1. Fundamentals of subatomic physics
I Generalities
A Introduction Fundamental question: What is an atom?
Very small sphere
(R=10-10 m),
Even smaller nucleus
(R= 10-14 à 10-15 m)
+ electrons
(green pea seen from
a distance of 100m!)

2. B Definitions
The nucleus is heavier.
(by far! a proton is 2000 times heavier than an electron…).
Sub-atomic physics: physics of infinitively small.
Can be divided in 2: - Particle physics (high energies)
- Atomic physics (Nuclear Physics)
The nucleus is made of 2 kinds of particles:
proton and neutron
Mass at rest ~2000 x that of an electron.
1 a.m.u. ≈ 1.66 10-27 kg
A
A nucleus X of atomic mass A and proton number Z:
Z protons
(A-Z) neutrons
Z X
€

3. Isotopes: same Z, ≠ A (i.e. ≠ neutron number)
123
53 I, 125I, 127I, 131I
53 53 53
€

4. Isobars: same A (mass), ≠ Z
131
53 I, 131Cs
55
€

5. Isomers: same Z, same A, ≠ energetic state
99 99m
43Tc, Tc,
43
€

6. Atom
Nucleus

7. C Fundamental interactions
In order to be able to explain ALL interactions around us:
4 fundamental interactions:
Gravity
Strong
Electromagnetic
Weak

8. Gravitational Interaction
Gravitation, tide, astronomy, …
Attractive force on any kind of objects (energies) but with a VERY weak intensity:
Visible effect on massive objects only

9. Electromagnetic interaction
At the birth of all electric and magnetic phenomenon.
Attractive or repulsive force,
On all objects that have an electric charge.
Allows for atomic cohesion.
Responsible for chemical and biological interactions.
Can create electromagnetic waves
(light, radio waves, radars, X rays…).
Allow the explanation of almost all day-to-day phenomenon.

10. Strong interaction
From nucleus discovery:
How can the nucleus components stay confined in such a small volume?
Not gravitational…
Not electromagnetic...
With those 2 interactions only, the protons (positive charge) would strongly
repulse each other, to the point of leaving the nucleus…
Hence another interaction : Strong interaction
Allows for nucleus cohesion, ties neutrons and protons
Also responsible for nuclear reactions
(star and therefore sun energy source)

11. Weak interaction:
A 4th interaction became necessary to explain ß radioactivity:
Disintegrating nuclei emit one electron that is accompanied by another particle,
the anti-neutrino (we’ll see that in more details later on).
That particle crosses the entire earth without interacting, whereas the electron is
absorbed within some mm in matter…
The difference was explained by the hypothesis that the anti-neutrino undergo a
much weaker interaction than the electron (or photons).

12. Summary

13. D Elementary particles
a) Standard model
The standard model is the actual theory that allows to explain all observable
phenomenon at the particle scale.
The standard model: takes into account ALL KNOWN particles
+ 3 interactions that affect the particles (excludes gravity)
The standard model explains all natural phenomenon but gravity (that still resists
to theoreticians)
Elementary particles within the standard model:
b) Elementary particles
There are 2 kinds of elementary particles:
♦ ”matter” particles,
♦ ”radiation” particles that are the vehicle of fundamental interactions.

14. ♦Matter particles
♦12 in total, split in 2 categories
Fundamental “bricks” of atoms:
♦Quarks (6 plus the corresponding anti-particle: anti-quarks)
Sensitive to the 3 kinds of interactions.
Compose particle called hadrons.
Quarks are never free : they stay within hadrons.
♦leptons (6 plus the corresponding anti-particle: anti-leptons)
Not sensitive to strong interaction.
There are
3 charged leptons (electron, muon et tau)
3 neutral leptons (neutrinos electronic, muon et tau).
And again:
3 charged anti-leptons (electron, muon et tau anti-neutrinos)
3 neutral anti-leptons (electron, muon et tau antineutrinos).
Remark: Two hadron types can be distinguished:
Baryons made of 3 quarks: nucleons (protons et neutrons).
and therefore anti-baryons (anti-protons and anti-neutrons) are made of 3 anti-quarks.
Mesons made of 2 quarks (one quark and one anti-quark).
(There is therefore no "anti-meson")

16. ♦ “Radiation” particles:
Analogy:
Action-reaction principle, the 2 ships will separate.
The interaction is made by exchanging an intermediary object: the balloon.
This object is called interaction interaction vector.
Fundamental interactions are explained in the same way.
There’s always one (or many) vector particle(s) for each particle interaction.
These vector particle are called “radiation” particles.
There are 12 of them for the 3 fundamental interactions (excluding gravity):
♦ For strong interaction: 8 gluons
♦ For electromagnetic interaction: photon
♦ For weak interaction: W+, W- et Z0.

