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The Components of
Nuclear Binding Energy

The binding energy of nuclei is composed of two types of components. One is due to the formation of spin pairs: neutron-neutron, proton-proton, and neutron-proton. Each represents an attraction of about 3 million electron volts (MeV). However this is an exclusive form of binding energy. One neutron can form a spin pair with one other neutron and with one proton and no more. It is likewise for the spin pairing of protons.

The other source of binding energy is through the net interaction of the nucleons. It is of a net nature because the interactions of like nucleons (neutrons with other neutrons or protons with other protons) is a repulsion which diminishes binding energy. The interaction of unlike nucleons (neutrons with protons) is an attraction and augments binding energy. The magnitude of the binding energy due to a single interaction is a fraction of a MeV but the effect of a large number of these interaction may excede that of a single spin pairing or even two or three spin pairings..

Approximate Estimates of the
Components of Nuclear Binding Energy

The components of the incremental binding energy of neutrons can approximated as follows. For an even proton number look at the values of IBEn at and near n=p. Project forward the values of IBEn for n=p-3 and n=p-1 to get a value of ICEn for n=p; i.e.,

IBEn(p-1, p) + ½(IBEn(p-1, p) − IBEn(p-3, p) )

Likewise the values for IBEn can be projected back from n=p+1 and n=p+3 to get a value of IBEn for n=p without the effect of either an nn spin pairing or an np spin pairing. This procedure is shown below for the isotopes of Neon (10).

Here are the results of carrying out this procedure where possible.

The Components of
Nuclear Binding Energy
n=p nn np int Total BE
6 6.168778 5.7425935 6.8104565 18.721828
8 4.334681 7.092069 4.236986 15.663736
10 7.211359 2.891889 6.761111 16.864359
12 4.17529 4.58247 7.77433 16.53209
14 4.236986 3.049675 9.416625 16.703286
16 3.11241 2.46053 9.46942 15.04236
18 3.7767 1.5926 9.8842 15.2535
20 3.104 3.95965 8.57755 15.6412
22 5.3647 1.07885 9.85615 16.2997
24 3.5795 1.51235 11.24215 16.334
26 2.737 2.07015 11.37585 16.183
28 2.7405 3.02975 10.87075 16.641
30 2.947 1.265 10.79 15.002
32 3.465 1.5785 10.5365 15.58

Here are the graphs of the data.

The values for n=p for magic numbers would not necessarily fit in with the other values of n=p, but they appear to do so.

(To be continued.)


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