In recent years there have been rapid advances in theoretical models and calculational techniques for few-electron systems. Atomic structure calculations for three-electron systems include not only non-relativistic energy but also relativistic and quantum electrodynamic (QED) contributions. Rapid advances in the calculation of energy levels, ionization potentials, fine- and hyperfine-structure, and isotope shifts for Li and Li-like ions have created a need for improved experimental data, as many measurements have uncertainties too large to be good tests of theory.
We have used non-resonant, two-photon laser spectroscopy to observe the 2S-4S transitions of 6,7Li. The structure of these levels is shown in Fig. 1. As the laser scans across each of these transitions, four lines are observed as shown in Fig. 2. For each of these resonances, we manually set the laser to the transition center. A computer controlled vacuum Fabry-Pérot wavemeter determines the laser frequency, with respect to an I2-stabilized helium-neon (He-Ne) laser, with an accuracy of a few parts in 109. From these measurements we obtain precise transition energies between ground state and excited state hyperfine levels. Because the ground state hyperfine splitting is known to extremely high accuracy , we are able to calculate the excited state hyperfine constants for the 4S state with a precision of about 1 MHz for both isotopes.
The centers of gravity of the 4S level for both isotopes are determined with an absolute accuracy of better than 2 MHz. These are the highest precision measurements of the energy levels to date, reducing the uncertainties by a factor of better than twenty. The transition isotope shift is also determined to better than 2 MHz, an order of magnitude improvement on the uncertainty of earlier measurements.
 A. Beckmann, K.D. Böklen, and D. Elke, Z. Phys. 270, 173 (1974).
Figure 1: 2S-4S level diagram
Figure 2: 2S-4S two-photon spectra