用耦合团簇方法计算矩阵元时的“修饰”线和顶点及Cs原子性质的测定
"Dressing" lines and vertices in calculations of matrix elements with the coupled-cluster method and determination of Cs atomic properties
摘要：
我们考虑用耦合簇方法计算矩阵元素。这样的计算正式涉及无限数量的条款，我们设计了一种方法的部分总和（敷料）的结果系列。我们的形式主义是建立在一个扩展的产品$C^\dagger C$的集群振幅$C$到一个总和的$n$体插入。我们考虑两种类型的插入：粒子/空穴线插入和两个粒子/两个空穴随机相位近似插入。我们演示了如何“打扮”这些插入和制定迭代方程。我们说明敷料方程的情况下，当集群运营商被截断在单，双激发。以单价系统为例，我们升级耦合簇图的矩阵元素与着装插入，并突出相关的四阶图的关系。用相对论方法计算了Cs原子的超精细常数$A(6s)$和$6s_{1/2}-6p_{1/2}$电偶极跃迁振幅.最后，我们增加截断耦合集群计算，否则省略了四阶图。由此产生的分析Cs是通过四阶多体微扰理论完成的，并揭示了三重和断开的四重激发的重要作用。
英文摘要：
We consider evaluation of matrix elements with the coupled-cluster method. Such calculations formally involve infinite number of terms and we devise a method of partial summation (dressing) of the resulting series. Our formalism is built upon an expansion of the product $C^\dagger C$ of cluster amplitudes $C$ into a sum of $n$-body insertions. We consider two types of insertions: particle/hole line insertion and two-particle/two-hole random-phase-approximation-like insertion. We demonstrate how to ``dress'' these insertions and formulate iterative equations. We illustrate the dressing equations in the case when the cluster operator is truncated at single and double excitations. Using univalent systems as an example, we upgrade coupled-cluster diagrams for matrix elements with the dressed insertions and highlight a relation to pertinent fourth-order diagrams. We illustrate our formalism with relativistic calculations of hyperfine constant $A(6s)$ and $6s_{1/2}-6p_{1/2}$ electric-dipole transition amplitude for Cs atom. Finally, we augment the truncated coupled-cluster calculations with otherwise omitted fourth-order diagrams. The resulting analysis for Cs is complete through the fourth-order of many-body perturbation theory and reveals an important role of triple and disconnected quadruple excitations.
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