${\mathrm{Cm}}^{15+}$ and ${\mathrm{Bk}}^{16+}$ ion clocks with enhanced sensitivity to new physics

We perform calculations of the electronic structure of ${\mathrm{Cm}}^{15+}$ and ${\mathrm{Bk}}^{16+}$ ions and demonstrate that they have transitions which combine the features of atomic optical clocks with the enhanced sensitivity to the variations of the fine-structure constant $\alpha$. The high sensitivity is due to large nuclear charge $Z$, high ionization degree $Z_i$, and the effect of level crossing, which enables optical transitions between states of different configurations. These are the $6p_{1/2}-5f_{5/2}$ and $6p_{1/2}-5f_{7/2}$ transitions in the single-valence electron approximation. The variation of $\alpha$ may be due to the interaction with scalar and pseudoscalar (axion) dark-matter fields. Therefore, ${\mathrm{Cm}}^{15+}$ and ${\mathrm{Bk}}^{16+}$ clocks are promising candidates to search for these fields.