Background

Electron emission can be explained as being from nuclides in which there are neutrons which are not paired with protons. A similar analysis should explain positron emission but positron emission is much more complicated than electron emission. First of all, some of the nuclei of most unstable structure emit protons instead of positrons. A few such nuclei decay by the capture of an inner orbit electron.

The analysis here is based upon the analysis of the binding energies of almost three thousand different nuclides. That analysis reveals that nuclei are held together by the spin pairing of nucleons. But spin pairing is exclusive in the sense that a neutron can pair with one other neutron and with one proton and no more. The same goes for a proton. But in addition to the spin pairing there is an interactive force between all nucleons which involves like nucleons being repelled from each other and unlike nucleons being attracted. This force between nucleons can be explained by nucleons having a nucleonic charge. If the nucleonic charge of a proton is taken to be +1 then the nucleonic charge of a neutron is −2/3. This results in the minimum energy balance between the numbers of protons and neutrons being where the number of protons is equal to two-thirds of the number of neutrons. For more on this analysis of nuclear structure see What holds a nucleus together?.

In contrast, the conventional analysis of nuclear structure hypothesizes a uniform attractive force between all nucleons, called the nuclear strong force. It is called the strong force because at small separation distances between protons it stronger than the electrostatic repulsion between protons but at greater distances it is weaker. This hypothesis explains the existence of nuclei involving combinations of protons and neutrons but other than that there is no empirical evidence for its validity. The binding energies of nuclides provide evidence for the validity of the alternative explanation of nuclear structure given above.

The Explanations for Electron
and Positron Decay of Nuclei

The mechanisms analogous to those which explain electron emission apply to nuclides in which there are proton spin pairs not involving any spin pairing with neutrons. The conversion of one proton in a proton-proton spin pair into a neutron results in a net release of energy because the energy involved in the electrostatic and nucleonic repulsion between two protons is replaced by the nucleonic attraction between a proton and a neutron. There is no change in the energy associated with the spin pairing; i.e., the energy of a proton-neutron spin pair is the same as that of a proton-proton spin pair. There is also an energy gain from the conversion due to the interaction of a neutron with the rest of the nucleus which has a net protonic nucleonic charge. The energy released in these mechanisms goes to cover the energy required to convert a proton into a more massive neutron.

The Data

Here are the data for the nuclides with an excess of protons. There are only 187 such nuclides. But many of those eject protons rather than positrons. Shown below are life times (half-lives) of nuclides which emit positrons and the half-lives have been measured. They are ordered by their lifetimes and their rates of decay.

In all known cases there is radioactive decay for these nuclides.

There are numerous cases in which the life time for the nuclide with three proton spin pairs is substantially shorter than the one with two pairs, which in turn is substantially shorter than the one with one proton pair. This is entirely reasonable in that lifetimes are inversely related to the probability of proton conversion and that would be proportional to the number of protons which are vulnerable to decay.

This hypothesis may be tested by using the reciprocals of lifetimes as a measure of the decay rates and hence of probabilities of decay. Here is the graph of the life time reciprocals versus the number of excess protons.

One extreme case was left out of the graph. There is visual confirmation that the decay rate is positively related to the number protons in the nucleus that are not linked with a neutron. This can be tested quantitatively using regression analysis. The equation includes the following variables

• pn = number of protons in pairs which are linked with neutrons
  This is the same as the number of neutrons in the nuclide.
• sp = number (0 or 1) of singleton protons
• (p-pn-sp) = number of proton in pairs which are not linked with neutrons

Since all of the protons are included in these variables if they are all zero there would be no protons in the nuclide and hence no positron emission. Therefore the constant in the regression equation should be zero.

The regression equation obtained is

(1/LT) = −0.18626pn + 13.76525sp + 11.88868(p-pn-sp)
     [-0.5]      [1.6]      [5.1]

The coefficient of determination (R²) for this equation is 0.31. The t-ratio of 5.1 for the coefficient for protons in pairs and not linked to neutrons strongly indicates that it is such protons which account for positron emission. The low values of the t-ratios for the other variables indicate the protons they represent are not involved in positron emission.

The low value of the R² indicates that some other variables are determining the values of the dependent variable.

Conclusions

Positron emission is associated with the number of proton pairs having no spin pair linkages with neutrons. In such a pair the conversion of a proton releases energy because the repulsions due to the electrostatic and nucleonic force are replaced by attractions. The energy associated with proton-neutron pairing is the same as that due to the proton-proton pairing. The energy released by the conversion of repulsions to attractions goes to supply the energy required to create the more massive neutron from a proton.