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 $4s_{1/2}$ and $4p_{1/2}$ in ${}^{207}\mathrm{Pb}^{53+}$. 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%.

Figure 1

Measured dielectronic recombination spectra with ${}^{207}\mathrm{Pb}^{53+}$ and with ${}^{208}\mathrm{Pb}^{53+}$.

Figure 2

Recombination rate coefficients A for ${}^{207}\mathrm{Pb}^{53+}$, the calculated ones are with different values of the hyperfine constant, $a$, as explained in the text. The comparison is absolute, both in energy and in A.

Figure 3

Calculated resonance positions for initial states ${}^{207}\mathrm{Pb}^{53+}(4s_{1/2}{)}_{F=0}$, upper sequence of levels, and ${}^{207}\mathrm{Pb}^{53+}(4s_{1/2}{)}_{F=1}$, lower sequence of levels. The gray line shows the cross section $s$ assuming statistical population of these two hyperfine structure components. From this cross section the rate coefficient, the black solid line, is generated. It should be compared to the measured rate coefficient for ${}^{207}\mathrm{Pb}^{53+}$, shown as black dots.