San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

Changes in the Pattern of the
Incremental Binding Energies
of Neutrons in the Neutron Shell
for 29 through 50 Neutrons

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 Chromium, atomic number 24.

The odd-even sawtooth pattern is the effect of the formation of neutron-neutron spin pairs. The sharper drops after 20 and 28 neutrons are the results of completions of shells. The sharp drop after 24 neutrons occurs because there are 24 protons so any increase in neutrons beyond 24 will not result in the formation of a neutron-proton spin pair.

After 30 neutrons there is slight change in the pattern. This is the topic of this webpage.

For Manganese (atomic number 25), Iron (atomic number 26), Cobalt (atomic number 27) and Nickel (atomic number 28) here are the displays.

A change in the pattern is a difference between the value a point and what a continuation of the trends of the lower and higher numbers 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. In the above displays there is possibly perceptible changes after 30 neutrons for Manganese but not for Iron, Cobalt and Nickel. However there is a change after about 40 neutrons. These numbers correspond to 2 and about 12 neutrons in the shell for 29 through 50 neutrons.

The changes near 40 neutrons are a bit more dramatic for Copper (atomic number 29) and Zinc (atomic number 30).

This last case also has definite change after 46 neutrons which does not occur for the other cases.

For the higher atomic numbered elements the display looks more like a gradual transition than an abrupt change.

The persistence of a phenomenon of a change in the pattern near 40 neutrons is demonstrated for elements with atomic numbers 24 through 30.

What the phenomenon would indicate is that a subshell or subshells is(are) being filled in the shell for 29 through 50 neutrons. It is notable that 42 is 28 plus 14 and 14 is a magic number representing the first three neutron shells of 2, 4 and 8 being filled.

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