Matter and Antimatter – Laws of Conservation in Nuclear Reactions
In analyzing nuclear reactions, we apply the many conservation laws
. Nuclear reactions
are subject to classical conservation laws for charge, momentum, angular momentum, and energy
(including rest energies). Additional conservation laws, not anticipated by classical physics, are are electric charge
, lepton number and baryon number
. Certain of these laws are obeyed under all circumstances, others are not.
At this point, we describe especially the relationship between antimatter and the following laws of conservation:
In particle physics
Law of Conservation of Lepton Number
, the lepton number
is used to denote which particles are leptons and which particles are not. Each lepton
has a lepton number of 1
and each antilepton
has a lepton number of -1
. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number
in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.
The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.
Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:
Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum), the third particle must be an electron antineutrino.
Law of Conservation of Baryon Number
In particle physics, the baryon number
is used to denote which particles are baryons and which particles are not. Each baryon has a baryon number of 1 and each antibaryon
has a baryon number of -1. Other non-baryonic particles have a baryon number of 0. Since there are exotic hadrons like pentaquarks and tetraquarks, there is a general definition of baryon number as:
where nq is the number of quarks, and nq is the number of antiquarks.
The baryon number is a conserved quantum number in all particle reactions.
The law of conservation of baryon number states that:
The sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.
For example, the following reaction has never been observed:
even if the incoming proton has sufficient energy and charge, energy, and so on, are conserved. This reaction does not conserve baryon number since the left side has B =+2, and the right has B =+1.
On the other hand, the following reaction (proton-antiproton pair production) does conserve B and does occur if the incoming proton has sufficient energy (the threshold energy = 5.6 GeV):
As indicated, B = +2 on both sides of this equation.
From these and other reactions, the conservation of baryon number has been established as a basic principle of physics.
This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons. Thus, the decay would violate the conservation of baryon number. It must be added some theories have suggested that protons are in fact unstable with very long half-life (~1030 years) and that they decay into leptons. There is currently no experimental evidence that proton decay occurs.
Law of Conservation of Electric Charge
The law of conservation of electric charge
can be demonstrated also on positron-electron pair production
. Since a gamma ray
is electrically neutral and sum of the electric charges of electron and positron is also zero, the electric charge in this reaction is also conserved.
Ɣ → e- + e+
It must be added, in order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy. If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles. The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.