Testing the fundamentals of helium theory.

The agreement of two independent measurements of a single parameter to within 8 parts in 10 billion would normally qualify as a great triumph of experimental physics. However, the precision of both experimental and theoretical determinations of energy levels in the helium atom has so greatly improved over the last two years that even this minute discrepancy looms large.

"The agreement is really quite remarkable," says theorist Gordon W.F. Drake of the University of Windsor in Ontario, who pioneered several techniques for calculating helium energy levels. "Tests [of such precision] have never been done before in systems more complicated than hydrogen. These results provide a profound test of our understanding of systems containing more than one electron."

At the same time, the tiny but significant difference between the two experimental results suggests a need for further evaluation of the experimental work to uncover possible errors. Craig J. Sansonetti and his colleagues at the National Institute of Standards and Technology (NIST) in Gaithersburg, Md., performed one of the experiments; William L. Lichten and his colleagues at Yale University in New Haven, Conn., did the other.

"I don't know what the cause of the difference is," Sansonetti says. "I have no quarrel with the Yale experiment, nor do I know of any error that could enter in our experiment that would make a difference." Sansonetti presented his viewpoint this week at an American Physical Society meeting in Washington, D.C.

With only two electrons moving under the influence of its nucleus, a helium atom has a deceptively simple configuration. In reality, various subtle effects, including the repulsive force between electrons, introduce complexities that vastly increase the difficulty of doing high-precision experiments and performing extremely accurate theoretical calculations involving helium.

Because each of a helium atom's electrons can have only certain, well-defined energies, one can picture a helium atom's energy levels as the rungs of a ladder. Theorists can calculate, in effect, the positions of these rungs, but experimenters can determine only the sizes of the gaps between rungs.

To find the actual value of a particular low-lying energy level in helium, the Yale group used a laser to excite helium atoms already in this state to a much higher energy level. By precisely determining the energy involved in the transition and by taking the difference between this measured value and the accurately computed energy of the upper level, the researchers deduced the energy level of the original, low-lying state.

Their measurement, like an earlier, less precise result obtained by the NIST team, differed significantly from the theoretically derived energy for this particular state. That disagreement between theory and measurement prompted John D. Morgan III of the University of Delaware in Newark and his collaborators to refine their theoretical calculations, bringing theory into closer agreement with experiment.

Meanwhile, using a different experimental approach that relies less on computed energy-level values, Sansonetti and his colleagues increased the precision of their energy-level determination to match the Yale effort. Taking experimental uncertainties into account, however, the NIST and Yale results failed to overlap.

Researchers in both camps have since expended considerable effort to learn why their results differ as much as they do, but they have had little success finding an explanation. "If this disagreement persists, one of us is going to have to either redo the experiment or think of another experiment to clarify the situation," says Yale's David C. Shiner.

Further refinements in the theoretical calculations -- to take into account effects that had previously been ignored as too small to matter at this level -- may help pin down which team will have to return to the laboratory.

Despite this nagging discrepancy, theoretical and experimental techniques have now advanced sufficiently to allow the helium atom to join hydrogen as a prime setting for testing fundamental physics, specifically as a sensitive probe of quantum electrodynamics -- the basic theory of how light interacts with matter -- in a many-electron atom.