17. Summary table:
Interaction Relative Interaction Particles Vector
intensity range involved particles
Strong 1 10-15 m Quarks Gluons
Electromagnetic 10-3 Infinite Charged Photons
particles
Weak 10-12 10-18 m Leptons W+, W-, Z0
Quarks
Gravity 10-40 Infinite all Graviton ?

18. E Conclusion:
The standard model has never been put in default (until now) …
This is NOT the ultimate theory of physics for a main reason:
This model cannot accommodate gravity!
In particular, the gravity vector particle (the graviton) has never been observed...
There are other limitations, (i.e. particle mass prediction).
Physicist big dream is unifying all interactions (Universal model).
For now, this development still resists to experiments (even though electromagnetic
and weak interaction could be merged as electroweak interaction).
This opens nice perspectives,
Both from experimental and theoretical point of view...

20. II Mass-energy relationship
A Introduction
Spectacular example in Nuclear Medicine:
At the base of PET imaging: two electrons (charged + and -) annihilate to give birth
to 2 gamma photons emitted at 180°…
Conversion of 2 material objects (electrons) into energy (photons)…
There is a tight relationship between mass (particle) and energy…
B Concepts of relativistic mechanics
Up to the early XXth century:
'mobiles' had a small speed vs. / light speed ( c=3.108 m.s-1).
Classical mechanics (Newtonian) remained valid.
But since… systems, experimental developments, etc.
’Classical' physics was questioned!
Example:
In classical physics (mechanics second principle), the ratio between particle
acceleration and the force leading to that acceleration is a constant:
F
=m
a
€

21. But for 'relativistic' particles (whose speed is close to c),
When studying
On one hand the force applied on the particle,
On the other hand the acceleration due to the force,
One can see that the ratio varies particle speed…
And therefore mass varies with speed:
With:
m0
m0: rest mass m= = γ .m0
ν: particle speed v2
1− 2
c: speed of light in vacuum c
In fact, when one is considering kinetic energy variations
€
For a particle of rest mass m0 moving in vacuum,
Accelerated in straight line by a constant force:
ΔEc = ( m − m0 )c 2 ΔEc = Δm.c 2
and:
This means => kinetic energy variation is equivalent to a variation in mass...
€ €

22. RQ: This is valid only if v ~ c…
Example: a plane (100 tons) @ mach 1 (1200 km.h-1)
1
Kinetic energy: Ec = mv 2
2
Ec = 5.5 . 109 J
This corresponds to a mass variation of 0.6 pg...
€
C Einstein general scheme, orders of magnitude
Einstein generalised the previous result:
To all total energy variation (ET) of a given system corresponds a mass variation:
ΔET = Δm.c 2
And here goes the famous E=mc2… m0
m= = γ .m0
RQ: Mass m is of course given by equation: v2
1− 2
€ c
This explains why a photon (rest mass equal to zero) still has an associated energy...
€

23. Orders of magnitude:
Mass and energy are equivalent, hence one can consider equally:
Particle Symbol Mass (kg) Rest mass (MeV)
Proton p 1.67261 . 10-27 kg 938.28
Neutron n 1.67492 . 10-27 kg 939.57
Electron e 9.10938 . 10-31 kg 0.511
RQ: 1 eV = 1.6.10-19 J
1 a.m.u. = 1.66043 10-27 kg <=> 931.5 MeV

24. III Strong interaction - binding energy
A Nuclei mass and binding energy
A stable nucleus: system bound by strong interaction of A nucleons.
It is therefore necessary to provide energy to the nucleus to split it into its components.
And mass and energy are equivalent concepts.
Hence the bound state as a mass inferior to the sum of the component masses.
And, the total energy of a nucleus of charge Z and mass number A
(with A=Z+N, where N is the neutron number) can be written:
M ( A, Z )c 2 = Zm p c 2 + Nmn c 2 − B( A, Z )
With:
mp: proton mass
mn: neutron mass
B(A,Z): Nucleus binding energy
€

25. Binding energy:
that has to be given to split the nucleus into its nucleons,
that is released when the nucleus is created.
The nuclear binding energies are enormous!
The nuclear binding energies are on the order of a million times greater
then the electron binding energies of atoms!

26. B Nuclear energy
From experience:
When the number of nucleons increases, the binding energy increases.
But the interesting parameter is the relative variation of binding energy.
It is possible to define binding energy per nucleon, noted B/A.
For A > 16, B/A is independent from A and is around 8 MeV.

