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Radiation and radiation dosimetry
Spring 2006Introduction
Audun Sanderud
Dep
art
men
t o
f P
hys
ics
Un
iver
sity
of
Os
lo
Dep
art
men
t o
f P
hys
ics
Un
iver
sity
of
Os
lo Contents• Interaction between ionizing radiation and
matter
• Radioactive and non-radioactive radiation sources
• Calculations and measurement of radiation doses (dosimetry)
• The effect of radiation on relevant substances like water and important biological molecules
• The understanding of: the biological effects of ionizing radiation measurement principles and methods the principles of radiation protection
Dep
art
men
t o
f P
hys
ics
Un
iver
sity
of
Os
loLearning objectives
• To understand primary and secondary effects of ionizing radiation
• How radiation doses are calculated and measured
• The understanding of the principles of radiation protection, their origin and applications
• This will provide a tool for evaluating possible dangers in the use of ionizing radiation
AtomsMatter
Dep
art
men
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f P
hys
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Un
iver
sity
of
Os
lo Overview
Ionizing
radiation
Radiation
scours
Interactions Effects
H2O
DNA
Molecules Cells Humans
Radiation
protection
§
Dosimetry
dD
dm
e=
-Photons
-Charged particles
-Neutrons
-Photons
Calculation Measurement
enAir
Air
Dæ öm ÷ç= Y ÷ç ÷ç ÷ç rè ø
AirAir
WD X
e
æ ö÷ç= ÷ç ÷çè ø
Interaction Between Ionizing Radiation And Matter,
Part 1 Photons
Audun Sanderud
Dep
art
men
t o
f P
hys
ics
Un
iver
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of
Os
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• Five interaction processes between photons and matter:Rayleigh scatteringCompton scatteringPhotoelectric effectPair- and triplet -productionPhoton-nuclear reactions
• Probability of interaction described by cross section
• Scattering and energy transfer described kinematics
• Joint gives the possibility to calculate radiation doses
Dep
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Un
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lo Photon Interaction
Scattering
Absorption
Dep
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Un
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loRayleigh/Coherent scattering
• Scattering of photons without loss of energy
• Photons absorbed by the atom, then emitted with a small angel
• Depend on photon energy, hν, and atomic structure
• The atomic cross section of coherent scattering:
• Special case hν → 0 : Thomson scattering
2æ ö÷çµ ÷ç ÷çè øR
Z
hs
n
Dep
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Un
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lo Photon attenuation
• Probability of a photon interaction: μdx
• Number of photons interacting : Nμdx
MatterPhotons
N
dx
N-dN
0
dNdN=Nµdx = µdx
N
µxN N e
Dep
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Un
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lo Average pathlength• The probability of a photon not interacting: e-
x
• Normalized probability:
0
, 1,µx µx µxni nip Ce Ce p µe
0
1Average pathlength: µxx xµe
µ
Dep
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Un
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lo Attenuation - Cross section • µ: Denote the number of photons with a
single energy E and direction which interacts per length unit
• µ=p/dx, probability of per length unit; macroscopic
• σ: Cross section target area; surface proportional with the probability of interaction
• σ=p/nvdx, σ: cross section, probability per atom density nv, and length unit; microscopic
• µ=(NA/A): mass density, (NA/A): number of atoms per mass unit
• Look at two spheres:
• equals total area: (r1+r2) 2
Cross sectionD
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Atom, radius r2
Incoming particle, radius r1
(direction normal to the surface)
• N particles move towards an area S with n atoms
• Probability of interaction: p=Scs/S = n/S• Number of interacting particles: Np= Nn/S
Cross section (2)D
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Atom cross section,
S
missedhit
Incoming particle
• The cross section of an interaction depend on:
- Type of target (nucleus, electron, ..)- Type of incoming particle- Energy of the incoming particle- Distance between target and particle
• Cross section calculated with quantum mechanics -
visualized in a classical window
Cross section (3)D
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• A wave beam interacts with a weak potential
• The Hamiltonian is:
• Free particle wave function:Initial:
Final:
What is the probability of elastic scattering by an angel θ of a photonof energy hν?
