Cluster structure of stable Boron-10 and Boron-11 and neutron cross section and spin dynamics as predicted by the Brightsen Nucleon Cluster Model. The element boron (Z=5) has two stable isotopes, boron-10 and boron-11. Classical physics based on the Mayer-Jensen shell model suggests that these two isotopes differ by the addition of a single neutron in the 1p3/2 shell. However, as discussed by Mr. Brightsen in a December 31, 1988 memo of the former Nuclear Science Research Corporation (personal papers), " why should two beta stable isotopes of this element [boron] show such a large difference in neutron cross-section?" As presented at the following link [Table of neutron cross-sections] the "absorption cross section for 2200 m/s neutrons" for boron-10 = 3835 barns (1 barn = 1E-24 cm^2) while the cross section for boron-11 = 0.0055 barns. Classical shell model dynamics offers no explanation how the presence/absence of a single neutron within the 1p3/2 shell can result in such a large difference in neutron cross-section in these two very stable isotopes (comments to the contrary are welcome).
However, according to the Brightsen Nucleon Cluster Model, the very small cross section for boron-11 compared to the very large cross section for boron-10 is approximated from the following cluster dynamics, in addition to complete balance of total spin dynamics:
Boron-11 = {[N-P]+[N-P]} alpha structure + {[N-P] + [N-P] + N-P-N]} lithium-7 structure
xs = 0.0 barns xs = 0.0454 barns ~ 0.0454 barns predicted vs 0.0055 barns experimentally observed
spin I = 0 spin I = 3/2 Total spin predicted I = 3/2 vs spin I = 3/2 experimentally observed
Boron-10 = [N-P] + [N-P] + [N-P-N] + [P-N-P]
xs = 0.0005 + xs = 0.0005 + xs = 0.0 + xs = 5333 barns ~ 5334 barns predicted vs 3835 barns observed
spin I = 1 spin I = 1 spin I = 1/2 spin I = 1/2 Total spin predicted I = 3 vs spin I = 3 observed
From the above it is clear that the large cross section in boron-10 results from the presence of a helium-3 [P-N-P] (e.g., 5333 barns), which must be reduced by interactions with other clusters to produce the experimentally measured cross section area of 3835 barns.
It is also well known from medical research that the addition of a thermal neutron to stable boron-10 results in a short lived excitation to an unstable boron-11 isotope, which undergoes fission to form a high energy alpha structure plus a lithium-7 structure, exactly as predicted above by the Brightsen Model for the structure of boron-11. See this link [BNCT] for information on Boron Neutron Capture Therapy now used to treat tumors. Analysis of the predicted cluster structure for boron-10 indicates that the slow thermal neutron must react with the [P-N-P] cluster given its very large neutron capture cross section. Interaction of the thermal neutron [N] with [P-N-P] would result in the formation of the alpha cluster {[N-P]+[N-P]} observed in boron-11 with release of Q energy that would allow the remaining three clusters to form the lithium-7 cluster. [Comments are welcome]
