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We examine energy level-crossings of fine-structure (FS) levels in theheavier highly charged ions (HCIs) with $d^6$ and $d^8$ configurations. Fromthe analysis, we find that some of these HCIs are tailor-made for atomic clockswith quality factors ranging from $10^{16}$ to $10^{18}$ and fractionaluncertainties below $10^{-19}$ level. Many of them are also realized to behighly sensitive to the observation of temporal variation of FS constant($\alpha$) and testing violation of local Lorentz symmetry invariance (LLI). Toprobe variations of $\alpha$ and LLI, we have determined their correspondingsensitivity coefficients in the investigated HCIs. Similarly, we have estimatedorders of magnitudes of the Zeeman, Stark, black-body radiation and electricquadrupole shifts of the clock transitions of the considered HCIs in order todemonstrate them as the potential candidates for atomic clocks.

A Hunt for Highly Charged Ions as Ultra-stable Optical Clock Candidates: Art of the energy level-crossing approach