Basic Radiation Interactions,
Definition of Dosimetric Quantities,
and Data Sources
J.V. Siebers
Virginia Commonwealth University
Richmond, Virginia USA
2009 AAPM Summer School
Learningg Objectives
j
1.
2
2.
©JVS: 2009 AAPM SS
To review
T
i andd describe
d
ib the
th bbasics
i off
radiation interactions for understanding
radiation dosimetry
To review definitions of quantities
required for understanding radiation
dosimetry
Constants Units Conversions
©JVS: 2009 AAPM SS
©JVS: 2009 AAPM SS
Scope
Radiation Types
Ionizing
Interactions can remove
atomic orbital electrons
Particulate
-electron
-positron
-proton
-neutron
p
- alpha
- etc.
©JVS: 2009 AAPM SS
Non-Ionizing
Electromagnetic
Types
yp of ionizingg radiation

Di tl iionizing
Directly
i i radiation
di ti
Direct interactions via the Coulomb force along a
particles track
 Charged particles

electrons
 positrons
 protons
 heavy charged particles

©JVS: 2009 AAPM SS
Direct Ionization
Coulombic Interaction
e
A charged particle
exerts
electromagnetic
forces on atomic
electrons
©JVS: 2009 AAPM SS

Energy transfer can
result in the ejection
of an electron
(ionization)
Indirectlyy Ionizingg Radiation
Uncharged particles that must first transfer energy to
a charged particle which can then further ionize
matter
 Two
T step
t process
 Examples

Electromagnetic
El
t
ti radiations:
di ti
x- or γ-rays
 Neutrons

©JVS: 2009 AAPM SS
Indirectly Ionizing Radiation
Ph t l t i Eff
Photoelectric
Effectt
e-
h


©JVS: 2009 AAPM SS
Ejected
Ej
t d
electrons
further
ionize
matter
Radiant Energy
gy R

R – Total energy
energy, excluding rest mass,
mass
carried by particles
Photons: E = hν = hc/λ
 Electrons + other CPs: kinetic energy T

©JVS: 2009 AAPM SS
Energy imparted ε

imparted
ε - Energy
Rin  R
out   Q

Q
Rin 
e-
mass to energy conversion
i resulting
li
from interactions or radioactive decay
if(m→E), Q>0
e-
h
h
if(E→m), Q<0
   Rin c   Rin u   Rout c   Rout u   Q
©JVS: 2009 AAPM SS
Rout
D
©JVS: 2009 AAPM SS
Dose
d
dm
Gyy 

Energy deposited per unit mass

1 Gy = 1 J/kg

Knowledge of D is the object of dosimetry
Equilibrium Part 1:
R di ti E
Radiation
Equilibrium
ilib i
h
e-
Rin  Rout
h
e-
ee-
 
Rin Q
 Rout
RE
©JVS: 2009 AAPM SS
h
h
dQ
d

D Q 
dm
dm

RE
Radiation Sources
S

Radioactive decay





Accelerated charged particles



Direct
X-ray generators
Atomic energy transitions



Alpha-decay
Beta-decay
Electron capture
Isomeric transitions
Characteristic X-rays
X rays
Auger electrons
Interaction products
©JVS: 2009 AAPM SS
Radioactive Decayy
General balance equations
A
Z
P
A AR
Z ZR
D  ZARR R   Q
Q  M
©JVS: 2009 AAPM SS
P
 MD  MR
Q
©JVS: 2009 AAPM SS
Radioactive Decay
Activity
dN
A  N  
dt
At  A0 e
t1 
2
©JVS: 2009 AAPM SS
ln 2

 t
Radioactive Decay

α


A
Z
P
A 4
Z 2
D  24 He   Q
 α ‘s have short range
 / 

A
Z
P
A
Z 1

A
Z
P
A
Z 1
D  10     Q
D  10     Q
 Neutrino ( , ) results in spectrum
p
of  energies
g



 Emax and E are tabulated
 ( , ) are non-ionizing
Electron Capture
 ZA P  10 e  Z A1 D  v   Q
 Can occur when   energetically prohibited
 Followed by characteristic x-rays or Auger electron
so e c Transition
a s o
Isomeric
A *
 Z P  ZA P  00    Q
 decay from meta-stable state
Internal Conversion
 ZA P*  01 e  ZA P  01 e   Q
 Competes with isomeric transition
 Results in ejection of atomic electron
©JVS: 2009 AAPM SS
©JVS: 2009 AAPM SS
β+
Electron
Capture
©JVS: 2009 AAPM SS
O  N      1.732
1 732 MeV
M V
15
8
15
7
0
1

