Spin-Orbit Coupling inLi7andBe7

The magnetic spin-orbit coupling of the $p$-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 ${\mathrm{Li}}^7$ and 434 kev in ${\mathrm{Be}}^7$, 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 ($\mathrm{jj}$) coupling in heavy nuclei. ${\mathrm{Be}}^7$ is expected to be slightly larger than ${\mathrm{Li}}^7$ because of the added coulomb repulsion, so that the average value of the main term is expected to be smaller for ${\mathrm{Be}}^7$, 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 ${\mathrm{Li}}^7$ and ${\mathrm{Be}}^7$ 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 ($\mathrm{LS}$)-coupling interpretation that the two low states form a ${}_{}{}^2{}_{}{}^{}P$.