Abstract Collinear configurations of the helium-like atomic systems, relevant, e.g., for the quasifree mechanism of the double photoionization of helium, are studied, parameterized by the single scalar parameter − 1 ≤ λ ≤ 1 (“collinear parameter”) where λ = 0 corresponds to the electron-nucleus ( e − n ) coalescence and λ = 1 corresponds to the electron–electron ( e − e ) coalescence. In general, λ > 0 corresponds to the n-e-e configuration, and λ 0 to the e-n-e configuration. Simple mathematical representations of the expectation values of the Dirac delta function relevant for the collinear configurations are derived and calculated from fully three-body dynamics without approximation for the two-electron atomic wave functions with nuclear charge 1 ≤ Z ≤ 5 . Simple formulas for calculating the expectation values of the kinetic and potential energy operators in collinear configurations are derived. Unusual physical properties of the n-e-e collinear configurations found for certain ranges of λ are presented. The first few angular Fock coefficients for collinear configurations are derived as functions of λ . Highly accurate model wave functions describing the ground states of the two-electron atoms with a collinear arrangement of the particles are constructed. All results are illustrated in tables and figures.

中文翻译：

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氦原子和二电子离子的共线构型

摘要 研究了类氦原子系统的共线构型，例如与氦双重光电离的准自由机制相关，由单标量参数 - 1 ≤ λ ≤ 1（“共线参数”）参数化，其中 λ = 0 对应于电子-核 ( e - n ) 聚结，λ = 1 对应于电子-电子 ( e - e ) 聚结。通常，λ > 0 对应于 nee 构型，λ 0 对应于 ene 构型。与共线构型相关的狄拉克 delta 函数的期望值的简单数学表示是从完全三体动力学推导出和计算的，而不是对核电荷 1 ≤ Z ≤ 5 的双电子原子波函数进行近似。推导出了计算共线构型中动能和势能算符的期望值的简单公式。介绍了在某些 λ 范围内发现的 nee 共线配置的不寻常物理特性。共线配置的前几个角 Fock 系数是作为 λ 的函数导出的。构建了描述粒子共线排列的双电子原子基态的高精度模型波函数。所有结果都在表格和图中说明。构建了描述粒子共线排列的双电子原子基态的高精度模型波函数。所有结果都在表格和图中说明。构建了描述粒子共线排列的双电子原子基态的高精度模型波函数。所有结果都在表格和图中说明。