Particle Interactions

Annihilation

When particles and antiparticles meet, they annihilate each other, releasing their combined mass as energy in the form of photons:

Because momentum and energy have to be conserved, two or three photons are created.  If there is sufficient energy, other particles may be created as well.  For example, the collision between an electron and a positron may give rise to two muons:

                        e-   +   e+  ---->  m+      +     m-

The reverse process can apply as well.  Electrons and positrons can be formed when a gamma ray passes through matter.  This pair production is a good illustration of the interchangeability of mass and energy.  We can see this by applying a magnetic field.  The opposite charges make circular paths in opposite directions.

Lepton Interactions

There are six particle-antiparticle pairs known.  Leptons (Greek – “light thing” or “small coins”) are the smallest of the fundamental particles.  They have the following properties:

• fundamental particles without structure

• they interact by the weak interaction.  If they are charged, they interact by the electromagnetic interaction, but NOT the strong interaction.

• charge and lepton number are conserved in all allowed lepton processes.

There are three categories of lepton number, L_e, L_m, and L_t.  Each lepton has a lepton number, 0 or 1, in each category, and each antilepton has a number 0 or -1 in each category.  You need to know the lepton numbers.

The names of the leptons are:

Each particle has an antiparticle; for the electron, it is the positron, the muon the antimuon, and the tau, the antitau.  We show the anti-particle either by an opposite charge (e+) or by putting a bar across the symbol.

Consider this decay:

Notice how the lepton number and charge are conserved.  This means that the decay can proceed.  If leptons interact with hadrons, the hadrons are considered to have a lepton number of 0.

Hadrons

There are a very large number of particles that are classified as hadrons, which are subdivided into two further classifications, the mesons, and the baryons. 

• Hadrons interact by the strong, weak, and electromagnetic force.    

• They are not fundamental particles but have a structure.

• They have non-zero rest masses, about 1 GeV/c²

• They have an associated value of charge, Q,and baryon number B.

Hadrons with zero baryon number are called mesons; those with baryon number of 1 are called baryons. 

Mesons

These particles have a smaller rest mass than the baryons (and a lower rest mass than the tau lepton).  They have:

• Zero baryon number. 

• Short lifetimes.

• Antiparticles

Here are a few mesons:

 Notice how short the lifetimes are of these mesons.

We should note the following:

• Mesons have TWO quantum numbers that must be conserved in interactions.  The charge is denoted by Q, the baryon number by B.  Mesons have a baryon number of 0.

• Mesons have a lepton number of 0.  This must be conserved in any interactions with leptons.

Here is a typical decay:

Notice the conservation of charge and baryon number.

Here are some more:

Baryons

These are the heavyweights of particle physics, and include the familiar proton and neutron.

• They are made up of three quarks

• They have quantum numbers such as charge and baryon number, which must be conserved in interactions.

  Let us look at the properties of the baryons:

Typical Decay

The proton is the only stable baryon.  All the others spontaneously decay, although the neutron within a nucleus is stable, apart from beta decay.  The decay times are incredibly short, except the isolated neutron which takes about 8 to 10 minutes.  Baryons decay to protons, either directly (S+ --> p + p⁰) or indirectly (W- --> L⁰ + K, then L⁰ -->  p +  p-).  Mesons decay to photons or leptons.

As in radioactivity, the decay of particles is random.  The values quoted are the mean lifetimes, not half-lives.

 It is believed that gluons are shuttled backward and forward between the quarks like rugby footballs. 

Mesons bind the baryons together with the strong force.   

The proton is the only baryon that is stable in isolation.  The neutron on its own decays to a proton by beta minus decay after about 14 minutes.  The decay is as a result of the weak interaction that occurs within nucleons.

Beta decay

Beta emission is completely different to alpha.  Beta particles can be negative (b-), which is more common, or b+ in which a positively charged particle is given off.  For beta b- emission we know the following:

• b- particles are given off by neutron-rich nuclei

• b- particles are electrons

• b- emission is accompanied by the simultaneous emission of an antineutrino, <n_e>.

It is worth noting that the electron and antineutrino are NOT present in the nucleus before the beta decay.  We can write the same for a b+ decay.  A neutron decays to give a b+ with a neutrino.  The b+ particle is called a positron, which is the same size as an electron but has a charge of +1.  We can write general equations to describe beta decay.

  The key thing to be aware of at the particle level is that beta decay is due to the weak interaction, whereby a neutron is turned into a proton:

Feynman Diagrams

We can show this using a Feynman diagram, which we will use as a pictorial representation of what is going on.  They were first devised by Richard Philips Feynman (1918 – 1988) who was an American particle physicist.  At the nucleon level we see:

At the quark level we see:

Beta plus decay is mediated by the W+ particle, to release a positron and an electron neutrino.

There are many other interactions that can be summed up with Feynman diagrams, for example:

• electron capture

• neutrino-neutron collisions

• antineutrino-proton collisions

• electron proton collisions.

When we attempt these, we need to know what the interaction is in terms of the four fundamental forces.

Photons

The forces between electrically charged particles are thought to be transmitted by photons, which are emitted and absorbed by the particles.  We normally associate photons with the particle properties of electromagnetic waves. 

Gluons

As separate particles, gluons have never been directly identified.  They are however the mediators of the strong nuclear force and there is compelling indirect evidence for them.  They are thought to be fundamental particles.  There are eight gluons that have been identified theoretically from quantum chromodynamics, each having a different “colour”, although all have zero rest mass and zero charge.  The nucleons in the nucleus are thought to be held together by mesons such as the pi-meson.

W+, W-, and Z

These are thought to mediate the weak force.  W+ mediates beta plus decay, W- beta minus.   The weak force is little understood, but is thought to be responsible for fusion in stars.  The role of the Z boson is unclear.

Presentation
Now try