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Balancing the Equations

It has been discovered that Nature has specific rules for particle interactions and decays, and these rules have been summarized in terms of conservation laws.

Conservation of baryon number

  • Each of the baryons is assigned a baryon number B=1 and for anti-baryons B=-1. This can be considered to be equivalent to assigning each quark a baryon number of 1/3 and each anti-quark a baryon number of -1/3(see data sheet).
  • Mesons, with one quark and one antiquark, have a baryon number B=0.
  • No known decay process or interaction in nature changes the net baryon number.

All baryons have a baryon number of +1 and all anti-baryons a baryon number of -1

Conservation of lepton number

This rule is a little more complicated than the conservation of baryon number because there is a separate requirement for each of the three sets of leptons, the electron, muon (a heavy electron!) and tau (not on the syllabus - even heavier than the muon!) and their associated neutrinos... each type of lepton has to be conserved. (See here for more background).

NB The matter lepton is negative and its antiparticle positive!

A lepton number of 1 is assigned to the electron and the electron neutrino and -1 to the positron electron antineutrino

 

Each class of leptons has a lepton number of +1 and its anti-leptons a lepton number of -1

Remember from GCSE that when b-decay occurs a neutron changes into a proton inside the nucleus.

For a particle equation to be 'allowed' charge, baryon quantum number and lepton number have to balance.

There is a problem here; we need another lepton to balance the equation. It needs to be an anti-matter particle with no charge; it must therefore be an anti-neutrino.

If we amend the equation we get:

  • For positron emission the proton inside the nucleus changes into a neutron.
  • Work out the equation in rough as above.
  • Sometimes a nucleus captures an electron from a low energy orbital - electron capture (& Sang page 55) making a proton transform into a neutron.
  • Work out the equation in rough as above.
  • Collisions between particles occur making protons and neutrons mutate. Try the following:
  • electron-proton collision
  • neutrino-neutron collision
  • antineutrino-proton collision
  • Work out the equations in rough as above.

Now check your results against the Feynman diagrams of those events..