One-electron atoms and ions are of particular importance for tests of the theory of quantum electrodynamics (QED) because it is possible to calculate the non-QED contributions to the energy levels with high precision using the Dirac equation. The lowest-order QED terms scale as Z⁴, where Z is the nuclear charge, and so increase as Z² relative to the gross structure. Terms of higher order in Z also become relatively more important for high-Z systems. Thus spectroscopic studies of hydrogen-like ions can provide tests of fundamental theory in a "strong-field" regime which is not accessible in the extremely precise work achieved on atomic hydrogen.

Interestingly, 2s Lamb shift measurements in the range Z=15-18 are all a little lower than the theoretical predictions, with the most precise measurement, for P¹⁴⁺, lying 2.1 standard deviations below theory. Recent calculations of higher-order corrections to the self-energy, although larger than previously expected, do not completely remove this hint of a discrepancy. Improved accuracy is clearly required to provide a critical test of theory.

All 2s Lamb shift measurements for medium-Z hydrogen-like ions have employed fast ion beams. The accuracy of most such experiments is inherently limited by the Doppler effect, and uncertainties associated with the high velocity of the ions in a fast beam form a significant source of error in all measurements performed to date. Various methods have been employed or suggested for reducing the sensitivity of fast beam experiments to Doppler corrections. However, it is conceptually much simpler to reduce Doppler-related errors by performing a measurement on slow highly charged ions, such as those trapped in the Oxford EBIT.

In medium-Z hydrogen-like ions, the 2s_1/2 - 2p_1/2 and 2s_1/2 - 2p_3/2 transitions lie in the infra-red or visible regions of the electromagnetic spectrum, and thus in many cases are accessible for study by laser spectroscopy. The laser resonance technique relies on the metastability of the 2s_1/2 state, and is illustrated in the diagram below.

Partial term diagram of the Si13+ ion, showing the transition which would be induced in an n=2 laser resonance experiment.

Laser radiation is used to excite ions from the 2s_1/2 state to either the 2p_1/2 state or the 2p_3/2 state, from which they rapidly decay to the ground state. The resonance is monitored by observing the rate of emission of Lyman-alpha photons as a function of the laser frequency. In the case of excitation to the 2p_1/2 state, a measurement of the resonance frequency yields the Lamb shift directly. In contrast, inducing the transition to the 2p_3/2 state relies on the fact that the fine structure splitting is much more accurately known theoretically in order to obtain a value for the Lamb shift. However, in practice, a direct determination of the 2s Lamb shift is much more difficult, since the large natural width of the 2p state requires the laser to be tuned over a large fraction of its frequency.

We have chosen to begin our studies by measuring the 2s Lamb shift in hydrogen-like Si¹³⁺. The 2s_1/2 - 2p_3/2 interval in Si¹³⁺ was first observed by our group in 1990 using a fast ion beam, but as yet there exists no precision measurement for this ion. Our choice of Si¹³⁺ from among the ions for which suitable laser wavelengths exist is based on a compromise between resonance signal strength and ease of ion production, trapping efficiency and Lyman-alpha detection efficiency.

To saturate the 2s_1/2 - 2p_3/2 transition in Si¹³⁺ we require a laser intensity of about 10 kW mm^-2. Such intensities are attainable using an extremely high finesse enhancement cavity to buid up the output power from a frequency-stabilized laser. The 2s_1/2 - 2p_3/2 interval in Si¹³⁺ lies at approximately 734 nm. The trapped ions will lie at the laser beam waist within this cavity, and to keep the loss factors as low as possible the high reflectivity mirrors must lie within the EBIT vacuum chamber. The Lyman-alpha count rate will be monitored using a lithium-drifted silicon X-ray detector.

Schematic diagram for the laser system for an
n=2 resonance experiment on Si.

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