Hyperfine-induced frequency shifts for the candidate clock transitions in the Ni12+61 ion

The ⁶¹Ni¹²⁺ ion is a promising candidate for a novel ultraprecise optical clock, owing to its two clock transitions with narrow natural linewidth between levels with low degeneracy. Using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, we calculated the hyperfine-induced Land\'e g factors for the ³P₀0.16em0exF=3/2 and ³P1,20.16em0exF=1/2 states, as well as the hyperfine-induced electronic quadrupole moment of the ³P₀0.16em0exF=3/2 state in the ⁶¹Ni¹²⁺ ion. The effects of the electron correlations and relativistic effects on the concerned atomic parameters were evaluated in detail based on the active space approach. It is found that the valence-valence and core-valence electron correlations have the dominant influence on the atomic parameters concerned, while the core-core and the higher-order correlations are non-negligible for evaluating the uncertainties. Additionally, the relative quadratic Zeeman shifts, the relative electric quadrupole shift, and the corrections arising from the hyperfine-induced effect were evaluated. It is demonstrated that the hyperfine interaction strictly eliminates the electric quadrupole shift of the M1 transition 3s²3p⁴0.28em0ex³P₁-³P₂, and significantly reduces the electric quadrupole frequency shift for the E2 transition 3s²3p⁴0.28em0ex³P₀-³P₂ by a factor of 4×10^-6. The hyperfine-induced corrections to the relative quadratic Zeeman shifts are factors of 2×10^-4 and 6×10^-7 for the M1 and E2 transition, respectively. It means that the hyperfine-induced effects need to be identified precisely for an ultraprecise ⁶¹Ni¹²⁺ optical clock aiming for a precision better than 10^-19 when the magnetic field exceeds 10.16em0exT or the gradient of the environmental electric field exceeds 10⁸0.16em0exV/m².