Electromagnetic Backgrounds and Angular-Momentum Barriers in Gravitomagnetic Searches with Hydrogen-Like Ions

Hydrogen-like ions cannot usefully bound the gyrogravitational ratio $χ$: in ${}^{95}$Mo$^{41+}$ gravity shifts the hyperfine constants by fractions of $10^{-39}$--$10^{-38}$ with the tensor structure of the hyperfine interaction, centroids cancel it, and the $2p$ lines are 1.3 eV wide. Isotopes wit