An improved value for the hyperfine splitting of hydrogen-like ²⁰⁹Bi⁸²⁺

We report an improved measurement of the hyperfine splitting in hydrogen-like bismuth (²⁰⁹Bi⁸²⁺) at the experimental storage ring ESR at GSI by laser spectroscopy on a coasting beam. Accuracy was improved by about an order of magnitude compared to the first observation in 1994. The most important improvement is an in situ high voltage measurement at the electron cooler (EC) platform with an accuracy at the 10 ppm level. Furthermore, the space charge effect of the EC current on the ion velocity was determined with two independent techniques that provided consistent results. The result of ${\lambda }_0=243.821\left(6\right)$ nm provides an important reference value for experiments testing bound-state quantum electrodynamics in the strong magnetic field regime by evaluating the specific difference between the splittings in the hydrogen-like and lithium-like ions. (paper)