Chapter 2. Radiation

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




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


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




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




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


Documents

Chapter 2. Radiation