Charged Particle Interactions Flashcards
What are the sources of charged particles for medical physics?
Produced in beam (thermal emission)
Results from photon/particle interaction
Radioactive decay
How are charged particles different from photons?
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
What happens in an elastic scatter?
No loss of energy (same energy)
What causes radiative energy loss?
Inelastic scatter from nucleus/atomic electron (photon emitted, Bremmsstrahlung/Cherenkov)
Inelastic scatter causing excitation
(atomic electron excited, delayed photon emitted)
What causes collisional energy loss?
Ionisation: electron goes in and 2 electrons exit the interaction (one is more energetic and called the primary)
What is the stopping power?
dE/dx
Energy loss of charged particles along path/ Equal to the average energy loss per unit length travelled in medium
What is the stopping power made up of?
Made up of collisional and radiative parts
What is the equation for mass stopping power?
Linear stopping power / density
What is the charged particle range, r_0?
How far a charged particle of a given energy will travel in a medium before being stopped (E=0)
Depends on velocity of CP
What are the approximations applied to the charged particle range equation?
CSDA: Continuous slowing down approximation
Straight ahead approximation
What is CSDA approximation?
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
What effect does the CSDA approximation have on r_0?
r_0 is always smaller than mean value of path length actually travelled - range straggling
What is the straight ahead approximation?
Any changes in direction are ignored (not true for electrons as they scatter but good for heavier particles)
What is the detour factor, d ?
d = z_av / r_0
(departure from linearity)
always less than 1
z_av = mean penetration depth
r_0 = CSDA range
When does detouring occur?
When energy is low due to interaction with atoms as it travels slowly and can interact more with atoms and be pulled apart
What does the detour factor depend on?
Energy
Z of medium
What are the two methods of measuring the CP range?
- Transmission method: beam of particles through material which will increase in thickness and detector measure fraction transmitted
- Measuring depth dose in a medium (e.g. water): Phantom is moved away from water surface
What is range straggling?
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
What happens at large depths of the depth dose measurement?
At large depths there is bremsstrahlung from electrons
What causes fragmentation tail on depth dose curve for heavy ions?
The fact heavy ions make more nuclear reactions possible
What is Coulomb’s law?
F = k q1 q2 / r^2
Large forces reduced by inverse square law
What can incoming charged particles interact with?
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)
What is the impact parameter (b) ?
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)
What does the type of interaction depend on?
Depends on distance of approach
Velocity of particle
Duration of collision
What is the energy lost by a charged particle proportional to?
dE/dx ∝ z^2 / v^2
v = velocity
What causes the peak in the Bragg curve?
1/v^2 factor in dE/dx equation
Particle energy changes dramatically as velocity is reduced
What does the Bethe formula assume?
Energy transferred is small compared to particle E
Orbital velocity of atomic electron «_space;v
What is the mean excitation energy I ?
Weighted average of all possible energy transfers from excitation and ionisation
depends on Z
(inside of Bethe formula)
What are the jumps in the mean excitation energy graph (1/Z vs Z) caused by?
Peaks represent full orbital shells which require a lot of energy to excite the electron drops to shells
What is the mean excitation energy equation?
n ln I = Σ N Z ln I
n = electron density
N = atoms of Z
What is the restricted stopping power?
Focuses on low energy loss interactions, at a “cut off energy” Ec
so no interactions with high energy transfers are considered
useful for dosimetry
What is the mass of a light incoming charged particle ?
Mass of struck electron/positron
What do the interactions with light charged particles cause?
Ejection of atomic electron (maximum energy transfer is 50% of the original electron energy)
What happens to light charged particle interactions at low energies?
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
What does stopping power vary with?
Particle kinetic energy
What are the losses of electrons at different energies?
At high energies: high radiative losses
At low energies: high collisional losses
