High-precision theory of few-body atomic and molecular systems

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Few-body atomic and molecular systems, such as H, He, Li, H2+ , are fundamental testing grounds for basic physics. Due to recent development of techniques, such as femtosecond optical comb, measurements on few body systems can now reach an unprecedented high precision, providing many exciting opportunities for theorists to explore fundamental physics by performing calculations on small but extremely important effects, such as high order relativistic and quantum electrodynamic (QED) effects. Through comparison between theory and experiment, one can test the existing theory and discover possible new physics, such as violation of fundamental symmetries; one can also extract precise values of fundamental constants, such as the fine structure constant and the electron-proton mass ratio, and study their variation in time. In the past 10 years, we have made significant advances in obtaining high precision solutions to the Schrodinger equation for three and four body atomic and molecular systems, which allows us to calculate relativistic and QED effects precisely. One of the important applications of our work is the precise determination of the nuclear charge radius of halo lithium, 11Li, in collaboration with two leading experimental groups at TRIUMF and GSI. To determine the charge radius, it is necessary to calculate the mass-dependent part of the isotope shift with high precision, including relativistic and QED corrections. While this was possible for one and two-electron systems since the 1980's, for Li and Li-like ions, the breakthrough came in 2000 when we succeeded in calculating the mass effect in transitions of neutral Li with an uncertainty of better than 5 parts per million. The significance of our method is that no other method is both independent of nuclear structure models and capable of yielding sufficient accuracy for the nuclear charge radius. Comparisons with our results are therefore capable of distinguishing amongst the various possible candidates for the nuclear forces. Our high precision theory that is now available creates new opportunities to develop measurement tools that would otherwise not exist, and opens up a new area of study at the interface between atomic physics and nuclear physics.