The Magnetic Moments of Light Nuclei

The sum of the magnetic moments of two nuclei which can be obtained from each other by interchanging neutrons and protons is shown to be related in a simple way to the probabilities of occurrence of each of the states of given spin and orbital angular momentum that can be combined to form the ground state. This result, which is independent of any nuclear model, has immediate application to the nuclei with equal numbers of neutrons and protons, in particular, to ${\mathrm{H}}^2$, ${\mathrm{Li}}^6$, ${\mathrm{B}}^{10}$, and ${\mathrm{N}}^{14}$. From the observed moments it is found that the ground state of ${\mathrm{B}}^{10}$ is a combination of about 50 percent ${}_{}{}^3{}_{}{}^{}S$ and 50 percent ${}_{}{}^3{}_{}{}^{}D$ function. The ground state of ${\mathrm{Li}}^6$ contains at least 70 percent but no more than 90 percent of the ${}_{}{}^3{}_{}{}^{}S$ term. It may contain as much as 30 percent of the ${}_{}{}^3{}_{}{}^{}P$ term, or 15 percent of the ${}_{}{}^1{}_{}{}^{}P$ term, or, finally, 10 percent of the ${}_{}{}^3{}_{}{}^{}D$ term. The ground state of ${\mathrm{N}}^{14}$ contains at least 52 percent but no more than 84 percent of the ${}_{}{}^3{}_{}{}^{}D$ function. It may contain as much as 48 percent ${}_{}{}^1{}_{}{}^{}P$ function, but the ${}_{}{}^3{}_{}{}^{}P$ term cannot contribute more than 24 percent or the ${}_{}{}^3{}_{}{}^{}S$ more than 16 percent. All of these results are based on the assumption that the only terms contributing appreciably to the ground states of the nuclei are those found to be near the ground state in the Hartree approximation. It will be possible to obtain similar information concerning the ground states of other light nuclei if a technique for measuring the magnetic moments of radioactive nuclei is developed.