Isomeric excitation energy for ${}^{99}$In${}^m$ from mass spectrometry reveals constant trend next to doubly magic ${}^{100}$Sn

The excitation energy of the 1/2${}^{-}$ isomer in ${}^{99}$In at $N=50$ is measured to be 671(37) keV and the mass uncertainty of the 9/2${}^{+}$ ground state is significantly reduced using the ISOLTRAP mass spectrometer at ISOLDE/CERN. The measurements exploit a major improvement in the resolution of the multi-reflection time-of-flight mass spectrometer. The results reveal an intriguing constancy of the $1\mathrm{/}{2}^{-}$ isomer excitation energies in neutron-deficient indium that persists down to the $N=50$ shell closure, even when all neutrons are removed from the valence shell. This trend is used to test large-scale shell model, $\mathit{\text{ab}}\mathit{\text{initio}}$, and density functional theory calculations. The models have difficulties describing both the isomer excitation energies and ground-state electromagnetic moments along the indium chain.