Chapter 2. Radiation
1.Radioactivity
2.Radiation interaction with Matter 3.Radiation Doses and hazard Assessment
1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides
2.1 Radioactivity
1) overview2) Photon Interactions3) Neutron Interactions4) Interaction of Heavy Charged Particles with
Matter5) Scattering of Electrons in a Medium
2.2 Radiation interaction with Matter
Radiation is everywhere
We live in a sea of radiation…
Cosmic
Inhaled Radon
RocksRadioactive Elements
PlantsBodies
1) overview
Discovery of Ionization by Radiation
X-rays and radioactivity discharged a charged electroscope. Curie and Rutherford attributed the discharge to the ionization of air by these rays.
Electroscopes
Charged Discharged
An electroscope consists of two gold leaves suspended from a metallic conductor in a glass jar
He + 25 eV He+ + e-
He+ + 54 eV He2+ + e-
Ionization energy (IE eV) per ion pair of some substancesMaterial Air Xe He NH3 Ge-crystalAverage IE 35 22 43 39 2.9
The minimum energy required to remove an outer electron from atoms or molecules is called ionization potential. Ionizing radiation also remove electrons in atomic inner shell, and the average energy per ion pair is considered ionization energy
Ionization Energy of GasesHigh energy particles and photons that ionise atoms and molecules along their tracks in a medium are called ionizing radiation
1) overview
directlyionizing radiation
indirectly ionizing radiation
1) overview2) Photon Interactions3) Neutron Interactions4) Interaction of Heavy Charged Particles with
Matter5) Scattering of Electrons in a Medium
2.2 Radiation interaction with Matter
Interaction of Photons with Matter
Photon Energies
Visible red light 1.5 eVvisible blue light 3.0 eV
UV few eV-hundreds eV
X-rays 1 to 60 keV
Gamma rays keV - some MeV
Interactions of gamma rays with matter:
photoelectric effect
Compton effect
Pair productions
KE=h-EB
Photoelectric process
a very crude approximation
Compton Effect of Gamma RaysSpectra of an Original and Scattered X-rays
at a Particular Fixed Angle.
Intensityarbitraryscale
Originalspectrum
scatteredspectrum
Feynman Diagram forthe Compton Effect
When a photon transfers part of its energy to an electron, and the photon becomes less energetic is called Compton effect.
re is the classical electron radius
Pair Production of Gamma Rays
Feynman Diagram for Pair Production
A negative charge in reverse isequivalent to a plus charge.
A nucleus or field.
Gamma photons with energy greater than 1.02 MeV produce a electron-positron pair is called pair production.
The fate of the positron?
Gamma-ray Three Modes of Interaction with Matter
Interaction of Photons with Matter
1 5/ MeV
Pairproduction
Photo-electric
Compton scattering
Photoelectric effect Compton scattering pair production
Attenuation of Gamma Rays by MatterIntensity of Parallel Gamma Rays as a
Function of Absorber Thickness.
Thickness x
Intensity, IGamma-ray intensity decreases exponentially as the thickness of the absorber increases.
I = Io e–μx
I: Intensity at distance xμ: absorption constantx: thickness
the interaction probability P(x) that a particle interacts somewhere along a path of length x is
The probability th that a particle does not interact while traveling a distance x
Average Travel Distance Before An Interaction
p(x)dx be the probability that a particle interacts for the first time between x and x + dx.
the average distance: the average distancesuch a particle travels before it interacts.
mean-free-path length
Half-Thickness: the thickness of a medium required for half of the incident radiation to undergo an interaction
What is the thickness of a water shield and of a lead shield needed to reduce a normally incident beam of 1 MeV photons to one-tenth of the incident intensity?
For water μx(1 MeV) = 0.07066 cm-1 and for lead μx(1 MeV) = 0.7721 cm-1
for water x1/10 = 32.59 cm, for lead x1/10 = 2.98 cm x1/2 = 0.898 cm x1/100 = 5.96 cm
1) overview2) Photon Interactions3) Neutron Interactions4) Interaction of Heavy Charged Particles
with Matter5) Scattering of Electrons in a Medium
2.2 Radiation interaction with Matter
Absorption of neutrons
Elastic scattering
• neutron collides with proton (e.g. hydrogen nucleus) and shares its kinetic energy
• dominant process with fast neutrons of energy < 6 MeV in tissue
Absorption of neutronsInelastic scattering
• fast neutron (~ 6 MeV and above) interacts with nucleus and causes disintegration
with the atomic nuclei
Neutrons lose very little energy per collision when they collide with heavy nuclei. Nuclei of hydrogen and neutrons have approximately the same mass. In collisions with hydrogen nuclei, neutrons can transfer almost all their kinetic energy to the hydrogen nuclei. Thus, hydrogen‑containing compounds such as H2O, paraffin wax, and hydrocarbons (oil and grease) slow down neutrons rapidly.
