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+, H2 are fundamental testing grounds for basic physics. Due to the recent development of experimental techniques, such as the femtosecond optical comb technique, measurements of few-body systems can now reach unprecedented precision, providing many opportunities to explore fundamental physics by performing calculations on important effects, such as relativistic and quantum electrodynamic (QED) effects. Through comparisons between theory and experimental data, one can 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 through helium fine structure, and the electron-proton mass ratio through transition frequencies in H2+, and study their variation in time. Over the past 20 years, we have made significant advances in obtaining high precision solutions to the Schrodinger equation for three and four body systems, which allows us to calculate relativistic and QED effects precisely. One of the important applications of our work is the determination of the nuclear charge radius of halo 11Li, in collaboration with two leading experimental groups at TRIUMF and GSI. To determine the charge radius, it is necessary to calculate the isotope shifts to high precision, including relativistic and QED corrections. While this has been possible for one and two electron systems since the 1980's, for Li the breakthrough came in 2000 when we succeeded in calculating the mass effect in transitions of Li with an uncertainty 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 and nuclear physics. The proposed research program will advance our efforts to further explore relativistic and QED effects for few-body atomic and molecular systems by developing new computational methods, which will pave the way to even more profound advances at the interface between atomic, molecular, and nuclear physics.