27. C N/Z graph
This graph shows how STABLE nuclei
are located in a N/Z representation, and
also along the N=Z line.
For small Z values,
Nuclei that possess the same number of
protons and neutrons are stable (along
the N = Z line). N
However, in order to be STABLE,
heavier nuclei need to have a “neutron
excess” (N > Z).
It looks as if neutrons where needed to
“stabilise” protons in large nuclei...
Z

28. IV Nuclear instability - radioactivity
A Definition
Within the incredibly small nucleus, the two strongest forces in nature
are pitted against each other. When the balance is broken, the resultant
radioactivity yields particles of enormous energy.

29. Transition : Modification of the energetic status of an atom nucleus
by disintegration or de-excitation
Disintegration : Spontaneous transition, with a change in atomic number.
The resulting nucleus can be:
at the fundamental energy state
at an excited energy state
(the return to the fundamental energy state: one or several γ transitions).
The available energy corresponds to the difference of atomic mass between parent
and daughter nuclei at the rest level.
Activity : Ratio between the mean number (dN) of spontaneous nuclear transitions
happening from a given energetic state during time interval dt. Activity is noted A
and is given by:
International unit: dN
The becquerel (Bq) = 1 disintegration.s-1 A=−
The curie (1 Ci = 37 GBq) is also used dt
€

30. Radioactive decay : the law of radioactive decay applies to ALL radioisotopes :
N0 is the initial number of nuclei,
dN
= −λN
dt
dN/dt represents the change of the number of nuclei with time.
dN
= −λdt
Activity is proportional to the number of nuclei at the€ t
time N
This introduces a constant λ: N dN t
€
λ radioactive constant, characteristic of a given radioisotope.
∫ N0 N
= − ∫ λdt
0
N t
[ln N ] N = −λ [t ]0
0
€
N
ln = −λt
N0
€
N = N 0 e− λt
€
€

31. Radioactive half-life :
Time T it takes for half of the original number of atoms to decay.
Also called physical half-life, noted: Tphy or T1/2.
RQ: This concept is characteristic of exponential processes...
N0 Radioactive decay
= N 0 e− λT
2
1
e− λT =
2
€
1
−λT = ln
2
€
ln 2 0.693
T= = Time
λ λ
€
€

32. B Application: ray spectra
Radioactivity: process allowing the evolution from an initial state to a final state
of inferior energy.
Example of spontaneous transitions: γ emission
A nucleus, at an excited state Ei,
Emits a photon of frequency ν
To reach a final state Ef of lesser energy
Hence the relationship: Eγ = hν ≈ Ei − E f
With Ef represents energy levels < Ei
h Planck constant (h = 6,62 × J.s-1).
€
(a) (b)

33. (a) (b)
(a) (b)
That energy: can be received by photon detectors
Gives birth to one or many rays.
Eγ = Ei
Example of Fig. (a), 5 different rays of energies:
Eγ = Ei − E2
Eγ = Ei − E1
Unstable nuclei emit one or ++ particles Eγ = E2 − E1
to reach a state of increased stability…
Eγ = E1
€

34. C Alpha radioactivity
α radioactivity: strong interaction.
Concerns mainly heavy nuclei (Z>82).
Corresponds to the emission of a helium nucleus (alpha particle ):
A
Z X→ A−4 Y (*) +2 He + (γ )
Z −2
4
(*) Means that Y can also be instable,
(γ) Means that alpha emission can be followed by γ emission.
Alpha particle (some MeVs) can be emitted at a speed of ~ 20000 km.s-1…
Very ionising! (we’ll see that later), but is quickly stopped:
some cm in air, some fraction of a mm in water or soft tissues...
€ 213Bi
α (2.16%) 209Tl
β (97.84%) β (100%)
213Po
α (100%) 209Pb
β (100%)
209Bi

35. D beta radioactivity
Disintegration ß-:
A
Z X→Z +1Y (*) +−1 e− + ν + (γ )
A 0
Characteristic of nuclei with an excess of neutrons
€ Can be explained by the conversion of a neutron into a proton (within the nucleus)
1 1 0
0 n→1 p+−1 e− + ν
€

36. This involves the anti-neutrino, whose mass is considered as null…
Explanation:
Conservation of energy gives the following relation :
(with only nuclear masses as a first step) :
2 2 2
m c =m c +m c +E
X Y 0 C − + EC ν + EC γ
β
With :
Ecß-: Kinetic energy of the β - particle
Ecγ: Kinetic energy of the γ ray (eventually)
Ecv: Kinetic energy of the anti-neutrino
€

37. Replacing nuclear masses by atomic masses gives:
M X c 2 − Zm0 c 2 − E L = M Y c 2 − (Z +1)m0 c 2 + m0 c 2 + EC − + ECν + ECγ − E L
'
β
Hypothesis:
♦ Binding energy differences are neglected ,
♦ γ ray energy is neglected
€ The relation thus becomes: 2 2
M X c = M Y c + EC − + EC ν
β
And the energy involved is: 2
β
( )
E d = M X c − M Y c 2 = EC − + EC ν = EC β
max
€
The neutrino (anti-) is therefore a way to
€ explain why a beta spectrum is observed,
with all energies between 0 to Eßmax.
This is a VERY important point to consider
in NM and dosimetry!

