Potential nucleon cluster structures in the 1s energy core of isotopes as predicted by the Brightsen Nucleon Cluster Model (note: the following comments are not those of Mr. Brightsen, but are the attempt of the Webmaster to offer ideas about the Brightsen Model to facilitate discussion ).
According to the Linus Pauling Close-Packed Spheron Model (see publications at this link: Research Notebook, #26, and above posting ), a variety of nucleon "spherons" upto A = 4 are possible within the 1s energy core of stable and unstable isotopes. The Brightsen Model predicts that free protons [P] and neutrons [N] do not exist in beta-stable isotopes, thus the Brightsen Model (following the formalism of Pauling Spheron Model) predicts the following potential nucleon clusters in the 1s energy core of nuclides:
| Number of Nucleons in 1s Energy Core |
2 (well)* |
3 (well) |
4 (well) |
| Predicted Clusters (either MATTER or ANTIMATTER) |
[NP] stable** |
[PNP] stable |
[NP]+[NP] stable, the alpha |
| |
[NN] unstable ? |
[NPN] unstable |
[NN]+[NN] unstable ? |
| |
[PP] unstable ? |
[NNN] unstable ? |
[PP]+[PP] unstable ? |
| |
|
[PPP] unstable ? |
[PP]+[NN] unstable ? |
* Note: the term "well" is used here to suggest possible energy states that allow the various types of clusters to remain separated within any given energy shell layer.
** Note: The term "unstable" as used here has multiple meanings ranging from unbound [PPP], a weak resonance pairing [NN], and beta-decay such as [NPN] transforming into a [PNP] cluster.
According to the classical Woods-Saxon shell model, energy levels of isotopes from the lowest to the highest are given the following notations: 1s, 1p, 1d, ....and so on. Only A=4 nucleons can be packed into the 1s energy layer, upto A=12 nucleons can exist in the next 1p layer, A=20 in the 1d layer, and so on (see any textbook with Woods-Saxon well potentials).
A number of observations are apparent concerning the 1s energy core of isotopes from the above tabled predictions of the Brightsen Model:
1. It is a fundamental prediction of the Brightsen Model that the free proton [P] and/or free neutron [N] do not exist in the 1s energy layer of isotopes--only clusters of [P] and [N] ! The Brightsen Model predicts that 1-H-1 (the "free proton") is comprised of various isodyne combinations of matter and antimatter "clusters", such as a matter [P-N-P] cluster bound via the "strong force" (with gravity/antigravity interactions ? ), to an antimatter [N-P] cluster.
2. According to the Brightsen Model, the "alpha" or helium-4 has two potential "cluster" dynamics in the above table: (a) a {[N-P]+[N-P]} structure formed by two boson clusters with unique total angular momentum, and (b) a {[N-N] + [P-P]} structure formed by independent nucleon fermions bound by isospin. However, in his publications and memos, Mr. Brightsen never discussed the possibility that helium-4 can form a beta stable isotope by resonance between a [N-N] cluster and [P-P] cluster. This view of the 1s energy core of isotopes is radically different from Mayer-Jensen shell model dynamics, which predicts that P binds to P, and N binds to N via isospin in two separate potential energy wells to form helium-4.
3. Also in contrast to the shell model, which predicts only two potential energy wells in the 1s level of isotopes (e.g., one for P-P interactions, and one for N-N interactions), it is suggested that the Brightsen Model "may" predict three different potential energy wells in the 1s energy core (a) one for 2 nucleon clusters (b) one for 3 nucleon clusters, and (c) one for 4 nucleons comprised of 2 clusters. From the above table, only one type "stable" nucleon cluster would exist in each of these three separate energy wells: the deuteron (well 2), helium-3 (well 3), and helium-4 (well 4). I am not aware of any mathematical models that construct nuclear dynamics starting from a prediction of three separate energy wells in the 1s energy core of isotopes (comments to the contrary are welcome).
For example, as discussed at at this internal (link), one potential isodyne cluster structure for the stable Boron-10 is predicted by the Brightsen Model as:
[N-P] + [N-P] + [N-P-N] + [P-N-P] = Boron-10
In order to balance the known spin I = 3 for Boron-10, and its large neutron cross section (3835 barns), the Brightsen Model predicts that the two [N-P] clusters are not coupled to form a alpha cluster, but may exist in the 1s energy layer as two separate [N-P] clusters, each with their own boson spin dynamics ( I=1), thus contributing I=2 of the total I=3 spin dynamic for boron-10. Because each [N-P] is a boson, the Pauli Exclusion dynamics would not apply, allowing two identicle [N-P] clusters to coexist in their own energy well #1. Because the 1s energy layer can only pack A=4 nucleons, the [N-P-N] and [P-N-P] clusters within boron-10 must be elevated to the next higher energy layer (1p), although I have no knowledge of dynamics of such an interaction in the 1p energy layer involving "nucleon clusters". Note that the very large neutron cross section of the [P-N-P] cluster (at 5333 barns) suggests that this cluster is predicted to be in the outer energy layer of boron-10 and explains not only its large cross section of 3835 barns, but also the fact that boron-10 has a high affinity to capture a thermal neutron [N], thus transforming the outer [P-N-P] cluster to an alpha particle {[N-P]+[N-P]}, which can exist in the 1p energy layer of the newly created boron-11 isotope.
Applying the suggested hypothesis of three energy wells from the above table in the 1s energy core, one possible shell model cluster dynamic for boron-10 is as follows:
Energy Layer Well 2 Well 3 Well 4 Maximum Allowed A
==================================================================
1p [N-P-N],[P-N-P] (empty) 12
1s [N-P], [N-P] (empty) 4
---------------------------------------------------------------------------------------------------------------------------------
4. Helium-5 is widely viewed as being unbound. Given the high binding energy of helium-4, the addition of a free [N] at low energy to helium-4 would be predicted by the above Brightsen Model energy well dynamics to result in the added free nucleon moving to the second energy layer (1p), since the 1s layer is complete with A=4 nucleons. However, because free nucleons in energy levels are not allowed in Brightsen Model dynamics, this mass 5 isodyne structure of helium-5 cannot be "bound", and it is predicted to quickly decay to the alpha + free neutron, a result well verified by experimental observations. Attempts to bind together deuterium [N-P] and tritium [N-P-N] result in the formation of the alpha [N-P]+[N-P] and a free [N]. Thus the Brightsen Model energy well dynamics as presented herein conforms to experimental results that helium-5 is unbound as relates to "alpha" decay. A similar argument can be formed for Lithium-5, with exchange of a free added [P] for the [N] to an alpha core. However, in his 1996 publication on the Nucleon Cluster Model, Mr. Brightsen states the following : "...detailed mass spectrometric data indicate that mass 5 is beta stable at helium (Z=2)...". , although no reference is given. Thus the Brightsen Model uniquely predicts that a mass 5 nuclide can be "beta-stable" while at the same time "alpha unstable" at Z=2. Comments are welcome
