Calculations of the Binding-Energy Differences for Highly-Charged Ho and Dy Ions

The binding-energy differences for 163Hoq+">${}^{163}\text{H}{\text{o}}^{q+}$ and 163Dyq+">${}^{163}\text{D}{\text{y}}^{q+}$ ions with ionization degrees q=38">$q=38$, 39, and 40 are calculated. The calculations are performed using the large-scale relativistic configuration-interaction and relativistic coupled-clusters methods. The contributions from quantum-electrodynamics, nuclear-recoil, and frequency-dependent Breit-interaction effects are taken into account. The final uncertainty does not exceed 1 eV. Combining the obtained results with the binding-energy difference for neutral atoms calculated in [I.M. Savelyev, M.Y. Kaygorodov, Y.S. Kozhedub, I.I. Tupitsyn, and V.M. Shabaev, Phys. Rev. A 105, 012806 (2022)], we get the secondary differences of the ion–atom binding energies. These values can be used to evaluate the amount of energy released in the electron capture process in 163Ho">${}^{163}\text{Ho}$ atom (the Q value), provided mass differences of highly charged ions 163Hoq+">${}^{163}\text{H}{\text{o}}^{q+}$ and 163Dyq+">${}^{163}\text{D}{\text{y}}^{q+}$ is known from experiment. The Q value is required by experiments on the determination of the absolute scale of the electron neutrino mass by studying the beta-decay process.