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Improved isotope-shift-based bounds on bosons beyond the Standard Model through measurements of the $^2$D$_{3/2} - ^2$D$_{5/2}$ interval in Ca$^+$

We perform high-resolution spectroscopy of the $3$d$~^2$D$_{3/2} - 3$d$~^2$D$_{5/2}$ interval in all stable even isotopes of $^A$Ca$^+$ (A = 40, 42, 44, 46 and 48) with an accuracy of $\sim$ 20 Hz using direct frequency-comb Raman spectroscopy. Combining these data with isotope shift measurements of the 4s$~^2$S$_{1/2} \leftrightarrow 3$d$~^2$D$_{5/2}$ transition, we carry out a King plot analysis with unprecedented sensitivity to coupling between electrons and neutrons by bosons beyond the Standard Model. Furthermore, we estimate the sensitivity to such bosons from equivalent spectroscopy in Ba$^+$ and Yb$^+$. Finally, the data yield isotope shifts of the 4s$~^2$S$_{1/2} \leftrightarrow 3$d$~^2$D$_{3/2}$ transition at 10 part-per-billion through combination with recent data of Knollmann et al (2019).