Fock-space relativistic coupled-cluster calculations of clock transition properties and systematic shifts in Ca + and Sr + optical clocks

We present a high-precision theoretical study of clock-transition related properties of single-ion optical frequency standards based on Ca + and Sr + ions. Using a relativistic coupled-cluster framework, we calculate the lifetimes of the metastable clock states, static and dynamic polarizabilities, electric quadrupole moments, and hyperfine structure constants. The accuracy of our calculated wavefunctions is benchmarked through excellent agreement with available experimental data. To achieve the precision required for optical clock applications, we systematically incorporate higher order electron correlation effects via perturbative triple excitations, as well as relativistic corrections from Breit interaction and quantum electrodynamic effects. Using the computed properties, we extract nuclear quadrupole moments, identify magic wavelengths for optical trapping, and evaluate the key systematic frequency shifts, including blackbody radiation, AC Stark, micromotion, and electric quadrupole shifts in Ca + and Sr + ions. For Ca + , our predicted magic wavelength near 395.8 nm is in excellent agreement with experiment, thereby strengthening the reliability of our additional predictions, including a far detuned wavelength near 1011 nm. For Sr + , where no experimental magic wavelength has yet been reported, our predictions provide essential guidance for future precision measurements. The results presented in this work offer a self-consistent and systematically improved set of atomic properties that are crucial for reducing uncertainties and optimizing next generation single ion optical clocks.