38. Disintegration ß+: A
Z X→Z −1Y (*) +1 e+ + ν + (γ )
A 0
This disintegration is characteristic of nucleus with an excess of protons.
It can be considered as the conversion of a proton into a neutron (within the nucleus)
1
1 p→01 n+1 e+ + ν
0
This involves the anti-neutrino, whose mass is considered as null…
€
Explanation: €
Conservation of energy gives the following relation :
(with only nuclear masses as a first step) :
m X c 2 = mY c 2 + m0 c 2 + EC + + ECν + ECγ
β
With :
Ecß-: Kinetic energy of the β+ particle
Ecγ: Kinetic energy of the γ ray (eventually)
€ v: Kinetic energy of the neutrino
Ec

39. Replacing nuclear by atomic masses gives:
M X c 2 − Zm0 c 2 − E L = M Y c 2 − (Z −1)m0 c 2 + m0 c 2 + EC + + ECν + ECγ − E L
'
β
Hypothesis:
♦ Binding energy differences are neglected ,
♦ γ ray energy is neglected
€ The relation thus becomes:
M X c = M Y c + EC + + ECν + 2m0 c 2
2 2
β
And the energy involved is:
€
( )
Ed = M X c 2 − M Y c 2 − 2m0 c 2 = EC + + ECν = EC +
β β max
€

40. Remarks :
♦ β+ particles (or positrons) are submitted to coulombian repulsion within
the nucleus.
♦ β+ decay is only possible if the atomic mass difference between mother
and daughter nuclei is more than 2m0c2.
18
Very famous β + decay:
9 F→18 O+1 e+ + ν + γ
8
0
€

41. E Other means of disintegration
Electron capture
“deep layers” electrons (typically K)
Have a (small) probability to be found inside the nucleus!
The weak interaction is the means to ‘capture’ that electron.
The K electron is captured by the nucleus, and a neutrino is emitted
Hence the equation:
*
A
Z X+−1 e(atomic) → ( Z −1Y (*) ) + ν + (γ )
0 − A
This equation can be explain by the process:
1 0 − 1
p+−1 e(atomic) →0 n + ν
€ 1
Electron capture is specific to nucleus with a proton excess.
Remarks
• Electron capture ‘competes’ with β + decay,
• The electron vacancy leads to an excited nucleus. This is noted by the ()*.
€
• Electronic capture has a greater probability of occurrence for heavy nuclei (high Z).

42. As for the preceding disintegrations, it is possible to write:
2 2 2
With: m X c + m0 c = mY c + ECν + EC γ
Ecv: neutrino kinetic energy
Ecγ: γ ray possible energy
Replacing nuclear masses by atomic masses gives:
€
M X c 2 − Zm0 c 2 − E L + m0 c 2 = M Y c 2 − (Z −1)m0 c 2 + ECν + ECγ − E L
'
Energetic hypotheses: EL-EL’ is neglected,
And thus: M X c 2 = M Y c 2 + EC γ + EC ν
€
The disintegration energy is:
E d = M X c 2 − M Y c 2 = EC γ + EC ν
€
€

43. Important remarks:
Daughter atom has a vacancy in a deep electronic layer.
That will be filled by a more superficial electron (L layer, for example) and will
create a characteristic X ray emission.
This is called fluorescence emission X.
But then a vacancy will exist for the layer L, etc…
This electronic rearrangement will create a lot of X ray emissions.
A Nuclear Medicine example of a radionuclide that decays by electron capture is:
*
123
53 I + e(atomic) → ( 123Te) + ν + γ
−
52
€

44. Internal conversion - Auger electrons
This process refers to electrons that can be ejected from the electronic cloud as a
consequence of interactions with a photon γ emitted from the nucleus.
(The nucleus is therefore originally in an excited state).
Ejected electrons are called internal conversion electrons.
These electrons can only be ejected if the γ photon energy (h ν)γ
is superior to the binding energy of the electron in layer K, L or other (EL)K,L...
This is given by the relation:
(hν )γ >> ( E L ) K ,L...
From a practical point of view, it is impossible to differentiate β - decay electrons
from those resulting from internal conversion.
€
They have, however, a characteristic emission energy (ray):
ECCI = (hν )γ − ( E L ) K ,L...
€

45. Raies characteristic rays interne
IC des électrons de conversion
Electrons- émis
Nombre de β ⎛ ⎞
⎜ EC − ⎟
⎝ β ⎠ max
emitted
EC −
β
Here again, the electron vacancy will be filled by more superficial electrons. This
will create X rays emissions characteristics of the electronic transition.
These fluorescence X rays can leave the atom (i.e. for heavy atoms) or eject
superficial electrons (for light atoms) by PE effect (to be seen later).
These fluorescence induced electrons are called Auger electrons.
And all vacancies created by Auger electrons will in turn be filled, etc...
The term “Auger cascade” is used to illustrate this phenomenon.

