Zong-Chao Yan

High precision theory for few body systems

Due to rapid developments in laser spectroscopy and laser cooling and trapping techniques, atomic transition frequencies and other properties can now be measured to an unprecedented precision. These experimental advances provide many excellent opportunities for theorists to test existing theories and to explore new physics. The challenge to theorists is to perform high-precision calculations for various small but extremely important contributions arising from relativistic and quantum electrodynamic (QED) effects.

Few-body atomic and molecular systems, such as He, Li, PsH, H2+, H2 hold a special place in our understanding of microscopic world. From a structure point of view they are simple: three and four body systems, they are, however, intrinsically complex and contain physics (this is true even for the atomic hydrogen, the simplest atom, if one explores relativistic and QED effects).

For these systems, an additional challenge to theorists is that the Schrodinger equation can not be solved exactly even in the nonrelativistic limit, due to the existence of Coulomb correlations. Thus, in order to match or even exceed modern spectroscopic accuracy, novel approximation methods need to be invented. New variational methods developed recently by us have shown a great promise of obtaining precise solutions to the Schrodinger equation for a general three or four body system.

For example, the ground state energy of Li has now been calculated to an accuracy of a few parts in 1012. The key to the success is the explicit inclusion of interelectronic distances in our variational basis sets, which is particularly powerful in handling complex correlation effects between electrons.

With these very precise wavefunctions, relativistic and QED effects can be treated perturbatively. The significance of these calculations is that they have set a new standard of accuracy, and they have stimulated several experimental groups, including Harvard (Gabrielse), NIST (Sansonetti), Florence (Inguscio), GSI at Darmstadt (Dax), York University (Hessels), Florida State University (Myers), and University of Northern Texas (Shiner) to perform high precision measurements for comparison.