Hyperfine Structure Formulas forLSCoupling

Formulas for the interval factor $A$ and the quadrupole coupling factor $B$ in the hyperfine structure formula, $W=W_J+\frac{1}{2}AK+BK(K+1\mathrm{}),$ are derived with Racah's tensor algebra. The results are directly applicable to light atoms ($Z<\mathrm{}50\mathrm{}$) that show good $\mathrm{LS}$ coupling. Data of White and Ritchl for manganese are analyzed, and an approximate value of the nuclear quadrupole moment in ${\mathrm{Mn}}^{55}$ of $Q=1\mathrm{}\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$ is obtained. This confirms another approximate value of $Q=0.5\mathrm{}\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$ recently obtained by microwave methods. An error in the calculation carried out by Brown and Tomboulian to evaluate the $Q$ of tantalum is noted. A relation satisfied by $X$ functions is derived, which simplifies their numerical evaluation.