Activity: Particle interactions

Aims

  • Introduce the idea of exchange particles.
  • Describe the force between electrons in terms of the exchange of virtual photons.
  • Construct Feynman diagrams to represent the interactions between electrons and photons.
  • Describe the nuclear force in terms of the exchange of virtual mesons.

Photons and electrons

We have seen that when we move a charge it sends out ripples in electric field.

You now also know that the moving charge will cause a perpendicular magnetic field which will also change. This changing electric and magnetic field is called an electromagnetic wave. This wave gives the probability of an interaction taking place and when this interaction is on a small scale it is like being hit by a particle, this particle is called a photon.

So if we have two electrons and move one we can think of a photon traveling from one to the other causing a force to be transmitted.

But electrons repel each other all the time so there must be a continual exchange of particles. These are know as virtual photons as they only exist between the particles and can't interact with anything else.

If we consider two electrons held in position by some sort of microscopic clamp.

  • Is there a force between the electrons?
  • Is there an exchange of virtual photons?
  • Do photons have energy?
  • Are the electrons losing energy?

So how can photons be created without energy being added?
The answer come from Heisenberg's uncertainty principle (HL only)

capital delta E capital delta t space greater or equal than fraction numerator h over denominator 4 pi end fraction

If the photon exists for only a short time Δt, then it can have energy ΔE ≥ h/4πΔt without violating the law of conservation of energy. Shorter time implies higher energy.

  • Bigger force requires higher energy photons, use this fact to explain why the force of repulsion must decrease with increasing distance.

Feynman Diagrams

These are diagrams used to represent particle interactions below is an example. This is called a vertex.

Here an electron emits a photon.
Note that the arrows and lines do not represent the paths of the particles they represent the progression through time (left > right). So we start with an electron it emits a photon and it's still an electron.

Rules for drawing vertices.

  1. straight lines are particles wavy lines are photons
  2. each vertex has 2 straight one wavy line
  3. time progresses left to right (sometimes drawn with time going up)
  4. particles point forwards in time antiparticles backwards.
  5. there is always one arrow entering and one leaving.

One of the neat things about Feynman diagrams is that once the diagram is drawn for a known interaction the arrows can be rotated to predict other ones.

  • Describe the interactions given by the following rotations of the previous diagram.

Here is a simulation that can be used to give the answer but try without first. I couldn't make the wavy lines so used dashes.

To represent the interaction between two electrons we need two vertices.

Here two electrons repel each other

  • Describe this interaction.

Try drawing Feynman diagrams for the following:

  • An electron annihilates with a positron to form a photon which creates a positron and electron pair.

  • A positron repels another positron

  • Why is the following diagram not possible?

Here is another simulation to play with.

A video about Feyman diagrams by sixty symbols

And a message from the great man himself.

Nuclear Force

According to the principle of Occam's razor, the simplest model is often the correct one (NOS) so it would make sense if all particle interactions involved an exchange particle. If this is the case what sort of particle would be responsible for the nuclear force?

We can estimate the mass of the particle using Heisenberg's uncertainty principle again (HL but SL can give it a go)

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The nuclear force is very short range, so only acts in the nucleus. We can say that the range is approximately equal to the size of the nucleus.

  • What is the range of the nuclear force?

Particles with mass can not travel faster that the speed of light (3 x 108 ms-1)

  • Estimate the shortest time possible for a particle to travel across a nucleus.
  • Using this time as Δt use the uncertainty equation to find ΔE.
  • Convert ΔE into MeV

So the particle has an energy of about 110 MeV which is equivalent to a mass of 110 MeVc-2 . The mass of a proton is about 931 MeVc-2 and the mass of an electron 0.5 MeVc-2 so this is a medium sized particle or meson.

This is what the Feynam diagram would look like.

We shall see later that this can be broken down into smaller components.

Weak Force

Maybe you can see a pattern forming? Charged particles can take part in electromagnetic interactions, nucleons can take part in strong interactions but what about neutrinos? They are neither charged or nucleons. These interactions are called weak interactions because they aren't strong.The range is very short (10-18 m) so the exchange particle has a very large mass (80 GeVc-2)

  • Try to construct a Feynam diagram for beta decay (the exchange particle is the W-)

  • Using your diagram make some predictions of other possible interactions.
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