46. V Conclusion: decay scheme of 99mTc
This illustrate some of the processes seen in the lecture…
99 m
43 Tc
6,007 heures
ec1 γ1
ec3 γ3 β1−
142,681 keV
140,511 keV
ec2 γ2 322,40 keV
99
Tc
43
99
Tc
43 β2−
2,14 × 105 ans
β− γ2
γ3
89,80 keV
293,60 keV
β3−
γ1
99
44 Ru 0 keV
Stable

47. Emission Electronic layer Energy (keV) Absolute yield (%)
ec1 M, N 1.73 < E < 2.13 99.11
K 119.467 8.7
ec2 L 137.46 1.12
IC
electrons M, N 139.96 < E < 140.50 0.23
K 121.64 0.61
ec3 L 139.64 0.20
M, N 142.22 < E < 142.64 0.05
ß1- - Max : 204 1.6 × 10-3
ß2- - Max : 293.60 100
ß3- - Max : 436.4 0.001
Decay Energy (keV) Yield (%)
2 (Tc) 140.511 89
3 (Tc) 142.68 0.021
1 (Ru) 89.8 0.7 × 10-5
2 (Ru) 232.7 0.9 × 10-5
3 (Ru) 322.4 0.98 × 10-4

48. References
- http://hyperphysics.phy-astr.gsu.edu
- http://marwww.in2p3.fr
- http://www.lal.in2p3.fr
- http://www.phys.virginia.edu
- S. Webb et al, The physics of medical imaging, Institute of physics
publishing - Bristol and Philadelphia (1993)
- F. Lagoutine, N. Coursol et J. Legrand, Table de radionucléides, CEA/
LMRI (1983)
Acknowledgement: T Carlier, NM, Nantes University Hospital

49. Interactions radiation - matter
Introduction:
One can distinguish charged particles interactions with matter
X or γ rays interactions with matter
Physics is different, effects are different…
But…
X or γ rays interactions with matter can give birth to:
• other electromagnetic radiations…
• charged particles (hence the link…)
Furthermore:
Nuclear Medicine: Radiopharmaceuticals (radionuclides)
• X or γ rays emissions
• Charged particles emissions (ß-, ß+, α)
Consequences on:
• Detection
• Dosimetry

50. High energy X and γ rays Interactions with matter
Introduction:
In the medical field, electromagnetic radiations: X and γ
Radiology, Nuclear Medicine
20 to 500 keV
Radiotherapy
1 to 100 MeV
The study of the interactions leads to:
Basic rules for radioprotection
Physics basis for radiotherapy
Physics basis for detectors for medical imaging
Plan of the study:
Macroscopic (experimental) aspects
µ and HVL
Microscopic (atomic) phenomenons
PE effect, Compton, pair production
Energy ranges
Consequences
Here it’s the particle side of electromagnetic radiations that’s considered

51. I Macroscopic effects:
{ }
Nt
Na
N0 N1
Np
Nd
Ns
Detector
Détecteur
N0 photons, energy E0=hν, moving in vacuum,
Homogeneous medium (a single chemical species),
Perfect detector,
N0 = Nt+Na+Ns+Np > Nt+∂Nd = N1
∂ : fraction of scattered photons that are detected

52. A Attenuation coefficient:
Relation between N0 and N1?
N
N0
N(x)
N(x+dx)
N(e)
0 x x+dx e x
N(x) - N(x+dx) = dN = - µ N dx

53. N(x) - N(x+dx) = dN = - µ N dx
The number of photons that disappear between x et x+dx is proportional to
• The number of photons reaching depth x
• The thickness of the layer considered (dx).
µ (proportionality constant) depends upon:
• Beam characteristics
• Medium crossed
This leads to a first order differential equation:
dN
= −µdx
N
Ln(N ) = −µx + C
N
Ln(N ) − Ln(N 0 ) = Ln( ) = −µx
N0
Therefore: N(x) = N 0 e− µx
€
€

