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0904505414

Hµnéi , 20-2.2006

1


M.Planck

Einstein

N.Bohr

M.Curie
2


Radius of observable universe
15000.000.000.light -years

Radius of Earth

cell
Atom
Atomic nucleus
3


Energy

Wide Range of Radiation
Energy and Intensity

GeV

Accelerator,
Cosmic rays
MeV

Industrial
application
Medical
diagnosis

Environment

1

102

104

Processing

Radioisotopes

keV

10-2

Medical
treatment

106

108

1010

1012

1014

4

Intensity(s-1)
Concentration
Bq/g
Dose(nGy/h))


interaction of particles and radiation with matter

The measurement of nuclear radiation is based on its
interaction with the detector.
In order to understand:
1* The function of nuclear radiation detectors
2* The absorption phenomena in
the measurement of the radiation

3* With respect to radiation protection.
 We shall deal with the most important mechanisms of the interaction
between nuclear radiation and matter in their basic features.
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To organize the discussions that
follow, it is convenient to arrange
the four major categories of
radiations into the following matrix:

Charged Particulate Radiations
Heavy charged particles
(characteristic distance ≅10-5m)

Fast electrons
(characteristic distance ≅10-3m)

Uncharged Radiations

Neutrons
(characteristic length ≅10-1m)

X-rays and γ rays
(characteristic length ≅10-1m)

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Mảnh giấy

Lá nhôm

Tấm chì
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Interaction of particles and radiation with matter
•

Ionization Losses Due to Collisions of Charged Particles Stopping power

•

Bohr's Formula for Specific Ionization. Relativistic Effects
and the Density Effect

• Dependence of ionization Losses on the Medium
•

ionization Losses on the Medium
. Radiation Losses for Electrons.
. Cherenkov Radiation
. n and γ -radiation Interaction with matter

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Interaction of Gamma Radiation with Matter
1. Photoelectriceffect

2 . Compton scattering
3. Electron-positron Pair
production
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Photoelectric
effect

M

γ-ray

e-

K

Photoelectric effect

L

ek

A.E

X

A.E :Auger electron
X-ray

K

L

M

hν
Te = Eγ - Ii

Photoelectric effect cannot take place for a free electron (not associated
with an atom).

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The law of conservation of energy:
 1


Eγ = me c
− 1
 1− β 2



2

The law of conservation of momentum :

(

Eγ / c = me βc / 1 − β 2

)

2
2
2
2
E γ / m e c = 1 / 1 − β − 1 = β / 1 − β or ( − β )/ 1 − β = 1
1

(1 — β)2 = 1 — β2
β = 0 and β = 1
Photoelectric effect is therefore possible only for bound
electrons.
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the photoelectric effect cross section

1/ With decreasing Eγ (increasing ratio of the electron binding to the
photon energy IK/Eγ ), the cross section increases first as 1/E γ , and later
(as Eγ approaches Ik) more rapidly as 1/ Eγ 7/2 .
2/ The probability of photoeffect depends very strongly on the charge
Z of the atom in which the effect is observed: σ phot ∝ Z5.

σphot ∝ Z5/Eγ
σphot ∝ Z5/Eγ7/2

for
for

Eγ >> IK,
Eγ > IK.

* Photoeffect is especially signifficant for heavy materials where
the probability is considerable even for high energies of γ-quanta.
* In light materials, this effect becomes significant only for relatively
low energies of γ-quanta.
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In Compton scattering the incoming gamma-ray photon is
deflect through an angle θ with respect to its original
direction. The photon transfers a portion of its energy to
the electron (assumed to be initially at rest), which is
then known as a recoil electron.
hν ’
incoming γ -ray

scattered γ -ray

θ
ϕ

hν
(Free electron)

Ee −

( recoil electron).
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hν ’
hν

scattered γ

-ray

θ
ϕ

incoming γ -ray

Free electron
Ee −

recoil electron.

Because all angles of scattering are possible, the
energy transferred to the electron can vary from zero to
a large fraction of the gamma-ray energy.
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Compton scattering

Compton scattering

E=hν

θ

φ

e-

.A photon interacts with an electron,
giving a partial energy, and scatters
for different direction.
.Energies of the scattered photon and
the secondary electron are calculated
by:
Scattered photon:
hν’= h / { 1 + α ( 1 -cos) }
 = h / m0c2
Secondary electron :
Ee = h ν - h ν’
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

1
hν = hν'+Te = hν'+me c 
−1
 1 − β2



2

(

)

me2c 4 / 1 − β 2 = me2c 4 + (hν ) 2 + ( hν ') + 2mec 2 h(ν − ν ') − 2hν hν '.
Pγ = P’γ + Pe, →

2

hν / c = hν ' / c + me β c / 1 − β 2 ,

me2 β 2c 4 / (1 − β 2 ) = ( hν ) + ( hν ') − 2hν hν ' cosθ
2

2

( c /ν ') − ( c /ν ) = ( h / mec )(1 − cosθ )
∆λ = λ '−λ = Λ (1 − cosθ ) = 2Λ sin 2 (θ / 2 ) ,

Λ= h/mec = 2.42 x 10-10cm: The Compton wavelength for electron
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1.The wavelength λ of the displaced line increases

with the scattering angle θ in such a way that:
∆λ = 0
∆λ = Λ

for
for

∆λ = 2Λ

for

θ = 0,
θ = π / 2, and
θ =π

2. However, for scattering at a given angle θ, the
quantity ∆λ is independent of λ.

∆λ is determined only by θ and is independent of λ
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3. The energy of a quantum scattered at an angle θ:



hν
(1 −cosθ )
hν' = hν /  +
1
2
me c



4. The kinetic energy of the recoil electron:
hυ
Ee − = hυ − hυ' = hυ

2

(1 − cosθ )

mec
hυ
1+
(1 − cosθ )
2
mec

Ee −

2

hυ

mec 2
= hυ
hυ
1+ 2
θ =π
mec 2
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Electron-positron Pair production

- Discovered by Dirac in 1928
γ

Pair production

e-

hν
511

e+
e−

e+
511

γ

- The process of pair production cannot
occur in vacuum and requires
a nucleus or an electron in the proximity.
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Eγ =

me − c 2
1 − β e2−

+

me + c 2

(1)

1 − β e2+

Pγ = Pe − + Pe +

(2)

It follows from formula (1) that:
me− c
me+ c
me β e− c me β e+ c
Eγ
Pγ = =
+

>
+
= Pe− + Pe+
2
2
2
2
c
1 − β e− 1 − β e+ 1 − β e− 1 − β e+
Pγ > Pe − + Pe +

However, this inequality cannot be true,
since in accordance with formula
(2) these vectors form a triangle.
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→ The threshold energy :

E0 ≅ 2me c = 1.02 MeV
2

(3)

in the Coulomb field of a nucleus
E0 = 4mec2 = 2.04 MeV

(4)

in the Coulomb field of an electron

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Pair production
A Photon produces an
electron (e-) and a positron
(e+) near the nucleus, and
total kinetic energy of both
electrons is :
Ee- + Ee+

=

h ν -2 m0c2

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Pair production

Positron combines with an
electron nearby, after
losing kinetic energy, then
the electron and positron
pair annihilates and emits
two photons ( annihilation
photon; m0c2 =511keV).
This process is called
positron annihilation.
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