Background

Free neutrons are unstable particles and decay with a half-life of a bit over ten minutes into protons and electrons. Within nuclei neutrons are generally stable but there are some nuclides that emit beta rays (electrons). Some of those have additional modes of decay. The ones which emit only beta rays are called pure beta emitters.

Below are compiled the statistics for pure beta emitting nuclides. Those statistics include the average and maximum energies of the emitted electrons as well as the half-lives. The change in binding energy is the difference between the binding energy of the nuclide that results from the conversion of a neutron and the original nuclide. This change in binding energy is expressed in millions of electron volts (MeV). The most notable aspect of those differences is how small they are. The values for all nuclides range from −27 MeV to +27 MeV. See neutron stability for those statistics.

The notation nEm denotes n×10^m.

There are duplications because some beta-emitting nuclides have multiple channels for beta decay. Here is the count in terms of the evenness-oddness of the proton and neutron numbers.

The effects of the evenness-oddness of the proton and neutron numbers on the change in binding energy due to a neutron conversion are:

A conversion of a neutron in the even-even case results in the loss of a neutron-neutron spin pair and the gain of a proton-proton spin pair. A neutron conversion in the odd-odd case results in the loss of a neutron-proton spin pair and the gain of a proton-proton spin pair. When the neutron number is odd and the proton number is even then a neutron conversion just results in a loss of a neutron-proton spin pair. When the neutron number is even and the proton number is odd then a neutron conversion results in a loss of a neutron-neutron spin pair and a gain of a proton-proton spin pair.

The predictive power of the change in binding energy is tested by plotting the maximum and average energy of the ejected electron versus the change in binding energy, as shown below.

Except for a few anomalous cases the relationships are nearly perfect linear ones. The regression equations for the relationships are:

E_max = 0.69294 + 0.89402ΔBE
E_av = 0.25647 + 0.36350ΔBE

The coefficients of determination are 0.84665 and 0.83631, respectively. The t-ratios for the coefficients are 16.3 and 15.7, respectively. This means that if a nuclide is known to be a beta emitter the change in binding energy is a good predictor of the amount of energy, average or maximum, carried by the emitted electron. However the change in binding energy is not a good predictor of whether or not a nuclide is a beta emitter.

The relationships appear to intersect the horizontal axis at the same point but that is not quite true. The maximum energy line intersects the horizontal axis at −0.775 MeV whereas the average energy line intersects it at 0.7056 MeV. The emitted electron gets its energy from some other source than the change in binding energy that results from the conversion of a neutron into a proton. That source would be the 1.8 MeV surplus mass of the neutron in excess of the combined mass of the proton and electron.

There should be some inverse relationship between the energy and the half-life of the emitters. There is but it is very weak, as shown below.

Although it is weak there is a definite relationship between the two variables, as is shown by the regression analysis. The regression equation is

log(E_av) = 2.27547 −0.05422log(T)

Although the coefficient of determination (R²) is only 0.119 the t-ratio for the coefficient is 2.5, indicating that the coefficient is significantly different from zero at the 95 percent level of confidence.

(To be continued.)