LECTURE 5: INTERACTION OF RADIATION WITH...
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LECTURE 5: INTERACTION OF RADIATION WITH MATTER
• All radiation is detected through its interaction with matter! INTRODUCTION: What happens when radiation passes through matter? Emphasis on what happens to emitted particle (if no nuclear reaction and MEDIUM (i.e., atomic effects) RELEVANCE: (1) Detection of Radiation (2) Radiation Safety (3) Environmental Hazards (4) Biological Effects − "Radiation Hypochondria" (5) Risk Assessment – Alternative Medicine TYPES OF RADIATION: (1) Positive Ions: X+q − α, fission, cosmic rays, beams (2) Electrons: β±, IC, Auger, cosmic rays (3) Photons: γ → x-ray → uv → visible (4) Neutrons: nuclear reactors, nuclear weapons, accelerators
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I. Positive Ions
Definition: Cation = ZA q
X+
, where q = atomic ionization state
A. Overview 1. Possible interactions: Nuclei σ ~ 10−24 cm2
Orbital e−s σ ~ 10−16 cm2
Result: ion-electron collisions dominate interactions 2. Qualitative Properties of ion-electron Collisions a. vI < < c (usually ~ 0.01 − 0.1 c) b. Mass (ion) > > Mass (e−) ; ∴ Many collisions required to stop ion c. Trajectory: straight line Analogy: bowling ball – ping-pong ball collisions B. Stages of Energy Loss 1. Electronic Stopping: vI > > ve- in atomic orbitals (95%)
a. Stripping: ZA qX+ → → Z
A ZX+ ; e.g., 816 2O+ → → 8
16 8O+
ion medium (electron sea)
~ 10−8 ;
Actual SRIM calculation of energy loss as ions stop in matter.
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i.e., ion loses all electrons (usually) in passing through matter
(∆X~100 atoms) b. Ion-Electron Collisions Multiple, sequential collisions ; straight-line trajectory c. Medium Effects (1) Ionization → Creation of multiple cations (from medium) –
electron pairs (2) Electronic Excitation: fluorescence (uv, x-rays, etc.) (3) Molecular Dissociation (free radical formation) 2. Intermediate Stopping: vI ≈ ve− (inner shells) a. Pickup: Incident ion begins to pick up electrons from stopping medium. K-shell first, since they have highest velocity (binding energy). b. Moderate Directional Changes (Dramatic size increase)
O +e-
v(1s)O e-
O e- O 8 7 5+ + + + → → → → → →6 O± 1,0
1s1 1s2 1s22s1 1s22s22p4±1
c. Ion slows down at each step and ionic charge is ≈ neutralized 3. Atomic ("nuclear") stopping: vI ≈ ve (valence shell) a. Ion charge ±1,0
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b. Elastic ion-atom collisions ∴ Mass (ion) ≈ Mass (medium atoms) – billiard ball collisions c. Result large directional changes: Straggling 4. Summary Go Stop 5. Concept of Range (R ≠ Rate) a. Definition: The average distance traveled by an ion with a given energy E during stopping process. b. Straggling: The distribution of ranges resulting from the statistical nature of the stopping process C. Energetics 1. Maximum energy loss per collision: ∆Emax
X+q e− a. ∆Emax is obtained when ion scatters at 180° (c.m.) From energy and momentum conservation (relativistic solution) ∆Emax = 4 E0 (Me/Mion) = E0/459 Aion (MeV) b. Example: 6 MeV 4He ion
∆Emax = 6.000 /459(4) = 0.003 MeV ∴ E(α)′ = 6.000 −0.003 = 5.997 MeV; i.e., long way to go 2. Average Energy Loss: <∆E> Average over all scattering angles, <∆E> ≈ 100 eV for 6.000 MeV α
∴ <Ncollisions> = E
E0
∆ =6 0000 0001
.. ≈ 104 − 105
3. Each collision creates a cation-electron pair; creates a measurable
current; basis for detectors
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D. Rate of Energy Loss: dE/dx: Specific Ionization (Related to radiation damage)
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1. Units: dEdx
MeVg / cm g /2= = ∝
MeVcm
MeV( cm )
;ρ
2 since ρ is a constant
i.e., thickness is expressed in g/cm2 2. Schematic Picture a. Assume a homogeneous sea of electrons
X+q (E = E0) X+q (E = E′) 3. Bethe-Bloch Formula – For Positive Ions in Matter Relativistically, by considering the momentum transfer to the electron (in the transverse direction) one can derive (see FKMM or ES for derivation):
−−−=− 22
2
2
42
)1ln(2ln4 ββπI
mvmv
neZdxdE
X+q
e−
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Where v is the velocity of the ion m is the mass of the ion Z is the atomic number of the ion
cv
=β
I is the ionization potential of the absorber n is the number of electrons per unit volume in the absorber This equation can be simplified in the non-relativistic case for fully-stripped ions (γ = q/Z = 1) :
∫ ∝∆∆
=ion
ion
EAZ
xEdx
dxdE 2γ
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Z,A,E
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FUNDAMENTAL EQUATION OF RADIATION DAMAGE BY POSITIVE ION a. Note: dE/dx increases with Z & A of ion dE/dx decreases with E of ion b. Terminology: dE/dx ≡ ionization ≡ energy loss ≡ radiation damage 4. Result: Bragg Curve Bragg peak – point at which maximum ionization occurs BASIC PRINCIPLE OF RADIATION THERAPY
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E. Range Determination Relation between Range and Specific Ionization:
∫=0
E
dEdEdxR
1. Calculations: Require knowledge of atomic orbital densities and binding energies. Some success for light ions 2. Range Graphs for 1H and 4He a. R is plotted for an Al absorber (ρ = 2.70 g/cm3) in mg/cm2 b. E of ion is expressed as E/A ; i.e., Eion = (E/A) Aion c. Examples: 500 MeV p: RP = 52 cm ≈ 20 inches 500 MeV α: Rα =R(125 MeV p) = 5.2 cm ≈ 2 inches 6 MeV α: Rα = 30µm (~ thickness of lung tissue)
A 100 MeV p has a range of 9000 mg/cm2. Density of Al is 2700 mg/cm3.Therefore, the thickness of Al required to stop a 100 MeV proton is:
cm3.327009000
=
What thickness of Al is necessary to stop a 500 MeV proton, the maximum energy of the IUCF synchrotron?