Dep
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Un
iver
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Os
loCalculating Rayleigh Cross section ( )V r
20
1( ) ( )
2H p V r H V r
m
/00
i ii p r E ti V e
/00
f fi p r E t
f V e
( )V r
0i
0f
20
2/3
2
22
4/ 40
2
1
16 h sin / 2
i fi p p r
Coulombfield
V Ze r
d md rV r e
d
Ze
• The photon energy loss due to the interaction is significant• The interaction is a photon-electron scattering, assuming the electron being free (binding energy neglect able)• Also called Compton scattering
Incoherent scatteringD
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h e-
h’
T
• Kinematics:
• Solution:
Compton scattering(1)D
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2 2 2
Energy conservation
cos cosMomentum conservation
sin sin
( ) 2 "Law of invariance"e
h h T
h hp
c ch
pc
pc T Tm c
n n
n nj q
nq j
¢= +
¢= +
¢=
= +
( )2
2
, , cot 1 tan2
1 1 cos e
e
h hh T h h
m chm c
n n qn n n j
nq
æ ö æö÷ç ÷ç¢ ¢ ÷= = - = +ç ÷ç÷ ÷ç çæ ö ÷ç è øè ø÷ç ÷+ -ç ÷ç ÷çè ø
Compton scattering(2)D
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1E-3 0.01 0.1 1 10 1001E-3
0.01
0.1
1
10
100 o
o
o
o
o
o
hv' (
MeV
)
hv (MeV)
• Klein and Nishina derived the cross section of the
Compton scattering• The differential cross section for photon scattering at angel , per unit solid angel and per electron,
may be written as.
r0: classic electron radius; distance between two electrons with potential energy equal electron rest mass energy; mec2= e2/40r0
Compton scattering-Cross sectionD
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2220
2
0 2
' 'sin
2 '
sin ,
e
e
d r
d
ed d d r
m c
q
q
s n n nq
n n n
q q f
æ ö æ ö æ ö÷ç ÷ ÷ç ç÷= + -ç ÷ ÷ç ç÷ ÷ ÷ç ç ç÷ç è ø è øWè ø
W = =
z
x
y
d
(The incoming photon
direction along the z-axis)
• The cylinder symmetry gives:
Compton scattering-Cross section(2)D
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22 2
0
' 'sin sin
'ed rd
s n n np q q
q n n n
æ ö æ ö æ ö÷ ÷ ÷ç ç ç= + -÷ ÷ ÷ç ç ç÷ ÷ ÷ç çç è ø è øè ø
• Denotes the probability of finding a scattered photon inside the angel interval [+d] after the interaction with the electron• The total cross section per electron e is: 2
2 20
0
' 'sin sin
'e r dp
n n ns p q q q
n n n
æ ö æ ö÷ ÷ç ç= + -÷ ÷ç ç÷ ÷ç çè ø è øò
• Atomic C. scat. cross section is then: ae
• Scattered photons are more forward directed as initial energy increase
Compton scattering-Cross section(3)D
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The
dif
fere
ntia
l cro
ss s
ecti
on, d
e/d
[c
m2 /
radi
an]
Photon scatter angel,
• The photon spectra of the scattered photons:
Compton scattering-Cross section(4)D
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( ) ( ) ( )
( )
( ) ( )
2
22 2 2 20
2
2 sin' ' '
1 1 cos
'1 1
' ' '
e e e
e
e e e e
d d dd d
d h d d h d d h
hh
hm c
d r m c m c m ch h
d h h h h hh
q
q q
s s s qp q
n n n
nn
nq
s p n nn n n n nn
W= =
W W
¢=æ ö÷ç ÷+ -ç ÷ç ÷çè ø
ß
æ öæ ö÷ç ÷ç ÷ç ÷= + - + - + ÷çç ÷÷ç ÷ç ç ÷è ø÷çè ø
• The cylinder symmetry gives:
Compton scattering-Cross section(5)D
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The photon energy, hv’ [MeV]
de/
d(hv’)
[cm
2/M
eV
]
• More correct treatment of the cross section gives a small atom number dependence:
Compton scattering-Cross section(6)D
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The photon energy, hv’ [MeV]
In
cohere
nt
ato
mic
cro
ss
sect
ion p
er
ato
m n
um
ber
a
/Z [
cm2]
• The energy transferred to the electron in a
Compton process:
Energy transferredD
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T h hn n¢= -
• The energy-transfer cross section:
• The average fraction of transferred energy:
'e tr e ed d dT h h
d d h d hq q q
s s s n nn n
-= =
W W W
e tr
e
T hs
ns
=
• Mean fraction of energy transferred to the electron:
Energy transferred(2)D
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• Photon is absorbed by an atom/molecule; resulting in an excitation or ionization
Photoelectric effectD
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• The vacancy is filled by an electron from an outer orbit and characteristic radiation is emitted
Ta
q
e-X X+
• The binding energy of the electron Eb most be accounted for:
Photoelectric effect (2)D
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b a bT h E T hv En= - - -;
