Finding the Ultranarrow P32→P30 Electric Quadrupole Transition in Ni12+ Ion for an Optical Clock

The Ni12+ ion features an electronic transition with a natural width of only 8 mHz, allowing for a highly stable optical clock. We predict that the energy of this strongly forbidden 3⁢𝑠2⁢3⁢𝑝4  3 𝑃 2→3⁢𝑠2⁢3⁢𝑝4  3 𝑃 0 electric quadrupole transition is 20 081⁢(10)  cm−1. For this, we use both a hybrid approach combining configuration interaction with a coupled-cluster method and a pure configuration interaction calculation for the complete 16-electron system, ensuring convergence. The resulting very small theoretical uncertainty of only 0.05% allowed us to find the transition experimentally in a few hours, yielding an energy of 20 078.984⁢(10)  cm−1. This level of agreement for a 16-electron system is unprecedented and qualifies our method for future calculations of many other complex atomic systems. While paving the way for a high-precision optical clock based on Ni12+, our theory and code development will also enable better predictions for other highly charged ions and other complex atomic systems.