Richard Feynman developed diagrams to illustrate particle interactions through the exchange of other particles. His diagrams use straight lines for particles and curved lines for the exchanged particles. The diagrams must conserve charge at interaction points. Electromagnetic interactions exchange photons, while weak interactions exchange W bosons. Annihilation occurs when a particle collides with its antiparticle and they destroy each other, producing gamma rays. Pair production is the reverse, where a high energy photon transforms into a particle-antiparticle pair.

1. Particles
Feynman’s Diagrams
Annihilation and Pair Production
Thursday, 24 November 2011

2. Feynman’s Diagrams
Richard Feynman designed a way to illustrate interactions between
particles through exchange particles. His idea is simple:
• Straight lines represent particles before and after the interaction
• Wavy lines connect the straight lines and represent the particle
exchange
• The charge must be conserved at each junction
• Particle lines point in the same direction for both attraction and
repulsion
• The direction of the lines does not show the direction of the
particles

3. Electromagnetic Interactions
The exchange particle responsible for electromagnetic interactions is a
photon. So, Feynman’s diagrams for e- - e- and e- - p interactions are:
After After
e- e- e- p
e- e- e- p
Before Before
electron – electron repulsion electron – proton attraction

4. - Decay
In Beta decay a neutron in the nucleus decays (turns) into a proton, a
fast moving electron ( -particle) and an anti-neutrino e
n p e e
Note that e- in this case is a fast moving electron ( -particle) emitted
from within the nucleus through the decay of a neutron into a
proton, and not an atomic electron that orbits around the nucleus.

5. Feynman’s Diagram for - Decay
The force responsible for - decay is the weak force. So, the exchange
particle is the W-. Draw Feynman’s diagram for this reaction.
After
p
e- e
W
n
Before
The neutron decays into a proton releasing a W particle which very
quickly decays into an -particle and an anti-neutrino.

6. + Decay
In anti-Beta decay a proton in the nucleus decays (turns) into a neutron,
a fast moving positron ( -particle) and a neutrino e
p n e e

7. Feynman’s Diagram for + Decay
The force responsible for + decay is the weak force. So, the exchange
particle is the W+. Draw Feynman’s diagram for this reaction.
After
n
e+ e
W
p
Before
The proton decays into a neutron releasing a W particle which very
quickly decays into an -particle and a neutrino.

8. Electron Capture
It is possible for a proton in the nucleus to “capture” an electron and
turn into a neutron releasing a neutrino e
p e n e

9. Feynman’s Diagram for e- capture
The force responsible for electron capture is the weak force. So, the
exchange particle is the W+. Draw Feynman’s diagram for this
reaction.
After
n
e
W
p e-
Before
The proton turns into a neutron by trapping an e-. The exchange particle
W leaves a neutrino after the reaction.

10. Electron – Proton Collision
When an electron and a proton collide the proton turns into a neutron
releasing a neutrino e
p e n e

11. Feynman’s Diagram for e- - p collisions
The force responsible for this collision is the weak force. So, the
exchange particle is the W-. Draw Feynman’s diagram for this
reaction.
After
n
e
W
p e-
Before
The proton turns into a neutron by colliding with an e-. The exchange
particle W leaves a neutrino after the reaction.

12. Neutrino – Neutron Collisions
When two particles collide they can give rise to new matter or cause the
particles involved to change. If a neutrino e hits a neutron with
sufficient Ek, the neutron turns into a proton and releases an
electron.
n e p e

13. Feynman’s Diagram e– n collision
The force responsible for e – n collisions is the weak force. So, the
exchange particle is the W+. Draw Feynman’s diagram for this
reaction.
After
p
e-
W
n
e
Before
The neutron turns into a proton by colliding against a neutrino. The
exchange particle W leaves an electron after the reaction.

14. Anti-neutrino – Proton Collisions
When an anti-neutrino e hits a proton with sufficient Ek, the proton
turns into a neutron and releases a positron (e+).
p e n e

15. Feynman’s Diagram e– p collision
The force responsible for e – p collisions is the weak force. So, the
exchange particle is the W+. Draw Feynman’s diagram for this
reaction.
After
n
e+
W
p
Before e
The proton turns into a neutron by colliding against an anti-neutrino.
The exchange particle W leaves a positron after the reaction.

16. Annihilation
When an anti-particle is created it can be observed, but only for a very
short time. This is because:
• It will soon collide against its particle
• The two destroy each other
• Their mass is converted in energy
This process is called ANNIHILATION.

17. Annihilation
Look at the annihilation of an electron and its anti-particle (positron)
e- e+

18. Annihilation
Why are two photons of energy produced and not just one? (Hint: any
collision must obey all conservation laws)
0 0 0
1 e 1 e 2 0
• One photon only could conserve charge and mass/energy
• But to conserve momentum two photons moving in opposite
directions must exist

19. Pair Production
A high energy photon like a -ray can vanish to form a pair particle –
anti-particle. This is the opposite of annihilation and we call it PAIR
PRODUCTION.
e+ e-

20. Pair Production
In what way would a third particle, e.g. nucleus or electron, get involved
in this reaction? (Hint: again all conservation laws must apply)
0 0 0
0 1 e 1 e
• The third particle recoils and carries away some of the energy of the
photon
• The recoil ensures that the momentum is also conserved