0
0
O  10 e  157 N  00  1.732 MeV
15
8
©JVS: 2009 AAPM SS
Accelerated Charged
g Particles

Di t use
Direct


Electrons, protons, …
Indirect via production of electromagnetic
radiation
Synchrotron radiation
 Bremmstrahlung

©JVS: 2009 AAPM SS
Synchrotron
Radiation
h
Magnetic Field
eSynchrotron image courtesy of http://www-project.slac.stanford.edu/ssrltxrf/spear.htm
©JVS: 2009 AAPM SS
Bremmstrahlung
h
brems
e-
©JVS: 2009 AAPM SS
Atomic Energy
gy Transition
Characteristic x-ray
xray h
©JVS: 2009 AAPM SS
Atomic Energy Transition
Auger Electron
e-
©JVS: 2009 AAPM SS
Quantifying
Q
y g Radiation Fields

Th far
Thus
f
R
 ε
 D

©JVS: 2009 AAPM SS
Radiation Fluence
dN

da
 pparticles 
 m 2 



©JVS: 2009 AAPM SS
N is number of particles
crossing
i sphere
h
surrounding P with crosssectional area da
Integrated over all
directions and energies
Single particle type
Equivalent
q
definition of fluence


l
nTracks

V



©JVS: 2009 AAPM SS
l = particle track
length through a
volume
l need not be
straight
Volume can be
irregular
U f l ffor M
Useful
Monte
t
Carlo applications
Energy
gy Fluence

Definition
dR

da

 J 
 m 2 
Poly-energetic
   E E  E  dE

Diff
Differential
ti l energy fluence
fl
 E  E   d  dE
©JVS: 2009 AAPM SS
Mono-energetic
  E
Attenuation
d   nt dl
 l  0 e  l
©JVS: 2009 AAPM SS
  nt 
1
 m 
 l  0 e


Attenuation coefficient
µ represents
t th
the iinteraction
t
ti ((removal)l) off
primaries from the beam
No consideration is given to what occurs as a
result of the interaction




 l
Secondary particles
Energy-to-mass conversion
…
To remove density dependence, tabulated as µ/ρ
[ 2/g]
[cm
/ ]
©JVS: 2009 AAPM SS
TERMA

Total Energy Release per unit MAss
  J  *
TERMA  

 kg 
 
Describes loss of radiant energy from uncharged
primaries as they interact in material
 Energy lost can be absorbed locally or at a distance

* For poly-energetic spectra
E 
©JVS: 2009 AAPM SS
TERMA    E  E  

E

 dE

 J 
 kg 
 
Aside:
Photon Interactions

©JVS: 2009 AAPM SS
To understand what happens with the
radiant energy removed, understand the
interactions
(e.g. γ interactions)
Photon interactions contributing to µ
   Rayleigh        
σ = Rayleigh + Compton scattering
 τ = photo-electric
 κ = pair production
 η = photo-nuclear

©JVS: 2009 AAPM SS
 m 
-1
Rayleigh
y g S
Scatteringg
Elastic coherent scattering of the photon
byy an atom
 Important for low energy photons
 Contributes
C t ib t < 20% to
t ttotal
t l attenuation
tt
ti
coefficient

©JVS: 2009 AAPM SS
Compton Scattering
e-
h





©JVS: 2009 AAPM SS
h 
NA Z

e
A
 cm2 


g


Compton
p
©JVS: 2009 AAPM SS
Photoelectric Effect
e-
h


©JVS: 2009 AAPM SS
Te  h  Eb  TA
Photo-electric



Z 34
 h 
23
τ increases when
shell can
participate in
reaction
©JVS: 2009 AAPM SS
Au
Pair Production
e-
h
pair
e+
Tavail  Te  Te  h  2 me c 2

©JVS: 2009 AAPM SS
mo c 2

T
di 
 radian
Triplet Production
Tavail  h  2me c
h
ee-
triplet
e+
©JVS: 2009 AAPM SS
h  2me c
T
3
2
2
Photo-nuclear interactions

(γ n) (γ
(γ,n),
(γ,Xn),
Xn) (γ,p),
(γ p) …

BE (Binding Energies) result in thresholds
>~ 10 MeV
Cross-section is small (η<0.1µ)
Neutrons are ppenetratingg


©JVS: 2009 AAPM SS
©JVS: 2009 AAPM SS
Pb attenuation coefficient
©JVS: 2009 AAPM SS
Relative importance of interactions
©JVS: 2009 AAPM SS
Summary photon interactions
©JVS: 2009 AAPM SS
Energy transferred to charged particles
per-interaction
i t
ti
nonr
 general
 tr   Rin u   Rout u   Q





