San José State University

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The Estimation of the Enhancement
of Binding Energy Due to the
Formation of a Neutron-Proton Pair

Nuclei are held together not just by the nuclear strong force but by the formation of spin pairs of nucleons. The binding energy due to the formation of pairs is dominant for the small nuclides and is exceeded by the strong force interactions for nuclides having more than about 30 protons.

The major problem is assessing the magnitudes of the binding energy enhancement due to the three types of nucleonic pairs: neutron-neutron, proton-proton and neutron-proton. Below is an illustration of the enhancement for neutron pair formation. A previous study dealt with neutron-neutron and proton-proton pairs. This study deals with the neutron-proton spin pair.

The first step is to compile the binding energies of all the nuclides which could contain only alpha particles. Such nuclides will be referred to as alpha nuclides. The next is compile that information for the nuclides which could contain only alpha particles plus one neutron. The corresponding differences is the effect of an additional neutron as a function of the number of alpha particles in the nuclide. The same thing is done to obtain the effect of an additional proton. Then the data for the binding energies of the nuclides which could contain only alpha particles plus a neutron-proton pair, a deuteron. The effect of the additional deuteron is then compared with the sum of the effects of an additional neutron and an additional proton. This comparison is displayed graphically below.

The magnitude of the enhancement due to the formation of a neutron-proton spin pair can be estimated by subtracting from the effect of an additonal deuteron the sum of the effects of an additional neutron and an additional proton.

The values appear to be asymptotically approaching a level of about 2 MeV. This is the value found for the binding energy due to the formation of a neutron-proton spin pair in a previous study using a different method.

The irregularity and higher values for small nuclides can be explained in that when a proton is added to a nuclide already containing an additional neutron there is the interaction of that proton with the neutron through the nuclear strong force. The magnitude of this interaction depends upon the distance between the neutron and proton. This distance is smaller in the small nuclides. In the larger nuclide the distance between the additional neutron and proton can be so great as to result in a negligible effect on potential energy and hence binding energy.

The addition of a proton to the alpha nuclides does not pickup the strong force interaction of a proton with the neutron that occurs when a proton is added to an alpha plus one neutron nuclide. It is then of interest to look at the effect of adding a second proton to the alpha plus deuteron nuclides. This is shown below.

In the graph the effect of an additional proton without the effect of the formation of a neutron-proton pair (deuteron) is estimated by taking the average of the effects of the first and second protons. This is added to the effect of a neutron and the result is labeled n+(p1+p2)/2. However the effect of the second proton could include the effect of the formation of a proton-proton pair. The difference then would then reflect the difference in the effects of a neutron-proton pair versus a proton-proton pair.

The same construction can be carried out considering the addition of a second neutron to alpha+deuteron nuclides. The effect of the second neutron is just about the same as the adding of a deuteron (neutron-proton pair). This is not so surprisingly, because the second neutron could form a neutron-neutron spin pair with the first neutron. The magnitude of the difference then reflects the difference in the effects on binding energy of the formation of a neutron-neutron pair versus that of a neutron-proton pair (deuteron).

The results say four things:

(To be continued.)


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