Helium theory gets high-precision test.

Helium theory gets high-precision test

The basic equations of quantum mechanics are so difficult to solve that theorists have no straightforward way to calculate the energies emitted or absorbed by even so simple an atom as helium. Nonetheless, by starting with a rudimentary model describing the behavior of the two electrons in a helium atom and then adding, step by step, the effects of more subtle interactions, they can make remarkably precise predictions concerning the energy-level transitions a helium atom can undergo.

Experiment has now caught up with theory. By making the most precise measurements to date of a particular energy-level transition in different helium isotopes, researchers have performed an unprecedented experimental check on the details of these calculations. The results reveal close agreement between the experimental and computed values of helium's so-called isotope shift.

"With a hundredfold improvement in prevision [over previous experiments], this is the most precise isotope-shift measurement ever made for a multielectron system," report physicists Ping Zhao, John R. Lawall and Francis M. Pipkin of Harvard University in the Feb. 4 PHYSICAL REVIEW LETTERS.

The team observed the same atomic transition in two different helium isotopes: helium-3 (whose nucleus consists of two protons and one neutron) and helium-4 (two protons and two neutrons). Theory predicts that the mass difference between the isotopes will have a small but noticeable effect on the specific wavelengths of light emitted or absorbed by a helium atom.

To measure this effect, Zhao and his co-workers constructed a special laser that produces light at an infrared wavelength of 1,083 nanometers, matching the wavelength of one particular helium-atom transition. A novel procedure allowed them to measure the wavelength difference, or isotope shift, between helium-3 and helium-4 without having to measure the exact wavelength corresponding to each transition.

"With this technique, the difference of [wavelengths] can be measured much more precisely than the [wavelengths] themselves," the researchers say.

The agreement between the theoretical calculations and experimental results provides by far the best confirmation yet that the computational techniques used to model a two-electron atom really work. "It would be straightforward to do more precise measurements, but we've already gotten to the point where we're past the theory," Pipkin says. "There's not much motivation [to go farther] at the present time."