解决原子物理学应用中的全阶方法收敛问题
Resolving all-order method convergence problems for atomic physics applications
摘要：
相对论全阶方法的发展，其中所有的单，双，和部分三重激发的狄拉克-哈特里-福克波函数包括所有订单的微扰理论导致许多重要的结果，研究基本对称性，发展原子钟，超冷原子物理，和其他，以及提供了许多原子性质的推荐值，对它们的准确性进行了严格的评价，用于大量的单价系统。这种方法需要线性化耦合簇方程的迭代解，从而在某些情况下导致收敛问题，其中相关校正特别大或导致振荡模式。此外，这些问题也导致了CI+全阶方法在多粒子系统中的类似问题。在这项工作中，我们已经解决了大多数已知的收敛问题，通过应用两种不同的收敛稳定器方法，减少线性方程（RLE）和直接反演的迭代子空间（DIIS）。给出了B、Al、Zn $^+$和Yb $^+$的实例。解决这些收敛问题，大大扩展了原子物种的数量，可以与全阶方法处理，预计将促进许多有趣的未来应用。
英文摘要：
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.
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