标题： 解决原子物理应用中所有阶数方法的收敛问题 显示英文标题

标题： Resolving all-order method convergence problems for atomic physics applications

摘要： 相对论全阶方法的发展，其中包含了狄拉克-哈特里-福克波函数的所有单重、双重和部分三重激发，并将其包括在微扰理论的所有阶数中，为研究基本对称性、原子钟的发展、超冷原子物理等提供了许多重要的结果，并且为大量单价系统的关键原子性质提供了经过严格评估的推荐值。 这种方法需要迭代求解线性化耦合簇方程，在某些情况下会导致收敛问题，特别是在相关修正特别大或导致振荡模式的情况下。 此外，这些问题也导致了在多粒子系统中的CI+全阶方法中出现类似的问题。 在这项工作中，我们通过应用两种不同的收敛稳定化方法——简化线性方程（RLE）和迭代子空间直接逆（DIIS），解决了大多数已知的收敛问题。 给出了B、Al、Zn$^+$和 Yb$^+$的例子。 解决这些收敛问题大大扩展了可以使用全阶方法处理的原子种类数量，并预计会促进许多有趣的未来应用。 显示英文摘要

摘要： The development of the relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function are included to all orders of perturbation theory led to many important results for study of fundamental symmetries, development of atomic clocks, ultracold atom physics, and others, as well as provided recommended values of many atomic properties critically evaluated for their accuracy for large number of monovalent systems. This approach requires iterative solutions of the linearized coupled-cluster equations leading to convergence issues in some cases where correlation corrections are particularly large or lead to an oscillating pattern. Moreover, these issues also lead to similar problems in the CI+all-order method for many-particle systems. In this work, we have resolved most of the known convergence problems by applying two different convergence stabilizer methods, reduced linear equation (RLE) and direct inversion of iterative subspace (DIIS). Examples are presented for B, Al, Zn$^+$, and Yb$^+$. Solving these convergence problems greatly expands the number of atomic species that can be treated with the all-order methods and is anticipated to facilitate many interesting future applications.