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Spin-Orbit Coupling in and
Phys. Rev. 82, 181 – Published 15 April, 1951
DOI: https://doi.org/10.1103/PhysRev.82.181
Abstract
The magnetic spin-orbit coupling of the -shell nucleons is shown to have the correct sign and about half the magnitude to account for the 45-kev difference of the first excitation energies, 479 kev in and 434 kev in , if these are interpreted as doublet splittings arising mainly from a spin-orbit coupling term of the same form as the Thomas term but stronger and presumably of mesonic origin, such as seems to be responsible for the appearance of () coupling in heavy nuclei. is expected to be slightly larger than because of the added coulomb repulsion, so that the average value of the main term is expected to be smaller for , and it is estimated that this coulomb expansion explains another one-fourth to the splitting difference, leaving about one-forth unaccounted for. These estimates are made both very simply by means of the droplet model and more reliably by minimizing the energy obtained with exchange interactions and three-dimensional isotropic oscillator wave functions. Energies attributed to spin-orbit coupling in other nuclei indicate that the main term should make the and doublet splittings about 50 percent larger than observed. This suggests that second-order perturbations may reduce both by nearly the same amount, leaving their estimated difference significant. The possibility of more drastic perturbations and their relation to the quadrupole-moment problem are discussed. The agreement of the estimated splitting difference in sign and order of magnitude is consistent with other evidence favoring the ()-coupling interpretation that the two low states form a .
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