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Chapter 2. Radiation. Radioactivity 2.Radiation interaction with Matter 3.Radiation Doses and hazard Assessment. 2.1 Radioactivity. Overview Types of Radioactive Decay Energetics of Radioactive Decay Characteristics of Radioactive Decay Decay Dynamics Naturally Occurring Radionuclides. - PowerPoint PPT Presentation
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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
NCRP National Council on Radiation Protection and Measurements
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
1) overview
directlyionizing radiation
indirectly ionizing radiation
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
Compton Effect of Gamma Rays
Spectra of an Original and Scattered X-raysat 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.
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.
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 Matter
Intensity of Parallel Gamma Rays as aFunction of Absorber Thickness.
Thickness x
Intensity, I
Gamma-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
the thickness of a medium required for half of the incidentradiation to undergo an interaction`
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 Sections
Uranium 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 Sections
The 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
4) Interaction of Heavy Charged Particles with Matter
Sketch 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.
- dE
dx =
KM zE
2
Range of Heavy Charged Particles in a Medium
Variation of Intensity as a Function of Thickness
Detector
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 Medium
Intensity (I ) of Electrons with the Same Kinetic Energyas a Function of Thickness (x) of Absorber.
I
x
Extrapolatedrange
Rangestraggling
absorberI0
Idetector
I0
x
Variation of Intensity as a Function of Thickness
Detector
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
能量损失
ee b
v
NZmv
eZ
dx
dE)(2
lg4
~ 22
421
2.1 Two-body collisionsFormula
Tacit assumptions:
Well defined Z1
Independent two body collisions
Stochastic 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
i
iiTNdx
dE
TdN
pdpd 2
INCIDENT ION BEAM
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
12
1vME 入射粒子能量: 靶粒子获得的能量: 2
222
1vMT
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
sintg
cos
M
M M
靶粒子得到的能量 )(T
2222
22
21
221
21max
2max
22
)2/(
12)(
p22
)(
422
1)(
bpvM
QQpT
p
btg
EMM
MMT
SinTvMT
为碰撞参数
b: collision diameterClosest distance in repulsive potential
1 2( )Q Q
V rr
1 221
02
Q Qb
M v
两体碰撞
i
iiTNdx
dE
TdN pdpd 2
b
bpN
vM
bp
pdN
vM
QQ pp
p
22max
22
22
21
0 22
2
22
22
21
)2/(2ln
4
)2/(
2 max
?max p2
2
( ) 14000
( )
dEdx e e
dEn ndx
L LM
m 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
eZ
dx
dE
utoffAdiabaticcv
pbdx
dE
b
aN
vM
ZZ
dx
dE
cutoffaScreeningpbdx
dE
p
)(2ln
4~
~
2ln
4~
~
?
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
d
VP
eZ
vtP
Pdt
vtP
eZ
dtKdtK y
22
421
2
2
21
21
12
2
)()(
22
PmV
eZ
m
qPT
KV
P
P
eZ
VP
eZq
y
y
electrons feels a constant force during collision time
p
btg
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 t
m mÿ1= - mω2y1
1 2( ) cos
Ky t t
m
2
( ) (1 cos )K
y t tm
2 2 21( ( )) ( ( ))
2T m y y
2
2(1 cos )
K
m
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 1
2
K Z eT
m mv p p
ωτ>>1
2
2 4
2 1KT
m p
ωτ≈2
max2( ) 2
p
v
max
vP
free
ee
einela
nn
nela
b
v
NZmv
eZ
dx
dE
utoffAdiabaticcv
pbdx
dE
b
aN
vM
ZZ
dx
dE
cutoffaScreeningpbdx
dE
p
)(2ln
4~
~
2ln
4~
~
?
22
421
max
22
22
21
max
max
2.4 Under which circumstances is classical mechanics applicable
'2 ( )r p
1
1
2 2
q
q q r r
2r q
2 2 21 2
2 ' 2
( ) ( ) ( )
( ) ( ( ))2
r pr
2 ' 2( ) ( ) ( )p p
2 '( ) ( )p
2
'( )
2 ( )r
p
'
2
( )1
( )
p
p
( ) , 1b
pp
1b
1( ) 1
( )
d
dp p
用 及 代入 , 判据为:
对 Lindhard 势
20
221
21
vM
eZZb
vM
h
0
vv
vZZ
vM
eZZb 11
22 0212
0
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。
br
bdr
ME
VEMdr
r
bErV
VEMdrT
b
b
b
0
0
0
12
2
22
)(
}22
exp{~
Eb
QQbV
r
QQV
21
21
)(
1) overview2) Photon Interactions3) Neutron Interactions4) Attenuation of Charged Particles
2.2 Radiation interaction with Matter