论文标题
使用有限元技术使用20位数字精度的两中心零方程的解
Solution of the two-center Dirac equation with 20 digits precision using the finite-element technique
论文作者
论文摘要
我们提出了两个中心库仑问题的精确相对论的数值解决方案。单位核电费的特殊情况与$ {\ rm H} _2^+$分子离子及其同位素的准确描述有关，该系统是一个主动实验主题。该计算采用了2-Spinor Minmax方法和有限元方法。计算出的总能量估计单位电荷的几次不确定性为$ 10^{ - 20} $，债券长度为2个原子单位。纯粹相对论贡献的分数不确定性为$ 1 \ times10^{ - 17} $。结果与将来的精度实验有关，而目前，rovbibrational转变频率的量子电动力处理引起的不确定性。是主导的。
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.
