Measurement of the Two-Loop Lamb Shift in Lithiumlike ${\mathrm{U}}^{89+}$

Using the SuperEBIT electron beam ion trap, we have measured the $2s_{1/2}\mathrm{\text{−}}2p_{1/2}$ transitions in ${\mathrm{U}}^{88+}$ and ${\mathrm{U}}^{89+}$. The measured value of $280.645\pm 0.015\mathrm{eV}$ for Li-like ${\mathrm{U}}^{89+}$ improves the available precision by nearly an order of magnitude and establishes a new benchmark for testing the total QED contribution to the transition energy within a fractional accuracy of $3.6\times {10}^{-4}$. We infer a value for the $2s$ two-loop Lamb shift in ${\mathrm{U}}^{89+}$ of $-0.23\mathrm{eV}$, from which we estimate a value of $-1.27\mathrm{eV}$ for the $1s$ two-loop Lamb shift in ${\mathrm{U}}^{91+}$.

Figure 1

Spectra obtained with the high-resolution SuperEBIT grating spectrometer. (a) Spectrum of the $2s_{1/2}\mathrm{\text{−}}2p_{1/2}$ transitions in ${\mathrm{U}}^{88+}$ and ${\mathrm{U}}^{89+}$ representing the accumulation of ten 30-min exposures. (b) Calibration spectrum showing the emission of heliumlike and hydrogenlike carbon (first order) and oxygen (second order). The spectrum results from the addition of four 30-min exposures.

Figure 2

Determinations of the $2s_{1/2}\mathrm{\text{−}}2p_{1/2}$ wavelength in ${\mathrm{U}}^{89+}$ from 17 separate spectra for one of several wavelength calibrations. The error bars represent statistical uncertainties of each individual measurement. The weighted average is indicated by the solid line.

Figure 3

Variation of the ${\mathrm{U}}^{89+}$ $2s_{1/2}\mathrm{\text{−}}2p_{1/2}$ wavelength determinations for seven spectral calibrations taken at different times interspersed among the uranium measurements. Error bars represent the statistical uncertainty of each individual calibration. The weighted average is indicated by the solid line. The dashed lines mark the uncertainty limits of the final wavelength result.