The Magnetic Moments ofH3andHe3

Abstract

A measurement of the magnetic moments of the nuclei ${\mathrm{H}}^3$ and ${\mathrm{He}}^3$ would yield information concerning the deviations from $L-S$ coupling in these nuclei. It is shown that the sum of the moments of the two nuclei can be directly related to the amount of admixture of the ${}_{}{}^2{}_{}{}^{}P$, ${}_{}{}^4{}_{}{}^{}P$, and ${}_{}{}^4{}_{}{}^{}D$ eigenfunctions with the ${}_{}{}^2{}_{}{}^{}S$ function. Thus the measurement of both moments would lead to direct information concerning the contributions of these functions to the ground state of the two nuclei. The individual moments depend to some extent on the detailed properties of the wave functions, but if only the ${}_{}{}^2{}_{}{}^{}S$ and ${}_{}{}^4{}_{}{}^{}D$ functions contribute appreciably to the ground state, and if particularly simple forms of these functions are assumed, the moment of each nucleus is shown to be expressible in terms of the amount of admixture of the two functions. If then the amount of ${}_{}{}^4{}_{}{}^{}D$ function is taken to be 4 percent on the basis of an estimate by Gerjuoy and Schwinger, the moments of ${\mathrm{H}}^3$ and ${\mathrm{He}}^3$ are found to be 2.71 and - 1.86 nuclear magnetons, respectively.