Average
©JVS: 2009 AAPM SS
=
=
=
photo
compton
pair
 tr


ni
ni
 tr
 l  0 e


Recall
Attenuation coefficient
µ represents the interaction (removal) of
primaries from the beam
No consideration is given to what occurs as a
result of the interaction




 l
Secondary particles
Energy-to-mass conversion
…
To remove density dependence, tabulated as µ/ρ
[cm2/g]
©JVS: 2009 AAPM SS
Mass-energy transfer coefficient

Describes the transfer of energy to charged
particles
ti l
tr   tr  
 
  h  
©JVS: 2009 AAPM SS
KERMA

Kinetic Energy Release per unit MAss
d  tr
KERMA  K 
dm
tr




©JVS: 2009 AAPM SS
*
 J 
 kg 
 
The transfer of radiant energy from uncharged primaries
to charged particles as they interact in a material
Energy transferred can be absorbed locally or at a distance
*Mono-energetic, integrate for poly-energetic
Net energy transfer
Ruru R
 trnet trnettr trRout
Routuu Rur Rout
 Rin inuu R out
uQ Q
nonr
nonr
r

r
Accounts for portion of kerma is radiated away
T’
Te-
h brems
hv
Compton example
h
Te-
 trnet  Te  hvbrems

h 
©JVS: 2009 AAPM SS
Mass energy absorption coefficient
Mass-energy
R di ti loss
Radiative
l
ffraction
ti g

g  1

 trnet
 tr
M
Mass-energy
absorption
b
ti coefficient
ffi i t
en
tr
 1  g 


©JVS: 2009 AAPM SS
Kerma Components
K  Kc  Kr

C lli i K
Collision
Kerma
d  trnet
Kc 
dm


en
Kc  

*
Portion of kerma that remains collisional energy losses
(non-radiative)
Radiative Kerma

©JVS: 2009 AAPM SS
Portion of kerma (transported elsewhere) by radiative losses
Exposure and W

Exposure
Historical
Hi
t i l radiation
di ti unitit
 Ionization density in air


Related to air collision kerma by mean energy
required to produce an ion pair
 e 
X   K c air  
 W air
W 
 ev 


33.97
 


 ip 
 e  air
©JVS: 2009 AAPM SS
dQ  C 
X
dm  kg 
C
 kg 
 
 1.602  1019 ( J eV )   1 ip 
J 


33.97
 1.602
  electron 
19
 C 
1
602

10
(
C
electron
)


 
Aside
Indirectly ionizing radiation

How many ionization events can be initiated by a
10 keV photo-electron?
1  ipp 
? ip  10  10  eV  

294
ip




33.97  eV 
3
©JVS: 2009 AAPM SS
Equilibrium Part 2:
Charged Particle Equilibrium
h
e-
ee-


e-
e-
 Rin c   Rout  c
h
   Rin c   Rin u   Rout c   Rout u   Q
   Rin u   Rout u   Q  ...   trnet

©JVS: 2009 AAPM SS
CPE
CPE
d  d  trnet
D

 Kc
dm dm
CPE
CPE
Charge
g pparticles


e-, e+, p, α, …
Sources



Accelerated beams
Radioactive decay
Reaction products




Coulomb force interaction




©JVS: 2009 AAPM SS
(e,γ) , …
(n,p), …
((e,e),
) …
Inverse square dependence
Semi-continuous
Semi
continuous rather than discrete interactions
Results in energy loss and directional change
Interaction can be classified by impact parameter
CP interactions
b = impact parameter
a = atomic
t i radius
di
n = nuclear radius
undisturbed incident trajectory
b

b>>a
Soft, atomic interaction

b~a
Hard, knock-on interaction

b<<a
Nuclear interactions
possible
©JVS: 2009 AAPM SS
a
Stopping
S
pp g ppower

E
Energy
loss
l
per unitit path-length
th l th
dE
S
dx

 MeV 
 cm 
S
dE

  dx
 MeV cm 2 


g


S
Separate
t components
t bby interaction
i t
ti
S

©JVS: 2009 AAPM SS

Scol


S rad

Stopping
S
pp g ppower formulations
Basedd on B
B
Bethe-Bloch,
th Bl h Heitler,
H itl …
 Electrons: ICRU 37

