Dielectronic resonance method for measuring isotope shifts.

Long standing problems in the comparison of very accurate hyperfine-shift measurements to theory were partly overcome by precise measurements on few-electron highly charged ions. Still the agreement between theory and experiment is unsatisfactory. In this Letter, we present a radically new way of precisely measuring hyperfine shifts, and demonstrate its effectiveness in the case of the hyperfine shift of 4s1/2 and 4p1/2 in 207Pb53+. It is based on the precise detection of dielectronic resonances that occur in electron-ion recombination at very low energy. This allows us to determine the hyperfine constant to around 0.6 meV accuracy which is on the order of 10%.