54. Consequences:
N(x) = N 0 e− µx
•
If µ is large, the number of interactions increase,
The photon number decreases quickly
•
N(x) is always < N(0)
•
N(x) is always > 0, one can never stop all photons!
€
•
µ is the linear attenuation coefficient (cm-1)
° µ increases with the density of the medium
° µ decreases with the energy of the incident photons
•
µ can be normalised by ρ :
µm is the mass attenuation coefficient (cm2g-1) µ
µm =
ρ

55. B Half value layer (HVL):
µ doesn’t provide an easy way to define how
a given material will absorb a given electromagnetic beam…
It is useful to define a variable derived from µ that illustrates the attenuation:
The HVL is the thickness of material that attenuates the beam by a factor 2:
N0
N (HVL) = N 0 e−µHVL = −ln(2) = −µHVL
2
Ln(2) 0.693
HVL is expressed as a length (cm). HVL = =
It is independent of N0. € µ µ
€
1 HVL
decreases the photon number by a factor
2
2 HVL
4
3 HVL
8
10 HVL
€ 1000 (1024)
n HVL
2n

56. II Photoelectric effect:
Most important effect at low energy, easiest to describe…
A Qualitative description
Photon (E0 = hν) interaction with an electron of inner shells
A photon interacts with a K or L shell electron (most likely).
If E0 is sufficient (>Eb):
- The photon disappears
- The electron is ejected out of the atom with Ek and:
E0 = Ek + Eb
Ek
E0
Eb

57. More likely to happen if E0 is close to Eb.
Probability :
null if E0 < Eb
high if E0 > Eb
low if E0 ≈ Eb
This is a resonance effect: narrow energy range,
Around electron binding energies (eV to 100 keV).
After a PE effect, the photon has disappeared
This correspond to an absorption, not an attenuation.
Fate of the electron?
interactions with medium
Useful in radiotherapy!
Fate of the atom?
ion, with a vacancy in inner shells...
The electronic cloud will reach a stable ionic form by:
Fluorescence photon emission
Auger electron emission

58. Fluorescence photon emission
Temps
time
0
Ekc
E
E0
Ei
E1
E
El b
E'i
Ep
Ea
atome à
Stable effet
Photoelectric émission du photon
Fluorescence
l'état basal photoélectrique de fluorescence
atom Effect photon
E
The atom is at an initial stable state (Ea <0)
PE effect produces an ion (Ei <0), and
Ei = Ea + Eb
If an outer shell electron fills the vacancy:
The resulting ion has an energy E’i,
Ep is the binding energy of the outer shell electron,
E’i = Ea + Ep

59. Temps
time
0
E
Ekc
E0
Ei
E1
E
El b
E'i
Ep
Ea
Stable
atome à effet
Photoelectric émission du photon
Fluorescence
l'état basal
atom photoélectrique de fluorescence
Effect photon
E
Ep is smaller than Eb (but the 2 are positive),
The resulting ion has an energy inferior to that of the initial ion: E’i < Ei
It is more stable, and the transition is spontaneous.
The energy difference induces the emission of a photon of energy E1, and
E1 = Eb - Ep
Eb is close to E0,
Eb decreases very quickly from a shell to another (Bohr) => Eb ≈ E0

60. But E1 cannot trigger another PE effect in an atom of the same kind!
The direction of emission of the photoelectron is independent
of the incidence direction of the photon.
Usually, the fluorescence photon is neglected,
And the incident photon is considered as absorbed...
Except in the case of scintillation detectors.
The electronic cloud rearrangement can be made by different steps,
++ fluorescence photons
The energy is equivalent to the ≠ between energetic levels.

61. Auger electron emission
If the energy released by the electronic cloud rearrangement
(migration of an electron from the shell of energy Ep to the shell of energy Eb)
Is superior to the binding energy (Eq) of an outer shell electron (likely),
This electron is expelled from the electronic structure. It’s an Auger electron.
Temps
time
0
E0
Ekc
E
Ei
E'
E’c
Ebl
E k
E''i
Ep+Eq
Ea
Stable
atome à Photoelectric
effet émissionelectron
Auger d'électron
atom
l'état basal photoélectrique
Effect Auger
emission
E
Its kinetic energy is:
E’c = (Eb - Ep) - Eq

62. The ion is left at an energetic state:
E’’i =
Energy (<0) of the atom that experienced PE effect
+
Electron binding energies (>0) of missing electrons:
E’’i = Ea + Ep + Eq
Most probable event for light elements (C, N, O)
Biologic effect equivalent to that of PE electrons
Importance of PE effect in life sciences:
1) Basis of EBRT with photons
2) Basis of radiologic imaging:
The X ray flux is modulated by biologic tissues absorption.
RQ : If no other effects, detected photons => absorbed photons => µ
3) Detectors in medical imaging: Based on the PE effect (photon flux on a
detector)

63. B Probability of occurrence:
In order to estimate the probability of PE effect,
Electromagnetic rays characteristics
Absorbing medium characteristics
=>
Probabilistic description of PE effect
Cross section (microscopic)
Absorption coefficient (macroscopic)
Particle cross section: direction de propagation du photon
Photon propagation direction
B
Disk of surface σpe
Around each particle,
In a plane ⊥ photon propagation. A
This surface : cross section
If the trajectory hits the surface: interaction
If the trajectory doesn’t hit the surface : no interaction
The elementary interaction probability is thus given by the target surface.
This model can be used for any kind of interaction:
For each interaction type, a relevant surface is defined!

