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A complete set of spectroscopic data is indispensable when using Rydbergstates of trapped ions for quantum information processing. We carried outRydberg series spectroscopy for $nS_{1/2}$ states with $38 \leq n \leq 65$ andfor $nD_{5/2}$ states with $37\leq n \leq 50$ on a single trapped $^{40}$Ca$^+$ion. From a nonlinear regression to resonance frequencies, we determined theionization energy of 2 870 575.582(15) GHz, measured 60 times more accuratelyas compared to the accepted value and contradicting it by 7.5 standarddeviations. We confirm quantum defect values of $\delta_{S_{1/2}}=1.802995(5)$and $\delta_{D_{5/2}}=0.626888(9)$ for $nS_{1/2}$ and $nD_{5/2}$ statesrespectively, which allow for unambiguous addressing of Rydberg levels ofCa$^+$ ions.

Precision measurement of the ionization energy of a single trapped $^{40}$Ca$^+$ ion by Rydberg series excitation