Multi-Configuration Dirac–Hartree–Fock Calculations of Pr9+ and Nd10+: Configuration Resolution and Probing Fine-Structure Constant Variation

We present high-precision multi-configuration Dirac–Hartree–Fock (MCDHF) calculations for the metastable states of Pr9+ and Nd10+ ions, systematically investigating their energy levels, transition properties, Landé gJ factors, and hyperfine interaction constants. Our results show excellent agreement with available experimental data and theoretical benchmarks, while resolving critical configuration assignment discrepancies through detailed angular momentum coupling analysis. The calculations highlight the significant role of Breit interaction and provide the first theoretical predictions of electric quadrupole hyperfine constants (Bhfs). These findings deliver essential atomic data for the development of next-generation optical clocks and establish lanthanide highly charged ions as exceptional candidates for precision tests of fundamental physics.