San José State University

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The Relative Magnitudes of the Binding Energies
Involved in the Formations of Neutron-Proton
and Proton-Proton Spin Pairs

BACKGROUND

The binding energies of 2931 nuclides are available as a function of the number of neutrons and protons they contain, BE(n, p). The binding energy of a nuclide is its mass deficit expressed in energy units via the Einstein equation, E=mc². The masses of nuclei are generally less than the masses of their constituent nucleons.

The incremental binding energy of a proton (IBEP) is defined as

IBEN(n, p) = BE(n, p) − BE(n, p−1)

The IBEP of a nuclide represents the effect of an additional proton on the energy and structure of a nucleus. If the number of protons is less than the number of neutrons then the addition of another proton will form a neutron-proton spin pair and if the number of prot ons is greater than the number of neutrons then no neutron-proton spin pair will form.

It is be emphasized that the term the binding energy associated with the formation of a spin pair is used to indicate that there are two components involved. One is the binding energy resulting from the formation of the spin pair itself. The other is the change in binding energy that results from any rearrangement of the nucleons as a result of the formation of the spin pair. To get a notion of the relative magnitudes of these two components, consider the case of the deuteron which is simply a neutron-proton spin pair. Its binding energy. is about 2.2 MeV and there is no other nucleons to experience rearrangement. Thus the binding energy due the formation of a neutron-proton is about 2.2 MeV. A review of the binding energies associated with the formation of a neutron-proton is on the order of 10 MeV in other situations so the energy resulting from the rearrangements is about 8 MeV.

The Analysis

In the graph below the line labeled p=n is the energy associated with the formation of a neutron-proton pair. It is approximately the same level as that due to the formation of a proton-proton spin pair p=n+1.

The graph of the data shows that while the effects of the formations of a neutron-proton and a prroton-proton are not equal for smaller nuclides they are for nuclides having about 30 neutrons (and protons).

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