Contemporary spectroscopic studies of astrophysical and laboratory plasmas frequently deal with extremely large values of principle quantum numbers of atomic systems. These atomic states are very sensitive to electric and magnetic fields of the surrounding medium. While interpreting the spectra of such excited atomic systems, one faces the problem of a huge array of radiative transitions between highly excited atomic levels. Moreover, external electric and magnetic fields significantly complicate the problem because of the absence of standard selection rules typical for the spherical quantization. The analytical expression in the parabolic representation for dipole matrix elements obtained by Gordon contains hyper-geometric series and it has a very complex structure. The matrix elements that involve the presence of electric and magnetic fields are calculated while using a representation closely related to the parabolic quantization on two different axes. This matrix element depends in a complex way on the transition probabilities in the parabolic coordinate system (Gordon’s formulas) and the Wigner d-functions. This circumstance leads to even greater computational difficulties. A method of simplification of these complicated expressions for transition probabilities is demonstrated. The semiclassical approximation for coordinate matrix elements (Gulayev) and recurrence properties of the Wigner d-functions are used. The $H_{n\beta }$ line is under consideration. Specific calculations for the transition 10–8 in the case of parallel and perpendicular fields are presented.

中文翻译：

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里德堡原子在交叉电场和磁场中的光谱

天体物理学和实验室等离子体的当代光谱研究经常处理原子系统的基本量子数的极大值。这些原子态对周围介质的电场和磁场非常敏感。在解释这种激发原子系统的光谱时，人们面临着在高度激发原子能级之间存在大量辐射跃迁的问题。此外，由于缺少典型的球形量化标准选择规则，外部电场和磁场使问题变得更加复杂。由戈登获得的偶极矩阵元素的抛物线表示形式的解析表达式包含超几何级数，并且具有非常复杂的结构。在使用与两个不同轴上的抛物线量化密切相关的表示形式的同时，计算涉及电场和磁场存在的矩阵元素。该矩阵元素以复杂的方式取决于抛物线坐标系中的跃迁概率（戈登公式）和维格纳d函数。这种情况导致更大的计算困难。说明了简化这些复杂表达式的转移概率的方法。使用Wigner d函数的坐标矩阵元素（Gulayev）和递归属性的半经典近似。的 该矩阵元素以复杂的方式取决于抛物线坐标系中的跃迁概率（戈登公式）和维格纳d函数。这种情况导致更大的计算困难。说明了简化这些复杂表达式的转移概率的方法。使用Wigner d函数的坐标矩阵元素（Gulayev）和递归属性的半经典近似。的 该矩阵元素以复杂的方式取决于抛物线坐标系中的跃迁概率（戈登公式）和维格纳d函数。这种情况导致更大的计算困难。说明了简化这些复杂表达式的转移概率的方法。使用Wigner d函数的坐标矩阵元素（Gulayev）和递归属性的半经典近似。的$H_{ñ\beta }$线正在考虑中。给出了在平行场和垂直场情况下对10-8跃迁的具体计算。