电场中氢原子发散微扰级数的恢复
Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
摘要：
我们考虑描述类氢束缚态在电场中的能量位移的微扰级数的重增（称为Stark效应或LoSurdo-Stark效应），它在电场强度中构成发散的形式幂级数.扰动级数在Borel平面上表现出丰富的奇异性结构。恢复的方法，出现导致一致的结果，即使在有问题的情况下，孤立的奇点或分支切割存在于正，负的实轴上的Borel平面。比较了两种重新计算方法：（i）Borel-Pade重新计算方法的一种变体，由于使用了领先的Renormalon极点，因此有了额外的改进（关于Renormalon的全面讨论，见[M. Beneke，Phys.Rep.vol.317，p.1（1999）]），以及（ii）Borel方法与通过保角映射的解析延拓和保角变量中的Pade近似的轮廓改进组合。在复杂的Borel平面中的LoSurdo-Stark效应的情况下的奇异性结构被证明是类似于量子色动力学中的（发散）微扰展开。
英文摘要：
We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.
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