The angular pattern in the hyperfine structure of Xe i and Kr i atoms

Recent reviews of the hyperfine structure of xenon and krypton have highlighted the variety of the values taken by the hyperfine coefficients A and B of these atoms. These variations, as functions of the atomic angular momenta, were however not explained quantitatively. This article shows the simple picture and angular momentum algebra that make it possible to account for the observed trend. The only necessary approximations are to consider the interaction of the outer electron negligible with respect to the coupling of the p 5 core with the nucleus, and to assume that the Racah (p5)jℓ[K]JF basis, conventionally used for the atomic states of noble gases, makes a fitting description of the hierarchy of their angular momentum couplings. The way the calculation corroborates the apparently erratic values of hyperfine coefficients A and B in Xe I and Kr I shows up as a confirmation of the validity of these approximations.