8. Introduction of Particles with Matter Flashcards

You may prefer our related Brainscape-certified flashcards:
1
Q

What are alpha, beta and gamma rays all examples of?

A

-ionising radiation

2
Q

Ionising Radiation

Definition

A

-interacts with matter as it passes through it, ionising nearby atoms

3
Q

What are the two mechanisms by which charged particles can lose energy?

A

1) Ionisation

2) Bremsstrahlung

4
Q

Ionisation

Definition

A
• as a charged particle moves through bulk matter, its electric field ionises atoms in the material
• this slows the particle
5
Q

Ionisation

Momentum Transfer Parallel to v

A

-momentum transfer parallel to v is negligible

6
Q

Ionisation

pe

A

pe = 2Ze² / 4πεovb

7
Q

Ionisation

Energy Transferred to a Single Electron

A

E = pe²/2m = 2/m (Ze²/4πεov)² 1/b²

8
Q

Ionisation

Number of Electrons in a Cylindrical Shell

A

nZmat2πb db dx

9
Q

Ionisation

Rate of Energy Loss

A
• dE/dx = 4πnZmat/mv² (Ze²/4πεo)² ln(bmin/bmax)

- where bmin and b max are the minimum and maximum impact parameters that can cause ionisation

10
Q

Maximum Impact Parameter

A

-if the particle is too far away, the amount of energy it can transfer is less than the ionisation energy
-to a good approximation, consider the Coulomb force to act only over a distance where |x|<b>
bmax = hv/πI
-where I is the mean ionisation energy</b>

11
Q

Minimum Impact Parameter

A

-b is only well defined up to uncertainty in position (of order of the de Broglie wavelength):
bmin = ℏ/2mev

12
Q

Bethe Formula

A
• subbing in expressions for bmin and bmax, we arrive at the Bethe Formula for stopping power due to ionisation;
• dE/dx = 4πnZmat/mev² * (Ze²/4πεo)² * ln(2me*v²/I)
13
Q

Bethe Formula Generalised for Relativistic Formula

A

-for relativistic (i.e fast moving) particles:
-dE/dx ∝ Z² Zmat/A 1/β² [1/2 ln(2meβ²γ²*Tmax/I²)-β²-𝛿(β)/2]
-where:
β = v/c
γ = 1/√[1-v²/c²]
and Tmax is the maximum kinetic energy that the charged particle can transfer to a single (stationary) electron

14
Q

What is Tmax?

A

Tmax is the maximum kinetic energy that the charged particle can transfer to a single (stationary) electron
Tmax = [2meβ²γ²] / [1 + 2γ me/M + (me/M)²]

15
Q

What is x?

A

-x is not a physical distance, we define x such that:
x = ρl
-where ρ is the density and l is the physical path length
-note that x has units of g/cm²

16
Q

Minimum Stopping Power

A

-occurs at βγ≈3

17
Q

Stopping Power vs βγ Graph

A
• minimum at βγ≈3
• below this, S(E) increases sharply
• above this there is a logarithmic increase
18
Q

Lorentz Contraction

A

-on a larger scale, relativistic effects become important, in particular the amount of Lorentz contraction

19
Q

Bremsstrahlung

Description

A

-Bremsstrahlung o braking radiation is the radiation emitted by an energetic charged particle as it decelerated in the presence of an electromagnetic field, e.g. due to motion through a medium

20
Q

Bremsstrahlung

Energy Loss

A
• energy loss is proportional to energy:

- dE/dx ∝ E

21
Q

Bremsstrahlung

Radiation Length

A

-get exponential decay, define radiation length Xo such that:
E = Eo*exp(-x/Xo)

22
Q

Ionisation Losses and Radiation Losses With Energy

A
• ionisation losses increase logarithmically with energy
• radiative losses increase linearly with energy
• there must be a critical energy above which radiative losses dominate and below which ionisational losses will dominate
23
Q

Bremsstrahlung

Total Energy Loss

A

-dE/dx = Eionisation + Eradiation

= [aln(E)+b]/E + kE

24
Q

Bremsstrahlung

Bragg Peak

A
• we find that stopping power peaks suddenly just before the particle comes to rest with the particle depositing the majority of its energy in a short distance
• this is known as the Bragg peak
25
Q

Cerenkov Radiation

Description

A
• another way that charged particle interact with their surroundings
• this is the electromagnetic analogue of a bow wave in water surfaces or a sonic boom in air
• when an object capable of causing disturbances in a medium travels through that medium, it causes waves to propagate outwards
• of the object travels faster than the waves can propagate, then constructive interference of successive waves creates a plane wave that propagates at a particular angle away from the objects direction of motion