|San José State University|
& Tornado Alley
the Incremental Structural Binding Energies
of Alpha Particles in the Fifth Shell
A previous study uncovered some interesting regularities in the incremental structural binding energies of alpha particles as a function of the number of neutron pairs in a nuclide. The Structural Binding Energy (ISBE) of a nuclide is its binding energy (BE) less the binding energy that is accounted for by the formation of substructures. The substructures are alpha particles and nucleon pairs. There are accepted values for the binding energies of an alpha particle and a neutron-proton pair (deuteron) but none for a neutron-neutron pair or a proton-proton pair. The value of the structural binding energies of nuclides were computed by deducting 28.29567 million electron volts (MeV) for every alpha particle they could contain and 2.22457 MeV if they contain a separate deuteron. (They can contain only one deuteron; two would form an alpha particle.)
The structural binding energies were compiled for sets of nuclides. First these values were compiled for the 25 nuclides which could contain only alpha particles. These nuclides are hereafter called alpha nuclides. From this compilation the incremental structural binding energies were computed. This same procedure was carried out for nuclides containing only alpha particle plus one through four neutron pairs. Since in each case the number of additional neutron pairs is held constant the ISBE's are independent of the value of the binding energy for a neutron pair.
The graph of these ISBE values is shown below.
The pattern up to 14 alpha particles is pretty much a jumble. For the range of 15 to 25 alpha particles there is a definite pattern for all five cases. Likewise for 26 and beyond there is a close correspondence among the five cases.
These correspondences involve a shell structure. There are four alpha particles shells for the range from one to 14 alpha particles. Fifteen to 25 is the fifth alpha particle shell and 26 to 41 is the sixth.
The increase in the incremental structural binding energy of an alpha particle with the number of neutron pairs represents the energy of the interaction of the additional alpha particle with the additional neutron pair.
For the first alpha particle in the fifth shell there is about 0.66 MeV increased structural binding energy per additional neutron pair. The regularities of these patterns are interesting but they are only part of a more interesting story. The ISBE's are compiled as a function of the number of excess neutrons in the nuclides. Excess neutrons here means the neutrons beyond those contained in the alpha particles of the nuclides. Here is the graph of the data for the first alpha particle in the fifth shell.
This bent line pattern indicates some sort of shell structure. The bend point near 10 excess neutrons and at 20 excess neutrons corresponds to the magic numbers of 8 and 20 for neutrons. The first alpha particle in the fifth shell is the 15th alpha particle for the nuclide. Therefore there are 30 neutrons in the alpha particles. Thus the total numbers of neutrons in the nuclides for these bend points are 38 and 50. Fifty neutrons is definitely a magic number for neutrons and 38 might be a secondary such number.
The pattern is seen more clearly in terms of the increments to the ISBE's for additional excess neutrons.
The sawtooth pattern has something to do with the formation of neutron pairs. The magnitude of the enhancement in binding energy varies over the range so something more is involved than strictly the formation of neutron pairs. This display reveals that the changes in the pattern occurs at about 8 and 20 excess neutrons.
The pattern for the second alpha particle (the 16th overall) in the fifth shell is even more interesting.
The values turn down at 18 excess neutrons and then turns up again. Eighteen excess neutrons corresponds to 50 total neutrons. Since 50 is a magic number it means that the crucial variable is the total number of neutrons rather than the number of excess neutrons. The graph of the increments to the ISBE's displays the same sawtooth pattern as in the previous case.
One more display will be shown. It is for the 15th alpha particle beyond the filling of the fourth shell.
This display encompasses the addition of an alpha particle beyond the fifth shell into the sixth shell. The bend point comes at 22 excess neutrons. However the 15th alpha particle corresponds to 30 alpha particles overall and hence to 2(30)+22=82 neutrons overall. Eighty two is a magic neutron number corresponding to the filling of a neutron shell. Thus the change in the pattern comes at the filling of a neutron shell.
There is a definite pattern to the influence of the number of neutrons on the incremental structural binding energies of alpha particles in the fifth shell and the operative variable is the total number of neutrons rather than the number of excess neutrons.
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