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Recent experimental progress in cooling, trapping, and quantum logicspectroscopy of highly-charged ions (HCIs) made HCIs accessible for highresolution spectroscopy and precision fundamental studies. Based on theseachievements, we explore a possibility to develop optical clocks usingtransitions between the ground and a low-lying excited state in the Cf$^{15+}$and Cf$^{17+}$ ions. Using a high-accuracy relativistic method of calculationwe predicted the wavelengths of clock transitions, calculated relevant atomicproperties, and analyzed a number of systematic effects (such as the electricquadrupole-, micromotion-, and quadratic Zeeman shifts of the clocktransitions) that affect the accuracy and stability of the optical clocks. Wealso calculated magnetic dipole hyperfine-structure constants of the clockstates and the blackbody radiation shifts of the clock transitions.

Optical clocks based on the Cf$^{15+}$ and Cf$^{17+}$ ions