• The atomic cross section is approximately when Eb=0 assumed:
72 2
2 4 5 22
22 2 sin 1 4 cose
ee
m cd hr Z
d h m c
t na q q
n
æ öæ ö ÷ç÷ç ÷÷= ç +ç ÷÷ çç ÷÷ç ÷çW è ø è ø
: Fine structure constant : Points to the emitted electron
Photoelectric cross section (d/d)/
Photoelectron – distribution angleD
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• The energy of characteristic radiation depend on
the electron structure- and transitions
• The K- and L-shell vacancies: photons with energy hK and hL are emitted after de-excitation
• Emitted photons are isotropic distributed
• The fraction of events that occur in the K- or L-
shell: PK [hb)K] andPL [hb)L]
• The probability of c.r. being emitted: YK and YL
• The energy transport away from the atom by c.r.:
PKYKhPLYLhL
Characteristic radiationD
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• Alternative path which the ionized atom dispose energy
• Shallow outer-shell vacancies are emitted from the atom with kinetic energy corresponding to its excess energy
• Low Z: most Auger• High Z: most characteristic radiation• Auger electrons are low-energetic
Auger effectD
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• It is observed:
Photoelectric cross sectionD
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• The fraction of energy transferred to the photoelectron
( )( )1K K K K L L L
tr
h P Y h P P Y h
h
n n nt t
n
- - -=
• But: Auger electrons are also given energy• The energy-transfer cross section of the electron:
, 4 5,1 3( )
n
m
Zn m
ht
nµ < < < <
bh ET
h h
nn n
-=
• Photon absorption when an electron-positron pair is created
Pair productionD
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• Occurs in a Coulomb force field from an atom nucleus or atomic electron (triplet production)
• Conservation of energy:
Pair production (2)D
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22 eh m c T Tn + -= + +
• Average kinetic energy after absorption:
2em c
Tq »
• Estimate of scatter angle of electron/positron:
22
2eh m c
Tn-
=
• Total cross section:2 2
0 increases with r Z P P hk a n»
• An electron-positron pair is created in a field from an electron – conservation of energy:
Triplet productionD
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21 22 eh m c T T Tn + - -= + + +
• Note that the atomic electron can gain significant kinetic energy
• Threshold photon energy: hv = 4m0c2
• Average kinetic energy after absorption: 22
3eh m c
Tn-
=
• Pair production most important:
Pair- and triplet productionD
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( ) 1 , 1 2, depending only on
( )
tripletC h
pair CZ
kn
k» < <
The photon energy, hv’ [MeV]
Ato
mic
cro
ss s
ect
ion a
/Z2
[cm
2]
C (Z=6)Al (Z=13)Cu (Z=29)Pb (Z=82)
Triplet production atp/Z2
• Photon (energy above a few MeV) excites a nucleus
• Proton or neutron is emitted
• (, n) interactions may lead to radiation protection problems• Example: Tungsten W (, n)• Not important in dosimetry
Photonuclear interactionsD
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• Total coefficient of photon interaction:
Attenuation coefficientsD
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Rsm t s kr r r r r
= + + +
• Coefficient of energy transfer to electrons:
• Braggs rule for mixtures of n-atoms/elements:
1
1
,n
ii i n
imix ii
i
mf f
m
m mr r=
=
æ ö æ ö÷ ÷ç ç÷ = ÷ =ç ç÷ ÷ç ç÷ ÷ç çè ø è øå
å
tr T
h
m mr r n
=
Attenuation coefficients (2)D
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http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html
Photon Interaction Summary
( )( )
( )
2
2
1 / 1 cos
cot 1 tan 2
e
e
hh
h m c
T h h
hm c
nn
n q
n n
n qj
¢=+ -
¢= -
æ ö÷ç= + ÷ç ÷çè ø
2220 ' '
sin2 '
ed r
d q
s n n nq
n n n
æ ö æ ö æ ö÷ç ÷ ÷ç ç÷= + -ç ÷ ÷ç ç÷ ÷ ÷ç ç ç÷ç è ø è øWè ø
( )1fe K K K K L L LT h P Y h P P Y hn n n= - - -
µtr/ρfeT
h
tr n
'e tr ed d h h
d d hq q
s s n nn
-=
W W
202h m c
h
nkr n
æ ö- ÷ç ÷ç ÷ç ÷çè ø
Photon interaction
Processes
Kinematics
Cross section
Meanenergy
transferred
2
a R
Z
hs
n
æ ö÷çµ ÷ç ÷çè ø
Compton Rayleigh Photo el.eff. Pair/triplet
T=0T = h-Eb-Ta
= h-Eb
h= 2m0c2 + Tˉ + T⁺
( )
4
3a
Z
ht
nµ
2 20a par
a para tri
r Z P
CZ
k a
kk
=
=
2
2
2
2
2
3
epar
etri
h m cT
h m cT
n
n
-=
-=
e tr
e
T hs
ns
=
Photon-nuclear reactions
SummaryD
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