20位精度双中心Dirac方程的有限元解法
Solution of the two-center Dirac equation with 20 digits precision using the finite-element technique
摘要：
我们提出了一个精确的完全相对论数值解的两中心库仑问题。单位核电荷的特殊情况与精确描述${\rm H}_2^+$分子离子及其同位素体有关，这些系统是一个活跃的实验课题。计算采用2-旋量极大极小法和有限元法。计算的总能量估计分数的不确定性的几倍$10^{-20}$的单位电荷和键长为2个原子单位。纯相对论贡献的分数不确定度是$1\times10^{-17}$。结果是相关的未来精密实验，而目前的不确定性所产生的量子电动力学处理的振转跃迁频率。占主导地位。
英文摘要：
We present a precise fully relativistic numerical solution of the two-center Coulomb problem. The special case of unit nuclear charges is relevant for the accurate description of the ${\rm H}_2^+$ molecular ion and its isotopologues, systems that are an active experimental topic. The computation utilizes the 2-spinor minmax approach and the finite-element method. The computed total energies have estimated fractional uncertainties of a few times $10^{-20}$ for unit charges and a bond length of 2 atomic units. The fractional uncertainty of the purely relativistic contribution is $1\times10^{-17}$. The result is relevant for future precision experiments, whereas at present the uncertainties arising from the quantum electrodynamic treatment of the rovibrational transition frequencies. are dominant.
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