lecture 5: interaction of radiation with...

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

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.

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

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

D. Rate of Energy Loss: dE/dx: Specific Ionization (Related to radiation damage)

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−

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

Z,A,E

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

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?

Why do the range curves for alpha particles and protons diverge at low energy?

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

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−

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)

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

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

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)