Thermal Neutrons Cross SectionsUranium for Fission Fuel in Nuclear Reactor
113Cd 233U 235U 238U c /b 19,820 46 98 2.7f /b 530 580 2.7×10-6
t1/2/y 1.6×105 7×108 4.5×109
Thermal Neutrons Cross Sections
Cross section () a measure of reaction probabilityThermal neutron cross sections (c)Thermal neutron cross section for fission (f)
1H 2H 12C 14N 16O 113Cd c /b 0.33 0.00052 0.0034 1.82 0.0002 19,820
Moderators: H2O vs. D2O vs. C
Thermal Neutrons Cross SectionsThe extremely large thermal neutron cross section of 113Cd makes cadmium a good neutron absorber or eliminator.
the neutron-capture reaction 113Cd (n, ) 114Cd leads to a stable isotope. These properties made cadmium a very desirable material for the nuclear technology industry.
Neutrons Capture Cross Sections of Cadmium Isotopes
106Cd 108Cd 110Cd 111Cd 112Cd 113Cd 114Cd c / b 1 1 0.1 24 2.2 19,820 0.3
Abundance/% 1.25 0.89 12.45 12.80 24.13 12.22 28.37
Conclusion:Slow neutrons (0.03 to 0.001 eV) are more effective for inducing fission of 235U
Fast neutrons (10 MeV to 10 KeV) favours neutron capture reaction of 238U
Light atoms are effective moderators
1) overview2) Photon Interactions3) Neutron Interactions4) Interaction of Heavy Charged Particles with
Matter5) Scattering of Electrons in a Medium
2.2 Radiation interaction with Matter
4) Interaction of Heavy Charged Particles with MatterSketch of Alpha Particle Paths in a Medium
source
Shield
Fast moving protons, 4He, and other nuclei are heavy charged particles.
Coulomb force dominates charge interaction.
They ionize and excite (give energy to) molecules on their path.
The Born-Bethe Formula for Energy Loss of Charged Particles.
- dEdx
= KM z
E
2
Range of Heavy Charged Particles in a Medium
Variation of Intensity as a Function of ThicknessDetector
Absorber
Intensity
thickness
sourcestraggling
Range
source
Shield
Particles lose all their energy at a distance called range.
Scattering of Electrons in a Medium
Fast moving electrons are light charged particles.
They travel at higher speed., but scattered easily by electrons.
An Imaginary Path of a particle ina Medium
source
Shield
Range of Light Charged Particles in a MediumIntensity (I ) of Electrons with the Same Kinetic Energy
as a Function of Thickness (x) of Absorber.
I
x
Extrapolatedrange
Rangestraggling
absorberI0
Idetector
I0
x
Variation of Intensity as a Function of ThicknessDetector
Absorber
Intensity
thickness
sourcestraggling
Range
Range of particles is not as well defined as heavy charged particles, but measured range is still a useful piece of information.
Braking Radiation of particles Influenced by Atom
Bremsstrahlung Radiation and itsFeynmann Diagram
E = h v
e– .h v
Feynmanndiagram
Bremsstrahlung (braking) radiation refers to photons emitted by moving electrons when they are influence by atoms.
Interaction of Beta particles with Matter
Beta particles interact with matter mainly via three modes:
Ionization (scattering by electrons)
Bremsstrahlung (braking) radiation
Annihilation with positrons
Ionization
Braking radiation
Annihilation
Example : At what energy does an electron moving through gold lose as much energy by bremsstrahlung as it does by ionizing and exciting gold atoms?
For gold Z = 79 and for equal energy loss by both mechanisms, we have find for electrons M = me
that E = 700/79 = 8.9 MeV.
Stopping power (~dE/ds)/p in mass units (MeV cm2/g) for protons and electrons.
Range or path length pR, in mass units (g/cm2), in the continuous slowing down approximation.
αβγioization radiation
2 MeV range(m) ion pairs/mm α 0.01 6000 β 2-3 60 γ *10 ~1
air
α β γionizing process D D Itrack Straight Defle Straightionization Large medium SmallPenetration weak medium long
1) overview2) Photon Interactions3) Neutron Interactions4) Interaction of Heavy Charged Particles with
Matter5) Scattering of Electrons in a Medium
2.2 Radiation interaction with Matter
能量损失ee b
v
NZmv
eZdxdE )(2
lg4
~ 22
421
2.1 Two-body collisionsFormula
Tacit assumptions:Well defined Z1Independent two body collisionsStochastic process, average E.L.
