Second-order hyperfine structure and its impact on new physics searches using isotope shift spectroscopy

Recent precision isotope shift spectroscopy experiments have reported King plot non-linearities that may uncover previously hidden nuclear properties or hint at new force-carrying bosons. Interpreting the data requires many isotope pairs, but sufficient stable spin-zero nuclei are not always available. In this paper we consider the use of isotopes with non-zero nuclear spin for these studies. We confirm that observed King plot non-linearity in strontium is explained by second-order hyperfine shift in the fermionic nucleus, and we discuss the limitations of using Yb isotopes with non-zero spin in King plot studies. By introducing a specific difference of two isotopes with nuclear spin, we allow for a promising addition to future experimental schemes.