类氦和类锂离子序列：临界电荷
Helium- and Lithium-like ionic sequences: Critical charges
摘要：
在非相对论量子力学中，我们研究了无限质量电荷中心Z和两三个电子的库仑系统：$(Z,e,e)$和$(Z,e,e,e)$。结果表明，在这两种情况下，在$Z$的总能量曲线是光滑的，没有任何可见的不规则性。因此，对于这两个系统，物理整数电荷$Z=1,2,...$并不像与电荷量化相关的那样发挥独特的作用。根据定义，临界电荷$Z_{cr}$是将束缚态的存在域与非束缚态的存在域（连续体）分开的电荷。对于这两个系统的临界电荷被发现，$Z_{cr,2e}=0.91085$和$Z_{cr,3e}=2.009$，分别。基于数值分析，构造了这两个系统的$(Z-Z_{cr})$的分数幂的Puixix展开式.我们的结果表明，存在一个平方根分支点奇点在$Z_{cr}$指数为3/2。本文简要地讨论了1/Z展开式的临界电荷与收敛半径之间的关系。
英文摘要：
In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without any visible irregularities. Thus, for both systems the physical integer charges $Z=1,2,...$ do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge $Z_{cr}$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, $Z_{cr,2e}=0.91085$ and $Z_{cr,3e}=2.009$, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of $(Z-Z_{cr})$ is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at $Z_{cr}$ with exponent 3/2. A connection between the critical charge and the radius of convergence of 1/Z-expansion is briefly discussed.
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