
WIPM Made Progress in FewBody BoundState QED Theory 

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Recently, a staged progress in fewbody boundstate quantum electrodynamic (QED) theory has been achieved from the theoretical atomic and molecular physics group at Wuhan Institute of Physics and Mathematics (WIPM), Chinese Academy of Sciences, by deriving the complete spinaveraged m(alpha)**6 order effective Hamiltonian for hydrogen molecular ions. The hydrogen molecular ion H2+ (and its isotopes D2+, HD+ etc.) is the simplest molecular ion in nature, which allows its rovibrational transition frequencies to be precisely measured experimentally and calculated theoretically using boundstate QED theory. Therefore, we can test boundstate QED theory and determine fundamental physical constants, in particular the protontoelectron mass ratio, by studying precision spectroscopy of hydrogen molecular ions. Currently, several experiments are underway, including the twophoton transition measurements in H2+ by L. Hilico and J.Ph. Karr of LKB (France), the rovibrational transition measurements in HD+ by J. Koelemeij of VU (Netherlands) and by S. Schiller of HeinrichHeine University (Germany), and the (v=0>v=6) transition measurements in HD+ by X. Tong of WIPM (China). The targeted precision of these experiments 10**(10) is a great challenge to theoretical calculations that need highorder relativistic and QED corrections up to m(alpha)**7 or even higher. The current status of theory is as follows. First, the theory group at WIPM has obtained the ultrahigh precision results for the nonrelativistic energy levels, as well as the leadingorder relativistic and QED corrections. Second, a series of works on higherorder relativistic and QED corrections were published by V. I. Korobov of Dubna and coworkers. In these works, the leadingorder relativistic and QED corrections were calculated in a threebody Coulomb scheme without any approximation; however higherorder relativistic and QED corrections, including orders m(alpha)**6, m(alpha)**7 and m(alpha)**8, were treated by taking the externalfield approximation and the BornOppenheimer approximation. Meanwhile, the twobody bound state results were also used to deal with the nuclear recoil correction of order (m/M) m(alpha)**6. In order to reduce theoretical uncertainties in transition frequencies due to the use of these approximations, a rigorous theory at orders of m(alpha)**6 and (m/M) m(alpha)**6 must be developed. In order to derive the order m(alpha)**6 and (m/M)m(alpha)**6 effective Hamiltonian, significant efforts were made by the theory group at WIPM to extend successfully the socalled nonrelativistic quantum electrodynamic (NRQED) theory from atomic systems to oneelectron molecular systems, without assuming the BornOppenheimer approximation. Renormalization procedure was also used to completely remove theoretical singularities among various operators. As a nontrivial test of the correctness of their derivation, the obtained theory was applied to the atomic hydrogen and all the results of the Dirac equation for hydrogen were reproduced. This progress signifies the first successful application of NRQED theory to molecular systems. The obtained effective Hamiltonian can now precisely describe the m(alpha)**6 order relativistic and QED corrections, including the nuclear recoil effects. Furthermore, their theory can also be applied to other oneelectron twocenter problems, such as the antiprotonic helium. The next step of the theory group is to calculate those effective operators numerically, which is as challenge as the derivation of the effective Hamiltonian. This work has been supported by the National Natural Science Foundation of China and the Strategic Priority Research Program of the Chinese Academy of Sciences.

