This work is on quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The five widely used distorted wave methods of the first- and second-order in the perturbation series expansions are compared with the available experimental data on $$\alpha $$ α –He collisions. These are the four-body boundary-corrected first Born (CB1-4B), the boundary-corrected continuum intermediate state (BCIS-4B), the Born distorted wave (BDW-4B), the continuum distorted wave (CDW-4B) and the continuum distorted wave-eikonal initial state (CDW-EIS-4B) methods. We address the complete breakdown of the CDW-EIS-4B method at all impact energies within its expected validity domain (100–10000 keV). Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wavefunctions for double continuum intermediate states. Finally, at all the considered intermediate and high energies, the practical aspects of the studied five methods are investigated by protracted evaluations of the convergence rates of total cross sections as a function of the number of quadrature points per axis in numerical computations of multi-dimensional (3D-5D) integrals.

中文翻译：

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用氦气中的 α 粒子捕获两电子的五种方法的总横截面：CDW-4B、BDW-4B、BCIS-4B、CDW-EIS-4B 和 CB1-4B

这项工作是关于量子力学四体扭曲波理论，用于在快速重多电荷离子和类氦原子系统之间的碰撞中捕获双电子。将扰动级数展开中的五种广泛使用的一阶和二阶扭曲波方法与 $$\alpha $$ α -He 碰撞的可用实验数据进行比较。它们是四体边界校正第一波恩 (CB1-4B)、边界校正连续介质中间态 (BCIS-4B)、玻恩畸变波 (BDW-4B)、连续谱畸变波 (CDW-4B) 和连续谱扭曲波-本征初始状态 (CDW-EIS-4B) 方法。我们解决了 CDW-EIS-4B 方法在其预期有效性域（100-10000 keV）内的所有冲击能量下的完全分解。更多，评估二阶理论的相对性能，有和没有双连续中间态的双电子库仑波函数的电化。最后，在所有考虑的中能和高能中，通过长期评估总横截面的收敛率作为多维数值计算中每轴正交点数的函数，研究了所研究的五种方法的实际方面。 (3D-5D) 积分。