The Hyperfine Structure ofSandPTerms of Two Electron Atoms with Special Reference toLi+

Abstract

The proper form of the interaction energy between the nuclear magnetic moment and the electronic system of a many electron atom is discussed. The results of the Dirac equation for a single electron are taken as the guiding principle. A form for the interaction energy is set up as an expression involving Pauli's spin matrices. No convergence difficulties occur in the form here given.The interaction Hamiltonian is applied to the $^{3}S$ and $^{3}P$ terms of two electron atoms for the case of Russell-Saunder's coupling. An exact formula is derived for the resultant hyperfine structure of $^{3}S$ terms and corrections to the Goudsmit Bacher formulas for $^{3}P$ terms are given. It is shown that the Land\'e interval rule for $^{3}S$ hyperfine structure levels is exact, and that therefore the ratio of intervals can be used to determine nuclear spin moments.The formulas are applied to the ${\mathrm{Li}}^{+}$ 5485A line. Proper functions for $S$ levels are worked out by the variational method and applied to the calculation of the magnetic moment of ${\mathrm{Li}}_{7}$. With Sch\"uler's wave-length data the nuclear $g$ factor is 2.13 on the assumption that the nuclear spin is 3/2.The accuracy of the calculation is discussed. It is likely to be good to at least 2% in $g$. As a by-product of the calculation the lowest energy level of ortholithium has been computed as \ensuremath{\lesssim} -1.1354 in units of the ionization potential of ${\mathrm{Li}}^{++}$. The empirical value is -1.1358.