Hyperfine Structure Formulas for LS Coupling

Formulas for the interval factor A and the quadrupole coupling factor B in the hyperfine structure formula, W=WJ+1/2AK+BK(K+1), are derived with Racah's tensor algebra. The results are directly applicable to light atoms ($Z<50$) that show good LS coupling. Data of White and Ritchl for manganese are analyzed, and an approximate value of the nuclear quadrupole moment in Mn⁵⁵ of Q=1×10^-24 cm² is obtained. This confirms another approximate value of Q=0.5×10^-24 cm² 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.