Pr10+ as a candidate for a high-accuracy optical clock for tests of fundamental physics

We propose In-like ${\mathrm{Pr}}^{10+}$ as a candidate for the development of a high-accuracy optical clock with high sensitivity to a time variation of the fine-structure constant, $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$, as well as favorable experimental systematics. We calculate its low-lying energy levels by combining the configuration interaction and the coupled cluster method, achieving uncertainties as low as $0.1%$, and improving previous work. We benchmark these results by comparing our calculations for the $|5{s}^{2}5p\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2}\ensuremath{\rangle}\ensuremath{\rightarrow}|5{s}^{2}5p\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}\ensuremath{\rangle}$ transition in ${\mathrm{Pr}}^{10+}$ with a dedicated measurement and for ${\mathrm{Pr}}^{9+}$ with a recent experiment, respectively. In addition, we report calculated hyperfine-structure constants for the clock and logic states in ${\mathrm{Pr}}^{10+}$.