Nuclear Spins and Magnetic Moments in the Hartree Model

Abstract

From the results of Feenberg and Wigner for the wave function and term character of the ground state of light nuclei (mass number between 6 and 16), the nuclear spins are determined. For those nuclei which contain (or lack) a single proton (or neutron) and an even number (singlet state) of particles of the other kind the considerations of Inglis suffice to determine the spin. For those nuclei which contain a half-filled $p$ shell in one kind of particle it is necessary to calculate the fine structure splitting explicitly. From the spins thus found and with the experimental values for the magnetic moments of the proton and neutron, the nuclear magnetic moments are calculated. The effects on the nuclear moment of the Heisenberg forces and of the motion of the $1s$ shell are considered. The moment of ${\mathrm{Li}}^{7}$ which is of particular interest, is calculated to be 3.07 nuclear magnetons. This is in agreement with the measured value of 3.20 n. m.