氢分子离子HD+超精细结构理论与精确计算

Hydrogen molecular ion, HD+, is the simplest stable heteronuclear molecule. The ro-vibrational transition frequency can be predicted with high-accuracy by quantum electrodynamics (QED) theory. The theoretical prediction combined with precision spectroscopy experiments make HD+ promised candidate for improving the accuracy of the proton electron mass ratio, one of the fundamental constants. In this project,we would like to carried out a deeply theoretical investigation on high-order relativistic and QED effects originated from spin interaction among the electron,proton and duteron. To overcome the bottleneck of extremely slow convergence of high-sigular operators, novel numerical method will be devoloped. Systematic analysis will be carried out for a large number of terms in various kinds of spin interactions to pick out the key term, which has main contribution to the ro-vibrational levels. The high-order relativistic and QED correction for electron-proton, electron-deuteron spin-spin interaction, as well as electron-spin orbital angular momentum interaction, will be calculated reliably with desired accuracy. Meanwhile, we also search for possible proposal to determine quadruple moment of deuteron by using HD+ precision ro-vibrational spectroscopy, or by transition between two hyperfine levels. The output of this theoretical project would help to determine accurately the centre frequency of experimental spectroscopy measurement, and also provide reliable and essential data in determining the proton -electron, proton-deuteron mass ratios. We would say the proposed project is of great significance for examination of the fundamental theory, determination of fundamental constants and basic nuclear properties.

氢分子离子HD+是最简单的稳定异核分子体系，量子电动力学理论可以高精度预言其振转跃迁频率，HD+精密理论预言结合精密光谱实验已成为提高质子电子质量比精度的优选体系。本项目拟开展HD+与自旋相关的相互作用的高阶相对论与QED理论研究，发展有效的数值计算方法克服高奇异算子期待值收敛慢的瓶颈，逐阶分析不同类型自旋相互作用对振转能级的贡献，严格计算电子－质子、电子－氘核自旋自旋相互作用、电子自旋－轨道角动量相互作用的高阶相对论修正和辐射修正，深层次理解HD+超精细结构；同时探索利用HD+精密振转光谱及超精细跃迁测定氘核电四极矩的可行方案。本项目将直接为HD+精密光谱实验振转跃迁中心频率的高精度确定提供理论支持, 结合HD+自旋无关的高阶QED理论结果将为确定质子电子、质子氘核质量比提供必要和可靠的理论输入值。本项目对于束缚态QED理论检验、基本物理常数及原子核性质的确定有重要的科学意义。

氢分子离子(H2+、HD+、D2+)是最简单的稳定分子体系，其振转跃迁频率可由量子电动力学理论高精度计算。本结题项目原计划开展HD+与自旋相关的相互作用的相对论与QED理论计算，深层次理解HD+超精细结构，并探索利用HD+超精细跃迁测定氘核电四极矩的可行方案。项目实施过程中，对原计划研究内容进行了拓展：研究体系扩展到同核氢分子离子体系H2+和D2+；增加了自旋无关相互作用的相对论与QED理论计算；开展了外电场下氢分子离子场特性的研究。主要成果包括：（1）贝特对数项（Bethe Logarithm）的精确计算是QED修正计算中最困难的部分，本项目利用赝态求和方法(Drake-Goldman方法)实现了氢分子离子（H2+）贝特对数项ppb（十亿分之一）精度的计算；（2）系统计算了H2+和HD+低能振转态（振动量子数v=0-4，转动量子数L=0-4）能级，包含相对论与QED修正领头项的严格计算和高阶修正的估算，整体理论预算精度达到0.4ppb，提出了利用HD+体系 (v=0,L=0)至(v=6,L=1)振转跃迁确定质子电子质量比的方案；（3）系统计算了D2+体系振转能级（v=0-4，L=0-4）相对论修正和相应的超精细结构常数，首次严格计算了氘核电四极矩对超精细劈裂的贡献，结合QED修正的计算得到D2+体系(v=0,L=0)至(v=1,L=0)基振动跃迁频率为47279981.638(25)MHz；（4）实现了非波恩-奥本海默近似下氢分子离子（H2+、HD+、D2+）基态和第一激发态电多极极化率和超极化率的高精度计算，为其他近似计算方法提供了检验基准，同时为分析相关实验的外场效应提供了重要的理论依据。本项目的研究成果对于分子体系束缚态QED理论检验、质子电子质量比的确定以及原子核性质（质子电荷半径、氘核电四极矩）的确定提供了关键的理论数据，并推动了国内精密测量物理实验的开展。