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We perform calculations of electronic structure of Cm$^{15+}$ and Bk$^{16+}$ions and demonstrate that they have transitions which combine the features ofatomic optical clocks with the enhanced sensitivity to the variations of thefine structure constant $\alpha$. The high sensitivity is due to large nuclearcharge $Z$, high ionisation degree $Z_i$ and the effect of {\em levelcrossing}, which enables optical transitions between states of differentconfigurations. These are the $6p_{1/2}-5f_{5/2} $ and $6p_{1/2}-5f_{7/2} $transitions in the single valence electron approximation. Variation of $\alpha$may be due to the interaction with scalar and pseudoscalar (axion) dark matterfields. Therefore, Cm$^{15+}$ and Bk$^{16+}$ clocks are promising candidates tosearch for these fields.

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