关联B-样条基组在少电子原子QED计算中的应用

Precision calculations and measurements on the spectra of helium and lithium atoms have important scientific significance and applications in examining atomic structure theory, determining fundamental physical constants and exploring the properties of nuclei. The precise theoretical predictions on these spectra rely on the calculations of quantum electrodynamics (QED) corrections, in which the Bethe-logarithm is of serious concern because the numerical accuracy of it is difficult to improve. In this project, we will develop a new configuration interaction method using the correlated B-spline basis set to take full account of the electron correlations, by combining the advantages of the Hylleraas and B-spline basis sets. This method will not only accelerate the convergence on the size of the basis set, but also eliminate the dilemma of the linear dependence in the Hyleraas and explicitly correlated gaussians methods. Using this newly-developed method, we will present the high precision results on the Bethe-logarihtm of the highly excited states in the two-electron atoms and ions, perform the massively parallel computations on the energy spectra and properties and improve the numerical accuracy of the Bethe-logarihtms of the three-electron atomic systems, solve the problem of the low accuracy of the Bethe-logarithm calculation in the inner shell of the helium negative ion, and finally improve the accuracy of the prediction on QED corrections. This project is of importance on exploring the new method in the field of precision spectra theory and the new applications of the B-spline basis.

少电子原子氦和锂光谱的精密计算和测量在检验原子结构理论、确定基本物理常数以及确定原子核基本性质上有重要的科学意义和应用价值,基于从头计算的理论预言精度强烈依赖于量子电动力学( QED)修正的计算精度,其中的贝特对数项因其计算精度提高异常困难而备受关注。本项目结合Hylleraas和B样条基组的优点，发展充分考虑电子关联效应的关联B-样条组态相互作用方法，既加快基组收敛速度，又消除Hylleraas与关联高斯 (ECG) 基组方法中线性相关的困难；提供两电子原子/离子高激发态贝特对数项的高精度理论计算结果，实现三电子原子/离子原子能谱、性质、和贝特对数项的大规模并行计算，提高三电子原子/离子体系贝特对数项计算精度；解决目前氦负离子内壳激发态贝特对数项计算精度过低的问题，整体提高QED理论预言精度。该项目实施对精密谱理论计算有方法学的意义，也将为B样条基组的应用开辟新的方向。

本项目研究目的是发展新的理论工具计算少电子原子非相对能级、相对论和QED修正，探寻多电子原子QED修正计算的高效途径。项目取得了以下创新成果：.（1）发展了基于关联B-样条基组方法求解氦原子非相对论能级、相对论和QED修正领头项的计算方法，实现了氦原子单、三重S态能级、Breit-Pauli算符、贝特对数项（Bethe-Logarithm）以及Araki-Sucher修正的高精度计算，提供了与传统Hylleraas和关联高斯基组不同的精密谱计算新路线；.（2）开发了任意精度下求解广义稠密对称矩阵特征值问题的并行求解器（Multiple-precision Symmetric Eigenproblem Software（MSEPS）），有效解决了大基组计算遇到的线性相关难题；.（3）精密计算了氦原子低能态的交流斯塔克频移，发现23S-21P禁戒跃迁1335nm 幻波长对有限核质量、相对论和QED效应非常敏感，提供了利用幻波长测量检验QED理论的新途径，提出了利用幻波长提高氦原子23S-33S双光子跃迁测量精度的方案；.（4）实现了6,7Li+离子23S和23P态超精细劈裂的高阶QED修正计算，结合实验测量确定了6,7Li原子核电磁分布半径，发现由6Li+的23S态超精细劈裂确定的核电磁分布半径与核物理方法得到的相应值存在6个标准误差；.（5）开发了适用于重原子的相对论原子结构从头计算程序，并成功应用于Ra+、Th3+离子的超精细结构常数、跃迁性质、电四极矩等性质的计算，为高精度原子钟研究提供了重要的理论数据。.在本项目资助下，已在Phys. Rev. Lett., Phys. Rev. A, J. Phys. B等原子分子物理主流期刊发表SCI论文11篇，培养博士毕业生4名。