64. Relation between cross section and attenuation coefficient:
It is possible to show that µpe = σpeP
With P the particle number by volume unit
NZ m ε
With:
P = ρ
and:
σ pe =
A En
ερNZ m
Thus:
µ pe =
€ AE n €
One can show that m = 4 and n = 3.
The photoelectric effect is all the more important that :
€ • photon energy decreases,
• material density increases
• Z is high (heavy elements)
RQ : For energies close to the medium electron binding energies,
there can be sharp µ increases (K, L edges).

65. III Compton effect:
Second important interaction mode for low and medium energy photons.
Predominant at medium energies since PE interaction probability decreases sharply
The incident photon interacts with a free electron of the attenuating medium.
Compton Effect: more complex than PE effect
Perturbation phenomenon
in radioprotection
in imaging
A Qualitative description
The incident photon (E = hν) hits a free electron.
The photon photon energy is imparted:
to an electron (kinetic energy)
to a secondary (or scattered) photon (θ) same photon? not important...
Trajectoire
Electron
de l'électron
trajectory
percuté
Free
Electron
electron
Photon incident (E) (E)
Incident photon libre
φ
θ Scattered
Photon
photon
diffusé
(E')

66. RQ : Free electrons?
• Metals
• Outer shell electrons, with Eb << E
These electrons can interact by Compton effect
There are relationship between:
• Incident photon energy
• Scattered photon energy
• Deflexion angle
Energy conservation: E + mc 2 = E ʹ′ + p 2 c 2 + m 2 c 4
E : Incident photon energy
E’ : Scattered photon energy
€
mc2 : Electron rest energy
c : Celerity of light in vacuum
Under the root square : scattered electron energy and momentum after the collision

67. Conservation of momentum:
1) Along the propagation axe of the incident photon:
E E ʹ′
= cosθ + p cos φ
c c
2) Perpendicular to the propagation axe of the incident photon:
E ʹ′
0= sin θ − p sin φ
€ c
p2 can be calculated through these equations:
2 2
p 2 c 2 = ( E − E ʹ′ cosθ ) + ( E ʹ′ sin θ ) = E 2 + E ʹ′2 − 2EE ʹ′ cosθ
€ 2
p 2 c 2 = ( E − E ʹ′ + mc 2 ) − m 2 c 4 = E 2 + E ʹ′2 − 2EE ʹ′ + 2mc 2 ( E − E ʹ′)
€ mc 2 ⎛ E ⎞ E
Which gives:
cos θ =
1−
⎜ −1⎟
And if: α=
E ⎝ E ʹ′ ⎠ mc 2
€
E ʹ′ ν ʹ′ λ 1
We get:
=
= =
This relation binds E and E’ with θ,
E ν
λ ʹ′ 1+ α (1− cosθ ) scattered angle, and E’ ≤ E (normal)
€
€
€

68. Importance of Compton effect in life sciences
The Compton effect makes everything difficult...
• Explains why one can be irradiated even OUTSIDE the primary beam.
(radiation safety consequences for patient and staff)
• Limits radiologic or isotopic imaging quality.
blurring effect, parasite...
B Probability of occurrence:
Total cross section
Same principle as for PE effect: one defines σC
Klein et Nishina: σ C = σ 0 fKN (α )
Where
σ0 is the Thompson cross section: 8 πr02
σ0 =
r0 = 2.818 10-15 m is the electron radius 3
And fKN is far too complex…
€
α is the primary photon energy to electron energy at rest ratio.
σC variation with E: slower than for PE effect€
=>
Compton effect preponderant at medium energies

69. Relation between cross section and attenuation coefficient:
NZ
One finds:
µC = σ C ρ
A
Since Z/A ≈ 0.5 for many chemical species
->
µC/ρ almost constant for a given energy.
€
Differential Cross Section
Since the scattered photon emission is NOT isotropic,
It is sometimes useful (imaging) to assess the cross section in a given direction :
Differential Cross Section.
Example : Proportion of primaries vs. scattered photons in an image?
depends upon patient and detector geometry.
The differential cross section give the probability of photon interaction by CE
and the probability that the scattered photon is emitted with an angle θ.
The calculation (Klein et Nishina) gives a complex result,
The representation can be cartesian or polar:
The Compton effect is anisotropic and anisotropy increases with energy.

