A more detailed diagram of the neutron's decay identifies it as the transformation of one of the neutron's down quarks into an up quark. It is an example of the kind of quark transformations that are involved in many nuclear processes, including beta decay.
The decay of the neutron is a good example of the observations which led to the discovery of the neutrino. An analysis of the energetics of the decay can be used to illustrate the dilemmas which faced early investigators of this process.
Using the concept of binding energy, and representing the masses of the particles by their rest mass energies, the energy yield from neutron decay can be calculated from the particle masses. The energy yield is traditionally represented by the symbol Q. Because energy and momentum must be conserved in the decay, it will be shown that the lighter electron will carry away most of the kinetic energy. With a kinetic energy of this magnitude, the relativistic kinetic energy expression must be used.
For the moment we presume (incorrectly) that the decay involves just the proton and electron as products. The energy yield Q would then be divided between the proton and electron. The electron will get most of the kinetic energy and will be relativistic, but the proton is non-relativistic. The energy balance is then
In the rest frame of the neutron, conservation of momentum requires
pcelectron = - pcprotonand pcelectron can be expressed in terms of the electron kinetic energy
The energy balance then becomes
When you substitute the numbers for this value of Q, you see that the KEe2 term is negligible, so the required kinetic energy of the electron can be calculated. The required electron kinetic energy for this two-particle decay scheme is
Note that the maximum kinetic energy of the recoiling proton is only about 0.4 KeV, so the recoil energies of other nuclei which have emitted beta particles is very small compared to the electron energies.
Likewise, the momentum of the electron for this two particle decay is constrained to be
Momentum and energy for the two-particle decay are constrained to these values, but this is not the way nature behaves. The observed momentum and energy distributions for the electron are as shown below.
The fact that the electrons produced from the neutron decay had continuous distributions of energy and momentum was a clear indication that there was another particle emitted along with the electron and proton. It had to be a neutral particle and in certain decays carried almost all the energy and momentum of the decay. This would not have been so extraordinary except for the fact that when the electron had its maximum kinetic energy, it accounted for all the energy Q available for the decay. So there was no energy left over to account for the mass energy of the other emitted particle. The early experimenters were faced with the dilemma of a particle which could carry nearly all the energy and momentum of the decay but which had no charge and apparently no mass!
The mysterious particle was called a neutrino, but it was twenty five years before unambiguous experimental observation of the neutrino was made by Cowan and Reines. The present understanding of the decay of the neutron is
This decay illustrates some of the conservation laws which govern particle decays. The proton in the product satisfies the conservation of baryon number, but the emergence of the electron unaccompanied would violate conservation of lepton number. The third particle must be an electron antineutrino to allow the decay to satisfy lepton number conservation. The electron has lepton number 1, and the antineutrino has lepton number -1.
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