1. Charged Particle Radiation
Interaction of radiation with matter - 1
Charged Particle Radiation
Day 2 – Lecture 1

2. Objective To understand the following interactions for particles:
Energy transfer mechanisms
Range energy relationships
Bragg curve
Stopping power
Shielding

3. Energy transfer mechanism
Energy transfer from radioactive particles to other materials depends on:
the type and energy of radiation
the nature of the absorbing medium
Radiation may interact with either or both the atomic nuclei or electrons
The interaction results in excitation and ionisation of the absorber atoms

4. Particle Interactions
When a charged particle interacts with an atom of the absorber, it may:
traverse in close proximity to the atom (called a “hard” collision)
traverse at a distance from the atom (called a “soft” collision)
A hard collision will impart more energy to the material

5. Stopping Power
The amount of energy deposited will be the sum of energy deposited from hard and soft collisions
The “stopping power,” S, is the sum of energy deposited for soft and hard collisions
Most of the energy deposited will be from soft collisions since it is less likely that a particle will interact with the nucleus

6. Stopping Power
The stopping power is a function of the charge of the particle, the energy of the particle, and the material in which the charged particle interacts

7. Stopping Power
Stopping power has units of MeV/cm – the amount of energy deposited per centimeter of material as a charged particle traverses the material
It is the sum of energy deposited for both hard and soft collisions.
S = = dE dx
Tot
dEs
dEh

8. Mass Stopping Power
Often the stopping power is divided by the density of the material, 
This is called the “mass stopping power”
The dimensions for mass stopping power are
MeV – cm2 g

9. Stopping Power
Stopping power is used to determine dose from charged particles by the relationship: D =  in units of MeV/g, where  = the particle fluence, the number of particles striking an object over a specified time interval dE
dx

10. Stopping Power
To convert to units of dose ..we do the following manipulation. D =  MeV/g = (1.6 x 10-10) Gy dE
dx dE
dx
Derivation of D = MeV/g = X J x 1.6 X x / g = 1.6 x J/kg = 1.6 x Gy
1ev = J x 1.6 X
1 gy = J/kg
1ev = 1.6 X J

11. Bragg Curve – Alpha Alpha Particle
Bragg Curve - plot of specific energy loss ( ie rate of ionization ) along the track of a charged particle
A typical Bragg curve is depicted in this graphic for an alpha particle of several MeV of initial energy.
The plot of specifc energy loss (which can be related to specifc ionization) along the track of a charged particle is called a Bragg Curve. A typical Bragg curve is depicted in this graphic for an alpha particle of several MeV of initial energy.
As the energy falls, the specific energy loss increases according to the Bethe-Bloch formula. As the energy falls below a threshold, however, an electron will attach to the alpha, dramatically lowering the specific energy loss.
The energy deposition of the electron increases more slowly with penetration depth due to the fact that its direction is changed so much more drastically. In fact, there is virtually no increase in energy deposited near the end of the track and the Bragg peak for electrons is not observed. Actually, a similar increase in ionization density is seen at the end of an electron track; however, the peak occurs when the electron energy has been reduced to less than about 1 keV, and it accounts for only a small fraction of its total energy. Therefore it seems that for electrons and their tortuous paths the energy deposition is spread in the transverse direction as it progresses forward in the initial direction, until the last 1 keV which is deposited pretty much along a straight line in the forward direction.
Alpha Particle
Energy loss curve – increase initially and virtually no energy deposited at the end of the track.

12. Bragg Curve –Beta Beta Path
The energy deposition of the electron increases more slowly with penetration depth due to the fact that its direction is changed so much more drastically
As the mass of the beta particle is the same as the orbital electrons they undergo several collisions … the torturous path
The plot of specifc energy loss (which can be related to specifc ionization) along the track of a charged particle is called a Bragg Curve. A typical Bragg curve is depicted in this graphic for an alpha particle of several MeV of initial energy.
As the energy falls, the specific energy loss increases according to the Bethe-Bloch formula. As the energy falls below a threshold, however, an electron will attach to the alpha, dramatically lowering the specific energy loss.
The energy deposition of the electron increases more slowly with penetration depth due to the fact that its direction is changed so much more drastically. In fact, there is virtually no increase in energy deposited near the end of the track and the Bragg peak for electrons is not observed. Actually, a similar increase in ionization density is seen at the end of an electron track; however, the peak occurs when the electron energy has been reduced to less than about 1 keV, and it accounts for only a small fraction of its total energy. Therefore it seems that for electrons and their tortuous paths the energy deposition is spread in the transverse direction as it progresses forward in the initial direction, until the last 1 keV which is deposited pretty much along a straight line in the forward direction.
Beta Path
Energy loss curve – virtually no energy deposited at the end of the track.