70. IV Pair production:
Electron rest energy: 511 keV.
An incident photon with energy above 2 x 511=1022 keV can induce
one electron (ß-) and one positron (ß+).
This phenomenon is called materialisation, pair creation.
Conservation of:
• Energy
• Momentum
• Electric charge
If E > 1022 keV, residual energy -> Ek
If Ek low, almost immediate recombination
If Ek high, the 2 particles can move apart,
and the pair production probability increases.
From a practical point of view:
• negligible if E < 5 MeV
• predominant if E > 100 MeV
Impact restricted to High Energy EBRT

71. Summary of X or gamma interactions

72. Charged particles matter interactions
Introduction:
Charged particle arriving in the neighbourhood of an atom:
• interactions with the nucleus
• interactions electrons
In all cases, the particle looses kinetic energy...
(Neutrons are not charged particles and won’t be considered here).

73. I Interaction with an electron of the target atom
Particle-electron interaction: Energy ∆Q transferred to the electron.
According to the ratio of ∆Q and W (electron binding energy):
•∆Q > W: target electron is expelled from its orbit.
With a kinetic energy (∆Q-W).
The target atom is ionised.
Expelled electron (called secondary electron) is capable to create ionisations
on its track (if its kinetic energy is high enough).
•∆Q < W: Target electron can be taken to a higher energetic state
(if ∆Q is sufficient). The atom is excited. The energy imparted is released
(as thermal or low energy electromagnetic energy).
•∆Q << W: ∆Q transformed in thermal energy (translation, rotation, vibration).
Phenomenon called collision (improper term).
Radiobiologic consequences VERY important
The incident particle energy loss is (on average) a characteristic of target atoms.

74. In the case of water: ionisation if ∆Q > 16 eV
But: for a ionisation, there are (on average) 3 excitations and ++ thermal effects
=> Mean energy per ionisation: 32 eV (34 eV in air).
The LET (Linear Energy Transfer):
Quantity of energy transferred to target medium by the incident particle,
per unit length of incident particle trajectory.
LET is expressed in keV/µm.
The Ionisation Density (ID) is the number of ion pairs created,
per unit length of incident particle trajectory.
It is expressed in ion pairs/µm.
If W is the mean energy per ionisation, then:
LET = ID x W
RQ: Charged particle beams can be completely stopped...

75. II Interaction with the nucleus of the target atom
Incident particle : according to the charge, attraction or repulsion from the nucleus.
Inflexion of the incident particle trajectory.
Energy loss is emitted under the form of X rays (Bremsstrahlung).
Photon energy < Ek of incident particle (never equal).
Slowing spectrum, continuous, from 0 to Ec.
Main medical application: X ray production.
Non-frequent event:
Frontal collision between a very energetic particle (α or proton) and the target nucleus:
Nuclear reaction (used for radioisotope production).

76. III Electrons and positrons
We’ll call both e+ and e- electrons…
If kinetic energy < 100 MeV, energy losses mainly by collision.
(Bremsstrahlung can usually be considered as negligible).
In water
Electron LET is low and decreases with electron kinetic energy.
For electron kinetic energies > 1 MeV:
LET ~ 0.25 keV/µm, ID ~ 8 ion pairs/µm
Trajectories are sinuous (zigzag).
Changes in direction: high energy transfer (collision or bremsstrahlung).
Trajectory ends when the electron lost all its Ek.
Path length in water:
L (cm) = E (MeV) / 2
(for energies above 1 MeV)

77. Mean depth of penetration:
Always inferior to total particle track length (zigzags).
2 electrons that have the same energy may have a different depth penetration…
The maximum range can be obtained through tables…
• in air: some m
• in water (soft tissues): 1 to 2 cm (and less for most MN ß emitters).
In the case of positrons:
When the particle lost all kinetic energy Ek,
it interacts with an electron of the medium and annihilates

78. IV Protons and alpha particles
Heavy particles when compared to electrons:
Energy losses have little impact on particle trajectory…
For equivalent energies, these particles are MUCH slower than electrons,
The LET is much higher:
In water, LET ~150 keV/µm, ID ~ 4500 ion pairs/µm
Straight trajectories
E(keV )
L(cm) ≈
LET (keV /µm)
Energy loss by bremsstrahlung is always negligible...
Mean penetration range: ~ particle track length (straight)
€
Varies little for 2 identical particles (with identical initial energy).
Order of magnitude: some cm in air,
Order of magnitude: some 10 µm in water and soft tissues.
-> no risk of external irradiation...

79. Summary: