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

Recent experimental progress in cooling, trapping, and quantum logic spectroscopy of highly-charged ions (HCIs) made HCIs accessible for high resolution spectroscopy and precision fundamental studies. Based on these achievements, we explore a possibility to develop optical clocks using transitions between the ground and a low-lying excited state in the Cf$^{15+}$ and Cf$^{17+}$ ions. Using a high-accuracy relativistic method of calculation we predicted the wavelengths of clock transitions, calculated relevant atomic properties, and analyzed a number of systematic effects (such as the electric quadrupole-, micromotion-, and quadratic Zeeman shifts of the clock transitions) that affect the accuracy and stability of the optical clocks. We also calculated magnetic dipole hyperfine-structure constants of the clock states and the blackbody radiation shifts of the clock transitions.