13. Range – Beta particle
Depends on the energy of the beta particles and the density of the absorber
Beta particle energy reduces as density of the absorber increases
Experimental analysis reveal that ability to absorb beta particle:
Depends on the number of absorbing electrons (electrons per cm 2)in the path of the beta ray – aerial density
Lesser on the atomic number of the absorber

14. Range - Energy relationship
Attenuation of beta particles
interposing layers of absorbers between beta source
The number of beta particles
reduce quickly at first
more slowly as absorber thickness increases
completely stops after certain absorber thickness
Range of beta particle - the thickness of absorber material that stops all particles

15. Range – Beta particle
Aerial density is related to the density of the absorber
td g/cm2 = ρ (density of the absorber) g/cm3 X tl (thickness of the absorber) cm
beta shields are usually made from low Z materials

16. Range – Beta particles
Calculate density thickness for aluminium of thickness 1cm .
Note: (Density of Al = 2.7g/cm3)

17. Range – Beta particles
Calculate density thickness for aluminium of thickness 1cm .
td g/cm2 = ρ g/cm3 X tl cm
td = 2.7g/cm2
A graph of beta energy VS density thickness is useful for shielding and identifying beta source

18. Range – alpha particles
Alpha particles least penetrating of the types of radiation
Alpha particles are mono-energetic. Therefore the number of alpha particles not reduced until totally eliminated at particular thickness of the absorber.
The thickness of absorber that totally stops alpha particles is the range of the alpha particle in the material.
The most energetic alpha particle travels few cms in air, while in tissue only few microns.

19. Linear Energy Transfer
LET is the rate of energy absorption by the medium
LET = keV per micron
DE = is the average energy imparted by the radiation of specific energy in traversing a distance of dx. dE dx

20. Linear Energy Transfer
Specific ionisation is the number of ion pairs formed per unit distance travelled by the radiation particle and very useful concept in health physics
Specific ionisation is very high for low energy beta particles and decreases as the energy increases.
Specific ionisation is high for alpha particles.
Travelling through air or tissue alpha particle loses on average 35 eV per ion pair it creates .
The high electrical charge and low velocity means tens of thousands of ion pair per cm of air travelled.

21. Shielding
Since heavy charged particles have a high specific ionization, they have minimal penetration ability. Alpha particles with energies of about 5 MeV (typical for common alpha emitting radionulcides) cannot penetrate the dead layer of the skin which is cm2/g.

22. Absorbed Dose
Absorbed dose is energy imparted per unit mass of material:
The unit of absorbed dose is the Gray (Gy)
(1 Gray = 1 joule/kg)
To calculate the dose from charged particles, we need to determine the amount of energy deposited per gram of material

23. Tissue Equivalent Stopping Power for Electrons
Energy (MeV)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Mass Stopping
Power, S/
(MeV-cm2)/g
4.2
2.8
2.4
2.2
2.0
1.9
1.8
These values are approximate and are from the Attix text and are applicable for electrons (beta particles). Note that the stopping power is greater for lower energy and decreases with increasing energy. This is because lower energy electrons travel slower and so impart more energy, so they have a higher stopping power and result in a greater dose.

24. Stopping Power Example
Calculate the dose from a 37,000 Bq source of 32P spread over an area of 1 cm2 on the arm of an individual for 1 hour
D =  (1.6 x 10-10) Gy
32P has a MeV beta particle (average energy). Assume that 50% of the particles on the skin interact with the skin dE
dx
The conversion constant in this equation, 1.6E(-10) comes from: (S/ in MeV-cm2/g)(1.6E-6 erg/MeV)(1 joule/1E7 erg)(1000 g/kg)(1 Gy/joule/kg)

25. Stopping Power Example
 = (½)(37,000 Bq)(1 dis/s/Bq)(1 hr)(3600 s/hr) = 6.67 x 107 dis 32P has a MeV beta particle (average energy) For tissue equivalent plastic and a beta particle with an energy of MeV, the stopping power is 1.96 MeV-cm2/g
The value of ½ indicates that half of the particulate radiation is assumed to interact with the skin, while the other half is emitted from the surface of the skin, but does not interact with the skin. Since beta radiation has a distribution of energies, the average beta energy is used. Remind the students that for beta radiation, the average energy = 1/3 of the maximum energy. The stopping power value was obtained from the appendix E in Attix text. In this case the time was assumed to be one hour. In actual dose reconstruction events the time may not be know, or may be known approximately, if at all. Under these cases, a dose rate may be established or a unit time such as a hour may be useful in terms of understanding the magnitude of the dose.

26. Stopping Power ExampledE
dx
D =  MeV-cm2/g
D = 6.67 x 107 X 1.96 X1.6 x J/kg D = Gy

27. Where to Get More Information
Cember, H., Johnson, T. E, Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2009)
International Atomic Energy Agency, Postgraduate Educational Course in Radiation Protection and the Safety of Radiation Sources (PGEC), Training Course Series 18, IAEA, Vienna (2002)