Hyperfine Structure in Intermediate Coupling

The theory is extended to intermediate coupling and to cosine laws of force between nucleus and electron varying with different powers of their distance apart. In addition to Goudsmit's constants $a^{\prime }$, $a^{\prime \prime }$, there appears a third coupling constant $a^{\prime \prime \prime }$ for each electron, which gives energy matrix elements for the same $l$ and different $j$. The theory is in approximate agreement with observation. The gross structure is used to determine the parameters of the theory of intermediate coupling and hence $\overline{\left(\frac{1}{r^3}\right)}$. This together with $a^{\prime \prime }$ gives nuclear magnetic moments having roughly the same value for different configurations and stages of ionization. The variation of $\frac{1}{r^3}$ as determined from gross structure shows changes in screening agreeing with those supposed to exist for ${\mathrm{}\left(6s\right)\mathrm{}}^2$ of Pb I, Tl I in order to explain the isotope shift as due to differences in nuclear radii. The discrepancies between gross structure and theory are shown to be connected with similar discrepancies in hfs and the discrepancies of the ratios $\frac{a^{\prime \prime }}{a^{\prime }}$ are reasonably explained by perturbations due to other configurations.