2.2 Collisions with atoms Elastic and inelastic energy loss
2.3 Adiabatic cutoff Momentum approximation free Harmonic model free bounded
2.4 Under which circumstances is classical mechanics applicable
两体碰撞
iiiTN
dxdE
TdN
pdpd 2
INCIDENT ION BEAM
质心C
M1,V-Vc
Vc ,M2
Vc
V-Vc
θp
质心系坐标散射
质心C
M1,V-Vc
Vc ,M2
Vc
V-Vc
θp
质心C
M1,V-Vc
Vc ,M2
Vc
V-Vc
θp
质心系坐标散射
φ
ψp
M1
M2
V1
V2
实验室坐标系散射
φ
ψp
M1
M2
V1
V2
φ
ψp
M1
M2
V1
V2
φ
ψp
M1
M2
V1
V2
实验室坐标系散射
图 1-1 粒子 - 粒子两体碰撞入射粒子散射角: Φ (实验室系)和 θ (质心系)靶粒子散射角: ψ (实验室系)2
121 vME 入射粒子能量: 靶粒子获得的能量:
2222
1 vMT
1M2M
cV
cV
cV
1V
2V
cV V
cV V
速度矢量相加关系
1 2V V和 分别是碰撞以后入射粒子与
靶粒子在实验室系下的速度
是入射粒子速度V cV 是质心速度是入射粒子速度V
22 2 ,
2
1 2
sintgcos
MM M
靶粒子得到的能量 )(T
2222
22
21
221
21max
2max
22
)2/(12)(
p22
)(4
221)(
bpvMQQpT
pbtg
EMMMMT
SinTvMT
为碰撞参数
b: collision diameterClosest distance in repulsive potential
1 2( ) Q QV rr
1 221
02
Q Qb
M v
两体碰撞
iiiTN
dxdE
TdN pdpd 2
bbp
NvMQQ
bppdN
vMQQ pp
p
22max
22
22
21
0 22
2
22
22
21
)2/(2ln
4
)2/(2 max
?max p2
2
( ) 1 4000( )
dEdx e edE
n ndx
L LMm Z L L
非弹性
弹性
2.2 Collisions with atoms Elastic and inelastic energy loss
Elastic moving the center of the mass of the atom-- nuclei
Inelastic leading to excitation of internal degrees of freedom--electrons
ee
einela
nn
nela
b
v
NZmv
eZdxdE
utoffAdiabaticcvpbdxdE
baN
vMZZ
dxdE
cutoffaScreeningpbdxdE
p
)(2ln
4~
~
2ln4
~
~
?
22
421
max
22
22
21
max
max
v tZ
e,m
P
动量变化:yqq
0 2/3
21
2/12222
21
)1(2
)()(
cos
dVP
eZ
vtP
PdtvtP
eZ
dtKdtK y
22
421
2
2
21
21
122
)()(
22
PmVeZ
mq
PT
KVP
PeZ
VPeZ
q
y
y
electrons feels a constant force during collision time
pbtg
22
谐振子模型:运动方程: mÿ=-mω2y+K 0≤t ≤τ 初条件: y=0 0y
令: 1 2( ) ( ) Ky t y tm
mÿ1= - mω2y1
1 2( ) cosKy t tm
2( ) (1 cos )Ky t tm
2 2 21 ( ( )) ( ( ))2
T m y y
2
2 (1 cos )Km
y the distance of the electron away from the equilibrium position
两个极端情况:ωτ<<1
2 2 41
2 2 2
( ) 2 1 12
K Z eTm mv p p
ωτ>>1
2
2 4
2 1KTm p
ωτ≈2
max2( ) 2pv
maxvP
free
ee
einela
nn
nela
b
v
NZmv
eZdxdE
utoffAdiabaticcvpbdxdE
baN
vMZZ
dxdE
cutoffaScreeningpbdxdE
p
)(2ln
4~
~
2ln4
~
~
?
22
421
max
22
22
21
max
max
2.4 Under which circumstances is classical mechanics applicable
'2 ( )r p
11
2 2q
q q r r
2r q
2 2 21 2
2 ' 2
( ) ( ) ( )
( ) ( ( ))2
r pr
2 ' 2( ) ( ) ( )p p
2 '( ) ( )p
2'
( )2 ( )
rp
'
2
( )1
( )
p
p
( ) , 1bpp
1b
1( ) 1( )
ddp p
用 及 代入 , 判据为:
对 Lindhard 势
20
221
21 vM
eZZb vM
h
0
vvvZZ
vMeZZb 1122 021
20
221
221 ap
TUNNELING ( WKB 近似)
λ
λ
POTENTIAL
b
E
b
WAVE FUNCTION
1)( V
b 为碰撞直径,即一定 E 下的最接近距离。
brbdrME
VEMdr
rbErV
VEMdrT
b
b
b
0
0
0
122
22
)(
}22exp{~
EbQQ
bV
rQQ
V
21
21
)(
1) overview2) Photon Interactions3) Neutron Interactions4) Attenuation of Charged Particles
2.2 Radiation interaction with Matter