Charged Particle Interactions

Question 1

What are the sources of charged particles for medical physics?

Answer 1

Produced in beam (thermal emission)

Results from photon/particle interaction

Radioactive decay

Question 2

How are charged particles different from photons?

Answer 2

They have mass and charge (make electric fields around them so Beer’s law can’t be applied)

Photons have few interactions per unit length unlike CP

Photons have bigger characteristic length

Photons have larger energy loss per interaction

Photons in theory have infinite penetration

Question 3

What happens in an elastic scatter?

Answer 3

No loss of energy (same energy)

Question 4

What causes radiative energy loss?

Answer 4

Inelastic scatter from nucleus/atomic electron (photon emitted, Bremmsstrahlung/Cherenkov)

Inelastic scatter causing excitation
(atomic electron excited, delayed photon emitted)

Question 5

What causes collisional energy loss?

Answer 5

Ionisation: electron goes in and 2 electrons exit the interaction (one is more energetic and called the primary)

Question 6

What is the stopping power?

Answer 6

dE/dx

Energy loss of charged particles along path/ Equal to the average energy loss per unit length travelled in medium

Question 7

What is the stopping power made up of?

Answer 7

Made up of collisional and radiative parts

Question 8

What is the equation for mass stopping power?

Answer 8

Linear stopping power / density

Question 9

What is the charged particle range, r_0?

Answer 9

How far a charged particle of a given energy will travel in a medium before being stopped (E=0)

Depends on velocity of CP

Question 10

What are the approximations applied to the charged particle range equation?

Answer 10

CSDA: Continuous slowing down approximation

Straight ahead approximation

Question 11

What is CSDA approximation?

Answer 11

All energy lost by continuous rate along particle track given by stopping power

(all energy loss fluctuations neglected)

Only refers to interactions that result in energy loss

Question 12

What effect does the CSDA approximation have on r_0?

Answer 12

r_0 is always smaller than mean value of path length actually travelled - range straggling

Question 13

What is the straight ahead approximation?

Answer 13

Any changes in direction are ignored (not true for electrons as they scatter but good for heavier particles)

Question 14

What is the detour factor, d ?

Answer 14

d = z_av / r_0

(departure from linearity)

always less than 1

z_av = mean penetration depth

r_0 = CSDA range

Question 15

When does detouring occur?

Answer 15

When energy is low due to interaction with atoms as it travels slowly and can interact more with atoms and be pulled apart

Question 16

What does the detour factor depend on?

Answer 16

Energy

Z of medium

Question 17

What are the two methods of measuring the CP range?

Answer 17

1. Transmission method: beam of particles through material which will increase in thickness and detector measure fraction transmitted
2. Measuring depth dose in a medium (e.g. water): Phantom is moved away from water surface

Question 18

What is range straggling?

Answer 18

Statistical variation at tail of graph which explains why the range measurements have a tail rather than a sharp drop-off

it varies with energy/medium

Question 19

What happens at large depths of the depth dose measurement?

Answer 19

At large depths there is bremsstrahlung from electrons

Question 20

What causes fragmentation tail on depth dose curve for heavy ions?

Answer 20

The fact heavy ions make more nuclear reactions possible

Question 21

What is Coulomb’s law?

Answer 21

F = k q1 q2 / r^2

Large forces reduced by inverse square law

Question 22

What can incoming charged particles interact with?

Answer 22

Individual electrons
(elastic if sub-excitation collision)

Nucleus
(nuclear reactions possible or scattering)

Coulomb field of whole atom
(applies to heavy particles at low velocity and scattering can occur if particles are slow)

Question 23

What is the impact parameter (b) ?

Answer 23

Distance of approach
b»a: soft collision (Coulomb force disrupts atomic structure - excitation/ionisation)

b~a: hard collision (individual electron ejected)

b«a: nuclear reaction (incoming electrons)

Question 24

What does the type of interaction depend on?

Answer 24

Depends on distance of approach

Velocity of particle

Duration of collision

Question 24

What is the energy lost by a charged particle proportional to?

Answer 24

dE/dx ∝ z^2 / v^2

v = velocity

Question 25

What causes the peak in the Bragg curve?

Answer 25

1/v^2 factor in dE/dx equation

Particle energy changes dramatically as velocity is reduced

Question 26

What does the Bethe formula assume?

Answer 26

Energy transferred is small compared to particle E

Orbital velocity of atomic electron &laquo_space;v

Question 27

What is the mean excitation energy I ?

Answer 27

Weighted average of all possible energy transfers from excitation and ionisation

depends on Z

(inside of Bethe formula)

Question 28

What are the jumps in the mean excitation energy graph (1/Z vs Z) caused by?

Answer 28

Peaks represent full orbital shells which require a lot of energy to excite the electron drops to shells

Question 29

What is the mean excitation energy equation?

Answer 29

n ln I = Σ N Z ln I

n = electron density

N = atoms of Z

Question 30

What is the restricted stopping power?

Answer 30

Focuses on low energy loss interactions, at a “cut off energy” Ec

so no interactions with high energy transfers are considered

useful for dosimetry

Question 31

What is the mass of a light incoming charged particle ?

Answer 31

Mass of struck electron/positron

Question 32

What do the interactions with light charged particles cause?

Answer 32

Ejection of atomic electron (maximum energy transfer is 50% of the original electron energy)

Question 33

What happens to light charged particle interactions at low energies?

Answer 33

CSDA approximation can’t be applied as fractional loss per interaction becomes too large

At E < 2 keV: Bethe-Bloch not used as incident velocity

Split electrons into core and valence electrons

Question 34

What does stopping power vary with?

Answer 34

Particle kinetic energy

Question 35

What are the losses of electrons at different energies?

Answer 35

At high energies: high radiative losses

At low energies: high collisional losses