Week 2: Interaction of radiation with matter part 1

Question 1

What are the two categories we can separate different types of radiation into?

Answer 1

Charged and Uncharged.

Question 2

Give examples of charged radiation.

Answer 2

Heavy charged particles - protons, alpha particles, muons, heavy ions.

Electrons.

Question 3

Give examples of uncharged radiation.

Answer 3

Gamma rays

Neutrons.

Question 4

Describe the situation in a collision between a heavy and light particle in the rest frame of the heavy particle.

Answer 4

The light mass approaches the heavy particle with velocity v. It then collides with the heavy particle and the travels away with velocity v. The heavy particle remains at rest.

Question 5

Describe the situation in a collision between a heavy and light particle in the rest frame of the light particle.

Answer 5

The heavy particle approaches the small mass with velocity v. The masses then collide and the the heavy particle continues on the same trajectory with approximately the same velocity. The small mass appears to move with velocity 2v.

In order for the two frames to agree on how fast the particles separate after the collision, the light particles must move at v more than the speed of the heavy particles.

Question 6

Show that in a head on collision between a light and heavy particle, the maximum change in energy of the light particle is much less than the energy of the heavy particle.

Answer 6

(2)

Question 7

What is stopping power?

Answer 7

The loss of energy with distance is quantified by the stopping power.

S = -dE/dx

Question 8

What is the negative sign for in stopping power?

Answer 8

The minus sign is because energy is lost as the particle moves through material.

Question 9

What is the range of a particle? What integral can be used to find a particle’s range?

Answer 9

The range, R, is how far a particle will travel through a medium.

(3)

Question 10

Derive an equation which relates the transfer of momentum to the energy transfer of a particle travelling through a “sea” of electrons.

Answer 10

(4)

Question 11

Describe Gauss’ law and write it down in it’s integral form.

Answer 11

The electric flux though a closed surface is equal to the charge enclosed by the surface divided by the the electric constant.

(5)

Question 12

How can the impact parameter be used to solve the Gaussian integral for the Bethe-Bloch formula?

Answer 12

(6)

Question 13

What is the energy transferred for a given value of b?

Answer 13

(7)

Question 14

How can we find the energy lost due to all interactions with electrons for a given value of b?

Answer 14

By multiplying the energy lost per interaction by the number of electrons.

(8)

Question 15

In what scenarios do the maximum and minimum energy transfers occur?

Answer 15

The maximum energy transfer occurs in the head-on collision.

The minimum energy transfer is assumed to be the mean excitation energy, I, the average energy required to ionise atoms of the medium.

Question 16

What is the Bloch approximation?

Answer 16

The Bloch approximation is the approximation for the mean excitation energy of different materials based on their atomic numbers.

I = 10Z eV

Question 17

What is the mass stopping power and why do we use it?

Answer 17

The stopping power is related to the electron density and therefore to the material density.

To remove this dependency, it is common to divide the stopping power by the density to give the mass stopping power.

Question 18

What observation can we make from the Bethe-Bloch formula?

Answer 18

The terms inside the square brackets vary only slowly with the energy if the charged particle. Much of the behaviour is driven by the terms outside of the brackets.

The stopping power of a material will be directly proportional to its atomic number, as this is what drives the number of electrons.

For a non-relativistic particle, the stopping power is approximately inversely proportional to v^2 over a broad range of values.

In physical terms, the slower a particle is moving, the more time it spends near each electron, allowing more energy to be transferred.

Question 19

What is the relationship between stopping power, charge and speed?

Answer 19

A common approximation for the behaviour of the stopping power with z and v is:

S is proportional to z^2 / v^2.

Question 20

What is the Bragg curve? What is the Bragg peak?

Answer 20

The Bragg curve plots the number of ions produced in the material per unit length against the depth.

The stopping power increases at low energies, so the amount of ionisation caused goes up as the particle slows down. This leads to a characteristic peak in the curves, known as the Bragg peak. Once it has been slowed down enough, the particle deposits lots of energy over a very small distance, and then stops.

Question 21

What is straggling?

Answer 21

Once the energy of the particle becomes low enough, it can be subject to changes in direction that did not occur at higher energies. This is known as straggling.

Question 22

In which ways can electrons lose energy?

Answer 22

Collisional - similar process to heavy charged particles.

Radiative - Due to their low mass, electrons are much more likely to exhibit Bremsstrahlung than heavier particles. This means at high energies, they lose energy by radiative means as well.

Question 23

What is the mathematical description of electron energy losses?

Answer 23

(9)

Question 24

List four different examples of heavy charged particles.

Answer 24

Protons, alpha particles, muons, heavy ions (i.e. 12C nucleus)

Question 25

What units are typically used for stopping power?

Answer 25

MeV mm^-1

Question 26

Explain how the electron density can be calculated from the properties of the material.

Answer 26

Given the density and mass number of the material, the number density of the atoms is found using Avogadro's law. The electron density can then be calculated by multiplying by the atomic number.

Question 27

Explain why the mass stopping power is commonly quoted instead of the stopping power.

Answer 27

The mass stopping power removes the density dependence from the value, allowing one number to be given as a reference and scaled for each application according to the density of the material involved. If this was not done, the stopping power would need to be given at many different densities.

Question 28

State two differences between the paths of heavy charged particles and electrons when interacting with matter.

Answer 28

Heavy charged particles move in relatively straight lines while electrons frequently change direction. Heavy charged particles have a well-defined range, while the range of electrons varies considerably.

Question 29

State the two mechanism by which electrons lose energy and give a brief description of how their relative importance varies with energy in a low Z material.

Answer 29

Collisional and radiative. Collisional losses will dominate up to MeV scale energies, then the radiative losses will become more important, eventually causing more energy loss than collisional processes once the electron energy is in the tens of MeV.