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 83 through 126 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 Gadolinium.

The odd-even sawtooth pattern is the effect of the formation of neutron-neutron spin pairs. The sharp drop after 82 neutrons is the result of a completion of a shell.

After 88 neutrons there is slight change in the pattern. This is the topic of this webpage.

For Terbium (atomic number 65) and Dysprosium (atomic number 66) 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. In the above there are perceptible changes after 88 neutrons and 92 neutrons, and possibly after 96 neutrons. These numbers correspond to 6, 10 and 14 neutrons in the shell for 83 through 126 neutrons.

The changes are even more dramatic for Promethium, atomic number 61.

This case also has definite change after 74 neutrons which does not occur for the other cases.

The displays look like the ones previously shown through Erbium, atomic number 68, and Thulim, atomic number 69.

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

The persistence of the phenomenon is demonstrated for elements with atomic numbers 61 through 69.

What the phenomenon indicates is that a subshell or subshells involving six neutrons is(are) being filled in the shell for 83 through 126 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.

HOME PAGE OF applet-magic
HOME PAGE OF Thayer Watkins