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Why do the range curves for alpha particles and protons diverge at low energy?
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3. Ranges of Other Ions in Al a. Scaling: Relative to protons
R(Zi, Ei, Ai) = A ZpA Z
i2
p i2 Rp(Ei/AI) =
AZ
i
i2
Rp (Ei/Ai)
b. Example: 500 MeV 20Ne ion
R (10, 500 MeV, 20) = 20102 • R 500
20
= 1
5 Rp(25 MeV) 15 (900 mg/cm2)
R (500 MeV 20Ne) = 180 mg/cm2 , or 0.67 mm 4. Methods exist to determine: a. dE/dx b. Other absorbers c. Compounds
we will not do this; procedures similar to finding range
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II. Electrons ( and Positrons prior to annihilation) A. Sources 1. Radioactive Decay: β±, IC, Auger, pair production 2. Electron Accelerators: Therapy, light sources 3. Cosmic-Ray Showers: lower atmosphere: X+q
B. Energy-Loss Mechanism -- σ(nucleus)/σ(atom) ≈ 10−8 again electron-electron collisions billiard ball 1. Ionization a. Repulsive charge-charge interaction b. Me = Me ; ∴ number of collisions much smaller c. Electrons relativistic above ~ 10 keV d. Products: scattered e− and cation-electron pair C. Range Energy Relation 1. Range determination – direct from graph
NET RESULT: Greater energy loss per collision; ∴ greater straggling; collisions less frequent ; ∴ ionization density much lower
e−
e−
e−
e−
e−
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Notice that a 1 MeV β has a range of 400 mg/cm2 in Al. What energy alpha particle has this same range?
Energy (in MeV)
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2. Absorber dependence At low Ee− , R ≠ f (absorber Z) 3. Example: 10 MeV e− in Al Re− ≈ 5500 mg/cm2 ≈ 2 cm (Rα (10 MeV) ≈ 10 mg/cm2 = 0.004 cm) (I estimated the 10 mg/cm2 from range chart above) D. Bremsstrahlung 1. When ve− ≈ c, e− − e− interactions decrease ; long range. ∴ higher probability of passing in vicinity of a nucleus ∴ path is bent due to Coulomb interaction and energy is radiated to
conserve momentum
2. Probability P (bremsstrahlung) = EZabs
P (ionization) 800 MeV 3. Result a. High Z – good photon producer b. Low Z – good shielding for high energy electrons. 4. Light Sources Create same effect by passing an electron beam through a magnetic field H.
By adjusting H and Ee− , can fine-tune Ehν. Gives uv and x-ray sources of high intensity and variable frequency;
significant role in future chemical research
hv
e-
+Ze-
θ
hν = f (θ, Ee, Z)
hν
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III. Electromagnetic Radiation -- Photons A. Sources: Electromagnetic Spectrum 1. Rearrangement of nuclear orbitals: γ-rays 2. Rearrangement of atomic and molecular orbitals: x-rays, uv … 3. Annihilation radiation ; e.g., e+ −e− → two 0.511 MeV γ s 4. Bremsstrahlung: electron deceleration 5. Cosmic ray showers B. Interactions 1. Photon: Carriers of Electromagnetic force ∴ must interact with electric charge Medium: a. electrons b. protons in nucleus 2. Mechanisms a. Photoelectric Effect: Eγ b. Compton Scattering: Eγ c. Pair Production: Eγ
h
e-
e-
νH
γ - e− most probable – size argument again
photon disappears e−
e−
Eγ ′ photon scatters
e+ e± pair produced
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C. Photoelectric Effect 1. Mechanism: Photon is completely absorbed by a charged particle; all
energy Eγ is transferred to an atomic electron, which is ejected from the atom 2. ∴ ONE COLLISION STOPS PHOTON γ e− (photoelectron); monoenergetic Ee− = Eγ − EB( n) ; i.e., electron is monoenergetic where EB(n) is electron binding energy for n orbital 3. When Eγ ≳ EB(n) , λγ ≈ λe- ∴ resonance-like situation; large wave function overlap leads to high absorption → probability 4. For Eγ ≳ EB
PPE ∝ ZE (MeV)
5
7 2γ / Best absorbers: ; heavy elements (Pb)
∴ Photopeak Detector sees electron (Einstein Nobel Prize)