|San José State University|
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The nuclei of atoms are composed of neutrons and protons. The mass of a nucleus is generally less than the combined masses of the nucleons (neutrons and protons) of which it is composed. This mass deficit expressed in energy units via the Einstein equation E=mc² is call the binding energy. Binding energy represents the energy which have to be supplied to break a nucleus down into its constituent nucleons.
The formation of a nucleon spin pair is manifested in terms a pattern in binding energy. For example, the formation of neutron-neutron spin pairs appears saw-tooth pattern in the incremental binding energies of neutrons. Similarly the formation of proton-proton spin pairs is manifested in terms of a saw-tooth pattern in the incremental binding energies of protons.
The formation of a neutron-proton spin pair is manifested by an entirely different pattern. If the neutron number is less than the proton number then each additional neutron results in the formation of a neutron-proton spin, regardless of whether the neutron number is odd or even.
As can be seen in the above graph, the level of incremental binding energy is higher for N less than or equal to 24, the number of protons. In the above graph there is also a sharper drop in incremental binding energy after N=28, where the shell is completely filled and additional neutrons go into a higher shell.
The incremental binding energies of neutrons were computed and then the data set is separated into those in which the neutron number is less than or equal to the proton number and those in which the neutron number exceeds the proton number.
There are 2582 incremental binding energies of proton in which the proton number is less than or equal to the neutron number. The average of these 2582 values is +7.00 MeV. For the 186 values for which the proton number is greater than the neutron number the average is +1.128 MeV. The difference is 5.87 MeV and this is roughly the average binding energy increment associated with the formation of a neutron-proton spin pair. The energy associated with the formation of a neutron-proton spin pairs differs according to the nature of the nucleus it is formed in.
The proportional frequency distributions for these two sets of data are shown below.
The evidence is overwhelmingly in favor of the proposition that whenever possible within nuclei neutrons and protons form neutron-proton spin pairs And the formation is exclusive in the sense that a neutron can form a spin pair with one and only one proton.
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