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The Differential Impact of
Additional Protons and Neutrons
on the Binding Energy of Nuclides

This material investigates the effect of additional protons and additional neutrons on the binding energies of nuclides. In part, it is intended to demonstrate the difference of the impacts of the two nucleons on binding energies.

In order to avoid conflating the effect of additional nucleons with the formation of alpha particles or proton/neutron pairs the analysis proceeds in terms of the addition of one type of nucleon to integral alpha particle nuclides; i.e., nuclides that could contain an integral number of alpha particles.

The Helium 4 Nuclide

Consider first the effect on binding energy of the addition of neutrons to an alpha particle, a He4 nuclide.

This is an interesting profile for a number of reasons. First, the addition of one neutron actually decreases the binding energy. Second there an alternating effect of smaller then bigger, which suggests that the formation of a pair of neutrons is a significant development. It is notable that six neutrons can be added to the two already in the He4 nuclide.

Only four protons can be added to the He4 nuclide and still have a stable nuclide. The net change in the binding energy for these are shown in the following graph with the net change for the addition of the first four neutrons for comparison.

The difference between the two lines increases with the number of added nucleons. The pattern is very regular, as shown below.

The effect of added protons compared to added neutrons is thus a reduction in binding energy by about 1.65 MeV. The effect of a proton compared to a neutron on binding energy is clearly demonstrated by comparing the binding energy of the H3 nuclide, 8.482 MeV, with that of the He3 nuclide, 7.718 MeV. The H3 nuclide consists of one proton and two neutrons; the He3 consists of two protons and one neutron. The reduction 1.764 MeV is generally attributed to the effect of the potential energy created by bring the two positive charged protons into close proximity. The magnitude of this figure of 1.764 MeV and the approximate 1.65 MeV from the comparison of the effects of additional neutrons and protons is quite striking.

The Berylium 8 Nuclide

The Berylium 8 nuclide can be considered to be made up of two alpha particles. The effects of additional neutrons on binding energy are:

As with the He4 nuclide there can be six neutrons added to the Be8 nuclide. There is also the alternating smaller greater pattern indicating the formation of pairs of neutrons is significant.

Again, as with the He4 nuclide, only four protons can be added. The effect of these four protons on binding energy is shown along with the effect of the addition of the first four neutrons.

Again, as with the He4 nuclide, the difference in the impact of neutrons and protons is very regular.

The magnitude of the difference per proton is significantly larger than that for the He4 nuclide.

The Results for Larger Alpha Particle Nuclides

The results for the C12, O16, Ne20, Mg24, Si28 and S32 nuclides follow the same pattern as shown above.

The pattern is clear. It consists of

The pattern continues for the larger alpha particle nuclides. However the larger alpha nuclides sustain the addition of fewer and fewwer protons until finally with Pd92 the addition of not even one proton can be sustained.

(To be continued.)

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