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Hyperfine-induced electric dipole contributions to the electric octupole and magnetic quadrupole atomic clock transitions

Hyperfine-induced electric dipole contributions may significantly increase probabilities of otherwise very weak electric octupole and magnetic quadrupole atomic clock transitions (e.g. transitions between $s$ and $f$ electron orbitals). These transitions can be used for exceptionally accurate atomic clocks, quantum information processing and search for dark matter. They are very sensitive to new physics beyond the Standard Model, such as temporal variation of the fine structure constant, the Lorentz invariance and Einstein equivalence principle violation. We formulate conditions under which the hyperfine-induced electric dipole contribution dominates. Due to the hyperfine quenching the electric octupole clock transition in $^{173}$Yb$^+$ is two orders of magnitude stronger than that in currently used $^{171}$Yb$^+$. Some enhancement is found in $^{143}$Nd$^{13+}$, $^{149}$Pm$^{14+}$, $^{147}$Sm$^{14+}$, and $^{147}$Sm$^{15+}$ ions.