Abstract
Hfs interval factor formulae for the states of ${d}^{2}s$ are derived by the method of Breit and Wills. The formulae for intermediate coupling are expressed in two forms: one involving the coefficients $C'\mathrm{s}$, the other the coefficients $K'\mathrm{s}$, corresponding to the representation of the functions of the states in intermediate coupling as a linear combination of the ($\mathrm{jj}$) and the ($\mathrm{LS}$) functions, respectively. The $(\mathrm{LS})\ensuremath{\leftharpoonup}\ensuremath{\rightharpoondown}(\mathrm{jj})$ transformation matrices as well as the interval factor formulae for ($\mathrm{LS}$) and ($\mathrm{jj}$) coupling are also given. As the coefficients are determined from the empirical multiplet separations, the energy matrices in both ($\mathrm{LS}$) and ($\mathrm{jj}$) coupling are listed. The theory is applied to the $5{d}^{2}6s$ $^{4}F$ states of La I and consistently accounts for the relative hfs separations of these states. The values obtained for the interaction constants of the $6s$ and $5d$ electrons are 0.119 and 0.0039 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively. The nuclear $g$-factor computed from these is $g(I)=0.71$. The corresponding value of the nuclear magnetic moment is 2.5 nuclear magnetons.
Published Version
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