  2




2

S


1
Z
2
2
ln 
  F      
2
r
m
c
N


 
e
e
A
2
2
2






A
  Collisional
2
I
m
c
e
 



S rad
2
e
r NA 2

Z E  me c 2 B r

13 A
137


Material dependent terms
©JVS: 2009 AAPM SS

  T me c 2

v
c
 2

F     1   2 1    2  1 ln 2 
8




©JVS: 2009 AAPM SS
Water--electrons
©JVS: 2009 AAPM SS
Material Comparisons
Electron stopping powers
©JVS: 2009 AAPM SS
Stopping
S
pp g ppower formulations

Scol

Protons/ Heavy charged particles: ICRU 49
 4 r me c N A
2
e
2
1
2
Z 2  1  2me c 2  2Wm
z
ln  2
A
 2  I 1  2






C 
2
      B1  B2 

Z 2



With Wm, the maximum energy
gy that can be
transferred to an electron in a single collision
 2me c 2  2 
Wm  
2 
1




©JVS: 2009 AAPM SS
2

me
1
 me  
  
1  2
2
M
 M  
1 

Material dependent terms
©JVS: 2009 AAPM SS
Water--protons
p
©JVS: 2009 AAPM SS
Recall KERMA

Transfer of radiant energy from uncharged
primaries to charged particles as they interact in
a material
d  tr
K
dm
K
Emax
 tr ( E ) 

E


E 0 E    dE
K  Kc  Kr
d  trnet
Kc 
d
dm
©JVS: 2009 AAPM SS
Kc 
Emax
 en ( E ) 

E
E 0 E      dE
CEMA

Converted Energy per unit MAss





Describes
D
ib energy transfer
f from
f
primary
i
charged
h
d particles
i l
to secondary charged particles (δ-rays)
Energy
gy transferred can be absorbed locallyy or at a distance
Defined in ICRU 60
Charged particle analog to KERMA
dE  J 
C=dEc/dm
C c  
dm  kg 
Emax

©JVS: 2009 AAPM SS
CC =integral().
0  E  E 
Scol  E 

dE
CEMA example
p

Thin slab


CP Φ

Energy loss
dE  
Sc

t
t
©JVS: 2009 AAPM SS
Fluence Φ of incident
mono-energetic charged
particles
CEMA
C 
δCPE

constant S/ρ
straight particle paths
When δ-ray equilibrium exists, CEMA = dose
Sc

 J 
 kg 
 
Restricted CEMA


Excludes
E
l d energy llosses to
t energetic
ti (E
(E>Δ)
Δ) δ-rays
(aka knock-on electrons)
Such δ-rays are added to the fluence Φ’
C   E  E 
L  E 

dE
 E  E    E  E    col
E   E 
©JVS: 2009 AAPM SS
Restricted Stopping Power
L




©JVS: 2009 AAPM SS

Scoll
dEke
k 



 dx
Includes energy transfers only up to energy Δ
Excludes energy losses from to energetic
(E>Δ) δ-rays
Δ is chosen with respect to the distance the δ-rays
can travel in the material of interest
Restricted
est cted C
CEMA
C  
Emax

 E  E 
L  E 

dE 
Energy loss for Ee > ∆


©JVS: 2009 AAPM SS
lim
lim
 Emax
lim
lim
 Emax
L

C  C

Scol



0
 E  E 
S col  E 

dE
Track end term & electrons
generated outside volume
Path Length and
Range

Variations in energy loss and scattering result in
different paths through a material ( & different
maximum penetration distances)



p = total distance traveled byy a pparticle w/o relation to
direction
R = average path length
CSDA Range
RCSDA  
To
0
©JVS: 2009 AAPM SS
1
dE
S (E) 
 g 
 cm 2 


Range
Rt = average depth of penetration in the original
particle direction
 R50 = range
g at 50% max dose
 Rp = practical or extrapolated range, intersection of
tangent @R50 with brems tail

©JVS: 2009 AAPM SS
Range-Energy
Relationships

Incident energy
E0  2.33R50

Average energy at depth (Harder’s Formula)
 depth 
E  Eo 1 

R
p


©JVS: 2009 AAPM SS
Equilibrium Part 3:
CPE Revisited



For an external beam
beam, if
no attenuation, CPE
exists beyond Dmax
But, e- production due to
attenuation
T
True
CPE cannott exist
i t
for external beam
©JVS: 2009 AAPM SS
Equilibrium Part 4:
Transient Charged Particle

For external
F
t
l
beams
D( x)   K c ( x)
TCPE

©JVS: 2009 AAPM SS
Neutron Interactions

….see text
t t
©JVS: 2009 AAPM SS
Problem #5

E h problem
Each
bl give
i
©JVS: 2009 AAPM SS
Problem #5
,
©JVS: 2009 AAPM SS
,
©JVS: 2009 AAPM SS
Thank you for your attention
©JVS: 2009 AAPM SS