Hyperfine Structure Formulae for the Configurationd2sApplication to5d26s F4States of La I

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 $C\text{'}\mathrm{s}$, the other the coefficients $K\text{'}\mathrm{s}$, 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 $\mathrm{}\left(\mathrm{LS}\right)\mathrm{}\leftharpoonup \rightharpoondown \mathrm{}\left(\mathrm{jj}\right)\mathrm{}$ 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 $5d^{2}6s$ ${}_{}{}^4{}_{}{}^{}F$ 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 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. The nuclear $g$-factor computed from these is $g\left(I\right)=0.71\mathrm{}$. The corresponding value of the nuclear magnetic moment is 2.5 nuclear magnetons.