Total cross sections in five methods for two-electron capture by alpha particles from helium: CDW-4B, BDW-4B, BCIS-4B, CDW-EIS-4B and CB1-4B (Q2184361)

The article under reviewing refer to a very laborious from the technical point of view scattering theory of many body systems, namely four body distorted wave for double electron capture in colissions between fast heavy multiply charged ions and helium like atomic systems. The author presents calculations made by 5 various distorted waves methods of the first and second order in the perturbation series expansion, which are subsequently compared with available experimental data on α-He collisions. The 5 methods are described in detail in the body of the article, but principially represents combinations of the first order Born distortted wave or the continuum distorted wave, the continuum -eikonal initial state methods. The relative performance of the second-order theories is evaluated with and without the eikonalization of the 2-electron Coulomb wavefunctions for double continuum intermediate states. Finally, the author is evaluating the convergence rate of the total cross sections as a function of the number of quadrature points per axis in numerical computations of multidimensional (3-5 dimensions) integrals.