Spin-orbit coupling of protons and neutrons within Helium-4 as predicted by the Brightsen Model.
Let Crepresent the neutron and Brepresent the proton, then the following configuration represents the 1s 1/2 ground state of Helium-4 (the alpha) in the classic shell model of Mayer and Jensen :
C8C9 B8B9
I = 1/2 1/2 1/2 1/2
Net I = 0 0
Helium-4 = I = 0
Note that the protons and neutrons are considered "independent particles" paired in a potential energy well via a process called "isospin" 89 in order to form a net spin I = 0 for each pair. The concept of isospin is required so that the two identical fermion pairs PP and NN can intermingle in the same energy shell without violation of the Pauli Exclusion Principal. Because each pair has a net spin I = 0, the total angular momentum spin for 4He as a whole is I = 0, which is well confirmed by experimental results. The total binding energy for Helium-4 is 28.3 MeV, and according to the current shell model, this energy must be equally shared such that 14.15 MeV binds the PP nucleons and 14.15 MeV binds the NN nucleons. Thus, according to the current shell model of Mayer and Jensen, none of the binding energy of Helium-4 is between N and P directly, but only within PP and NN nucleon pairs.
By comparison, the Brightsen Nucleon Cluster Model predicts that the 1s 1/2 ground state of Helium-4 has the following nucleon cluster paring and spin dynamics:
C
8B8 C8B8
spin up 8 [ N - P] [ N - P] 9spin down
Net I = 1 + 1-
Helium-4 = I = 0
The total angular momentum spin vectors within each [N-P] cluster are parallel resulting in a net cluster spin I = 1, which is the well known spin dynamic for the deuteron. However, because the proton and neutron are not viewed as "identicle independent fermions" in the Brightsen NCM, the Pauli Exclusion Principle and isospin concepts do not need to be applied to bind the two N-P clusters to form the stable isotope Helium-4. According to the Brightsen NCM, the two [N-P] clusters can have independent spin dynamics within the 1s 1/2 energy shell, thus, as shown, one cluster can have spin I = +1 in the up direction, while the other cluster has spin I = -1 in the down direction, resulting in the final spin I = 0 for the Helium-4 isotope. Although this antiparallel cluster spin dynamics conserves Pauli Exclusion, it is not required because the two [N-P] clusters are "bosons" and are thus exempt from Pauli Exclusion dynamics when interacting in energy shells. Thus, the Brightsen NCM uniquely predicts that the vast majority of the 28.3 MeV total binding energy of Helium-4 within the 1s 1/2 energy shell is found within the force particles (mesons ?) that bind the two [N-P] clusters, and not within the 2.22 MeV that bind together the N and P nucleons. Comments are welcome.