Determination of the $2s\text{−}2p$ excitation energy of lithiumlike scandium using dielectronic recombination

High-resolution spectroscopy of doubly excited states produced by dielectronic recombination (DR) of lithiumlike ${\mathrm{Sc}}^{18+}$ ions was performed by employing the electron-ion merged-beam technique at the heavy-ion storage ring TSR. The experimental procedure for measuring DR resonances with high precision is thoroughly described with an emphasis on the uncertainties of the experimental energy scale. Absolute measurements of recombination rate coefficients were carried out over the center-of-mass energy range $0–50\mathrm{eV}$ that comprises all DR resonances associated with $2s_{1∕2}\to 2p_{1∕2,3∕2}$ excitations. At relative energies below $300\mathrm{meV}$ resonances due to DR via ${\mathrm{Sc}}^{17+}$ $\left(1s^{2}2p_{3∕2}10l_j\right)$ intermediate states were found. Their positions could be measured with an uncertainty of only $\pm 1.8\mathrm{meV}$. The results are compared with theoretical calculations within the framework of relativistic many-body perturbation theory. By combining the precision of the experimental and theoretical results we derive a value for the $2s_{1∕2}\to 2p_{3∕2}$ excitation energy, $44.3107\left(19\right)\mathrm{eV}$, which is by more than an order of magnitude more accurate than the hitherto most precise value obtained from optical spectroscopy.

Figure 1

Schematic picture of the electron cooler in the Heidelberg storage ring TSR. The magnetic field that guides the electron beam is generated by five solenoid (marked $1,2,\dots ,5$) and two toroid (marked A,B) magnets. Additional dipole coils on top of the solenoid magnets allow for an exact positioning of the electron beam.

Figure 2

Schematic picture of the two different data taking modes that were used in the present experiment; the right panel shows mode 1 “Cool-Ref-Meas,” indicating the sequence and the duration of scan energies: cooling energy ($30\mathrm{ms}$), reference energy $\left(5\mathrm{ms}\right)$, and measurement energy $\left(5\mathrm{ms}\right)$. The left panel shows mode 2 “Cool-Meas-Ref.” After each voltage jump a time period of $1.5\mathrm{ms}$ (gray shaded areas) was allowed for the power supplies to settle in on the new condition before data taking was started. While the voltages in the “Cool” and “Ref” phases of a measurement are fixed the voltage in the “Meas” phase is ramped up or down during a cycle that typically comprises a thousand “Meas” voltages.

Figure 3

Absolute ${\mathrm{Sc}}^{18+}$ photorecombination rate coefficients measured as a function of relative energy. The vertical bars indicate the calculated [Eq. (1)] $2p_{j}n$ DR resonance positions.

Figure 4

Uncertainties $\Delta E_{\mathrm{rel}}$ of the calibrated energy scale as a function of $E_{\mathrm{rel}}$.

Figure 5

Comparison of the present RMBPT calculation and the storage-ring experiment on the total photorecombination of ${\mathrm{Sc}}^{18+}$ ions in the energy range of $2p_{3∕2}10l_{j^{\prime }}$ resonances. Experimental rate coefficients are represented by the solid dots. Error bars only slightly larger than the symbol size indicate the statistical uncertainties. The theory-based convoluted product $⟨\sigma v⟩$ (thick full line) was determined with the temperatures resulting from the analysis in Fig. 6. Calculated background from RR is shown separately (dotted line). The theoretical cross sections show the underlying resonance structure (right hand scale).

Figure 6

Fit of theoretical DR resonances to the experimental data. The resonance positions were allowed to vary (see text). In (b) hyperfine effects are additionally taken into account.