论文标题
小原子和分子系统的变分与扰动相对论能量
Variational versus perturbative relativistic energies for small and light atomic and molecular systems
论文作者
论文摘要
计算出较低核电荷数的两电子原子和分子的分子和扰动相对论能量。通常，观察到两种方法的良好同意。剩余的偏差可以归因于高阶相对论，也称为非辐射量子电动力学（QED），对No-Piair Dirac $ - $ coulomb $ - $ -COULOMB $ - $ BREIT（DCB）方程式的扰动方法的校正自动包含在所有$ $ a $ fine-finder-finder-finder-finder-finder-ally-al-α$α$α$α上。 DCB能量的多项式$α$依赖性的分析使得可以在不正则化的情况下确定对非相对论能量的领先相对论校正至高精度。 Breit $ -Pauli Hamiltonian的贡献（预期值都会缓慢汇聚，这是由于奇异的术语而逐渐收敛的，该贡献被隐式包含在变化程序中。 NoPair DCB能量的$α$依赖性表明，高阶（$α^4 E_ \ Mathrm {H} $）非辐射QED校正的5％是前阶的5％（$α^3 E_ \ Mathrm {h} $ { （是$^{2+} $），这表明由变化程序提供的重新召集对于中间核电数已经很重要。
Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac$-$Coulomb$-$Breit (DCB) equation to all orders of the $α$ fine-structure constant. The analysis of the polynomial $α$ dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit$-$Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The $α$ dependence of the no-pair DCB energy shows that the higher-order ($α^4 E_\mathrm{h}$) non-radiative QED correction is 5 % of the leading-order ($α^3 E_\mathrm{h}$) non-radiative QED correction for $Z=2$ (He), but it is 40 % already for $Z=4$ (Be$^{2+}$), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.
