We review some recent results on recursion relations which help evaluating arbitrary non-diagonal, radial hydrogenic matrix elements of $r^λ$ and of $βr^λ$ ($β$ a Dirac matrix) derived in the context of Dirac relativistic quantum mechanics. Similar recursion relations were derived some years ago by Blanchard in the non relativistic limit. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schrödinger case. An extension of the relations to the case of two potentials in the so-called unshifted case, but using an arbitrary radial function instead of a power one, is also given. Several important results are obtained as special instances of our recurrence relations, such as a generalization to the relativistic case of the Pasternack-Sternheimer rule. Our results are useful in any atomic or molecular calculation which take into account relativistic corrections.
Triple excitations in perturbed relativistic coupled-cluster theory and Electric dipole polarizability of groupIIB elements
我们用微扰相对论耦合团簇（PRCC）理论计算了Zn、Cd和Hg的电偶极极化率$α$。计算是使用Dirac-Coulomb-Breit哈密顿量和Uehling势结合真空极化修正完成的。在PRCC理论中，三重激发是微扰的，而在未微扰区，三重激发是非微扰的。我们的结果$α$，所有三个元素，是在极好的协议与实验数据。结果的另一个亮点是Breit相互作用的轨道能量修正。在文献中，我们只能得到Hg {E。Lindroth等人，J. Phys. B 22，2447（1989）}，并且与我们的结果几乎完全匹配。我们还提出了团簇振幅的线性化方程，包括三重激发，角因子。
Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements and static polarizabilities for alkali-metal atoms
