The incremental binding energy of a neutron (IBEn) in a nuclide with n neutrons and p protons is

IBEn(n, p) = BE(n, p) − BE(n-1, p)

where BE stands for binding energy.

The graph of IBEn as a function of the number of neutrons in the nuclide displays a definite pattern. Here the graph for the isotopes of Selenium.

The odd-even sawtooth pattern is the effect of the formation of neutron-neutron spin pairs. The sharp drop after 50 neutrons is the result of a shell being completely filled and any additional neutrons go into a higher shell. The sharp drop after 34 neutrons is due there not being neutron-proton spin pairs being formed. When the neutron number is less than the proton number any additional neutron forms a neutron-proton spin pair. Once the neutron number exceeds the proton number an additional neutron cannot form such a spin pair.

The formation of a neutron-neutron pair may offset the lack of a formation of of a neutron-proton pair, as shown in the case of Bromine.

After 56 neutrons there is slight change in the pattern. This is the topic of this webpage.

For Krypton and Stronium here are the displays.

A change in the pattern is a difference between the value a point and what a continuation of the trend of the lower number of neutrons. This may involve a change in the upper or lower levels of the pattern or a change in the amplitude of the fluctuations.

For Molybdenum (atomic number 42) the change in the pattern after 56 neutrons is barely, if at all, perceptible. However there is a perceptible change after 64 neutrons.

The persistence of the phenomenon is demonstrated in the display of the data for four and five elements together, as below.

Thus the shape of the relationship is a decline in IBEn with increases in the number of neutrons until the magic number of 50, then there is a sharp drop and a less steep decline in IBEn with increased neutrons until the number 56 and then a still less steep decline. This is shown below.

What the phenomenon indicates is that a subshell or subshells involving six neutrons is(are) being filled in the shell for 51 through 82 neutrons. After six the additional neutrons go into other subshells. It is notable that six is a magic number representing the first two neutron shells of 2 and 4 being filled.

It is remarkable that the phenomenon is not displayed in the incremental binding energies of protons, seen below for the nuclides with 68 neutrons.

Of course the phenomenon is not displayed for the incremental binding energies of neutrons when the number of protons is 42 or more. There may still be subshell(s) of six protons but their filling does not affect the incremental binding energies perceptibly.