Spin-Orbit Coupling in the Alpha-Model of Light Nuclei

Abstract

If light nuclei are approximated by the alpha-model, with the particles localized in clusters of four (or less), the particle with uncompensated spin is accelerated by the relatively weak attraction of alphas, or by the difference of the attractions of two clusters. Then the Thomas relativistic term is not in general larger than the Larmor magnetic term in the spin-orbit coupling in contrast to the result of the central model, wherein the acceleration may be attributed to unsaturated forces toward one center. The relative magnitudes of these terms are estimated for the alpha-model of ${\mathrm{Li}}^7$ and ${\mathrm{C}}^{13}$, two of the few nuclei to which it is here considered that the model might apply. The magnetic moment consistent with the Larmor-Thomas coupling in the alpha-model of ${\mathrm{B}}^{11}$ is found to be considerably larger than the experimental value. The quadrupole moment of the deuteron implies a spin-orbit coupling arising directly from angle-dependent nuclear forces. The appropriate "spin-orbit-spin" angle dependence suggested by the meson theory causes no first-order coupling in the alpha-model of ${\mathrm{Li}}^7$, however, and a rough estimate of the second-order doublet splitting shows that it may be considerably smaller than that due to the Larmor and Thomas terms.