beam or ba geometry measurements Increase etector signal ue to the aitional seconary photons I I B( t, ) e t B(t, ) = the builup factor as a multiplicative correction 35 Pop quiz What is the probability that a 6 kev gamma ray unergoes photoelectric absorption in 1 cm of soium ioie? (Note = 3.67 g cm 3 ) Knoll's problem.8 36

19 Raiation Measurement Systems/Lecture. Interactions Interaction of neutrons No charge, no coulomb interaction Can travel many cm Interacting w/ a nucleus ither isappear, be replace by seconary raiations (HCPs), or else the energy or irection is change significantly Neutron etectors utilize the conversion of the incient neutron into seconary charge particles Fast neutrons >.5 ev Slow neutrons <.5 ev 37 Slow neutron interactions lastic scattering ( n n ) Bringing the slow neutrons into thermal neutrons (.5 ev) Raiative capture reaction [or (n, ) reaction] Important in the attenuation or shieling Inirect etection of neutrons (n, ), (n, p), (n, fission) reactions Active neutron etectors 38

20 Raiation Measurement Systems/Lecture. Interactions Fast neutron interactions Prob. of neutron inuce reaction rops off rapily w/ increasing Scattering is ominant Recoil nuclei can be etecte in etectors The most efficient moerator, which slows own to lower energy, is hyrogen Inelastic scattering xcite recoil nuclei e excite, emitting gamma rays 39 Neutron cross sections For a fixe, the prob. per unit path length is a constant for any one of interaction mechanisms Microscopic cross section per nucleus [cm, barn (1 8 m )] Macroscopic x sec. N N = # of nuclei per unit volume tot Attenuation scatt capture I tot e t I Mean free path = 1/ tot ~cm for slow neutrons tens of cm for fast neutrons 4

21 Raiation Measurement Systems/Lecture. Interactions Interaction frequency, v [time 1 ] Neutron flux, (r) = vn(r)[length time 1 ] Reaction rate ensity reactions per unit time & volume reaction rate ensity ( r) n ( r) v reaction rate ensity ( r, ) ( ) 41 Neutron interactions in more etail Thermal neutrons (<.5 ev): Capture process pithermal neutrons (.5 ev kev): Resonances Fast neutrons ( kev MeV): Scattering Relativistic neutrons (> MeV): Spallation xamples of resonances 4

22 Raiation Measurement Systems/Lecture. Interactions Interaction types lastic scattering Inelastic scattering Nonelastic scattering Capture process Spallation lastic scattering nergy transfer: 1 H 1. H.89 4 He.64 1 C.8 56 Fe U Inelastic scattering Partial uptake of neutron by a nucleus Threshol reaction Use to moerate fast neutrons in the MeV region Incient ptl = prouct ptl e.g., 16 O(n, n ) 16 O* Nonelastic scattering Incient ptl prouct ptl e.g., 16 O(n, ) 13 C may show sharp resonances Threshol reaction 44

23 Raiation Measurement Systems/Lecture. Interactions Capture processes Capture of a neutron increases w/ ecreasing Proucing seconary raiation e.g., 113 C(n, ) 114 C, up to 9 MeV 1 B(n, ) 7 Li 6 Li(n, ) 3 H 1 H(n, ) H, =. MeV 14 N(n, p) 14 C, p =.6 MeV 45 Raiation exposure an ose Important for personnel protection at raiation proucing facilities & for the meical applications of raiation International Commission on Raiological Units an Measurements (ICRU) International Commission on Raiological Protection (ICRP) U.S. National Council on Raiation Protection (NCRP) 46

24 Raiation Measurement Systems/Lecture. Interactions Gamma ray exposure Linear quantity The charge Q ue to ionization create by the seconary electrons forme within a vol. element of air & mass m, when these seconary electrons are completely stoppe in air Q X m SI unit [C/kg] Historical unit, Roentgen (R) = 1 esu of charge (~ ion pairs) per.193 g (1 cm STP) of air 1 R = C/kg xposure rate X = the exposure rate constant (Table.1, Knoll) 47 Absorbe ose The mean energy absorbe from any type of raiation per unit mass of the absorber D m Historical unit, ra = 1 ergs/g SI unit, gray (Gy) = J/kg 1 Gy = 1 ra Note: 1 C/kg (exposure) = 33.8 Gy (ose) in air How much is 1 Gy? LD 5 = 5 Gy (tot. boy irraiation w/ photons) 5 Gy in water =.1 C increase in temp. 1 mgy = annual ose ue to natural raiation sources 48

25 Raiation Measurement Systems/Lecture. Interactions Dose equivalent Linear energy transfer (LT), L Ientical to the specific energy loss ( /x) excluing the bremsstrahlung Raiations w/ high L (e.g., HCP) result in greater biological amage even though the ose is the same Dose equivalent More aequately quantifies the probable biological effect of the given raiation exposure rather than the ose Define a unit of ose equivalent as the amount of any type of raiation that, when absorbe in a biological system, results in the same biological effect as one unit of absorbe ose elivere in the form of low L raiation H DQ Q = the quality factor, which increases w/ L Q = 1 for fast electrons an M raiations Q = ~ for alpha particles Historical unit, rem SI unit, sievert (Sv) 1 Sv = 1 rem 49 Fluence to ose conversion Fluence, =N/a ffective ose Representing an estimate of the overall biological effect of a uniform, whole boy exposure to the assume fluence H = h h = the fluence to effective ose conversion coefficient 5

26 Raiation Measurement Systems/Lecture. Interactions ICRP ose units H T,R quivalent ose in an organ or in tissue T ue to raiation R Introuce in ICRP publication 6 Obtaine from the absorbe ose D T,R average over a tissue or organ & multiplie by a raiation weighting factor w R that accounts for the ifferent biological effects of various raiations H T, R wr DT, R Not a point quantity but an average over a tissue or organ ffective ose, H H, w D, T T R T R w T H T R T R w T = the tissue weighting factors R 51 Operational ose quantities ffective ose is not a measurable quantity Instea, the operational quantities for use in practical measurements by the ICRP Weakly penetrating raiation beta particles w/ < MeV M raiations w/ < 15 kev Strongly penetrating raiation Photons at higher energies & neutrons at all energies 5