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

H、He、Li、H2+、H2等小体原子和分子体系是基础物理的基础试验场。由于最近实验技术的发展，如飞秒光学梳技术，对少体系统的测量现在可以达到前所未有的精度，通过计算重要的效应，如相对论和量子电动力学（QED）效应，为探索基础物理学提供了许多机会。通过对理论和实验数据的比较，人们可以发现可能的新物理学，例如对基本对称性的违反；也可以通过氦的精细结构提取出精细结构常数，通过H2+中的跃迁频率提取出电子-质子质量比等基本常数的精确值，并研究它们随时间的变化。在过去的20年里，我们在获得三体和四体系统薛定谔方程的高精度解方面取得了重大进展，这使我们能够精确地计算相对论和QED效应。我们工作的重要应用之一是与TRIUMF和GSI的两个主要实验小组合作，确定halo 11Li的核电荷半径。为了确定电荷半径，需要计算高精度的同位素位移，包括相对论和QED修正。虽然自20世纪80年代以来，对于一个和两个电子系统来说，这已经成为可能，但对于Li来说，突破是在2000年，当时我们成功地计算了Li跃迁中的质量效应，不确定性优于百万分之五。我们的方法的意义在于，没有其他方法既独立于核结构模型，又能对核电荷半径产生足够的精度。因此，与我们的结果比较能够区分核力的各种可能候选者。我们现在可用的高精度理论为开发原本不存在的测量工具创造了新的机会，并在原子和核物理学之间的界面上开辟了一个新的研究领域。该研究计划将通过开发新的计算方法，推动我们进一步探索少体原子和分子系统的相对论和QED效应，这将为原子、分子和核物理学之间的界面取得更深远的进展铺平道路。

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.