San José State University |
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for Each Other and for Neutrons |
Previous work established that the nucleons in a nucleus form alpha particles whenever possible. Other work (2) made the case that the interactions of the substructures of nuclei can be explained by protons and neutrons having strong force nucleonic charges. If the nucleonic charge of a proton is defined as +1 then that of the neutron is −2/3. This makes the net nucleonic charge of an alpha particle +2/3.
The nucleonic charge hypothesis would suggest that alpha particles repel each other under the action of the strong force. Definitely at distances where the strong force becomes smaller in magnitude than the electrostatic force alpha particles repel each other. The nature of the strong force interaction of particles in nuclei shows up in terms of the structural binding energies of the nuclei. The structural binding energy for a nuclide is its binding energy less the binding energy accounted for by the formation of substructures (primarily alpha particles) in that nuclide. The structural binding energies for all nuclides which could contain only alpha particles were compiled. These are hereafter called alpha nuclides. From this the structural binding energy for nuclides containing one alpha particle was subtracted. This is called the incremental structural binding energy (ISBE) for the addition of an alpha particle. The graph of this quantity is given below.
Alpha nuclides exist only up to and included 25 alpha particles. For that range definitely the ISBE is positive and thus there is a net attraction between alpha particles. This is an enigma because like particles generally repel. Perhaps this anomaly has something to do with alpha particles being nominally bosons whereas the nucleons are fermions.
Nuclides with more than 25 alpha particles exist but they must include some neutrons. Beyond 25 the ISBE for alpha particles is negative. Before that is dealt with let us consider a comparison of the ISBE of neutrons with that of alpha particles. This is of interest because, according to the nucleonic charge hypothesis, the nucleonic charge of the neutron is −2/3 while that of an alpha particle is +2/3. Thus they are, to some extent, mirror images of one another.
The ISBE for neutrons is computed by compiling the structural binding energies for all nuclides that could contain only alpha particles plus one neutron and then subtracting the structural binding energies of the alpha nuclides. The values are shown in the graph below along with the ISBE for alpha particles.
What is notable about the above display is that correspondence between the two curves. When the ISBE for alpha particles goes up the ISBE for neutrons goes down and vice versa. At the nuclide of 14 alpha particles (corresponding to the magic number of 28 for neutrons and protons) the curves switch levels; i.e., the ISBE for alpha particles goes the level where the ISBE for neutrons had been the ISBE for neutrons moves to the level where the ISBE for alpha particles had been.
It is almost as though the values follow a pattern of the sort
where K is a constant and U(#a) is a function of the number of alpha particles in the nuclide.
If this were the case the average of the ISBE for alpha particles and neutrons would be constant. Instead the picture is a bit less regular, as shown below.
The average is not constant but appears to be, after irregularity for the small nuclides, a linear function of the number of alpha particles. The regression equation, leaving out the first four data points, is
The coefficient of determination for the regression equation is 0.9045 and the t-ratio for the regression coefficient is 13.1.
It is reasonable that the ISBE's increase with the number of alpha particles. The ISBE has to do with the interaction of the additional alpha particle and the additional neutron with the alpha particles of the nuclide.
The regression equation for the ISBE for neutrons using the data for the alpha shell above 14 is
The coefficient of determination (R²) is 0.91313 and the t-ratio is 9.7. Thus the regression coefficient is statistically significantly different from zero at the 95 percent level of confidence.
For the alpha particles the analogous regression equation is
The coefficient of determination is only 0.10672 and the t-ratio for the regression coefficient is only 1.1, thus indicating that the regression coefficient is not statistically significantly different from zero at the 95 percent level of confidence. It is understandable that the ISBE for alpha particles in higher shells would be insignificant because the electrostatic repulsion becomes more important than the strong force at the greater distances between alpha particles. This does not occur for neutrons.
Below is shown the structural binding energies for nuclides which contain only alpha particles plus four neutrons.
The incremental structural binding energies beyond 25 alpha particles are negative, indicating a repulsion of those additional alpha particles for the rest of the alpha particles in the nuclide.
(To be continued.)
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