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

Dževad Belkić

doi:10.1007/s10910-020-01123-4

Abstract

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 –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.

Highlights

Over the years, an emphasis has been given to the electronic eikonal initial states (EIS)
We address the complete breakdown of the continuum distorted wave (CDW)-EIS-4B method at all impact energies within its expected validity domain (100–10000 keV)
For the special case with symmetric encounters, only a single numerical integration ought to be performed in QCB1−4B. Even for this particular case, the cross sections QCB1−4B have been generated by using the general program with any nuclear charges involving three-dimensional quadratures. This is done to bring closer the numerical effort invested in obtaining QCB1−4B to the more involved computations for QCDW−4B, QCDW−EIS−4B, QBCIS−4B and QBDW−4B

Summary

Introduction

An emphasis has been given to the electronic eikonal initial states (EIS). This heavy particle eikonalization should be contrasted to the CDW-EIS method where the electronic eikonalization is applicable only to asymptotically large electron-nucleus separation Such a theoretical argument suffices to anticipate that the hybrid second-order methods based upon the eikonalized Coulomb wavefunctions for the relative motion of heavy nuclei should exhibit a reasonably successful performance for one- and double-electron capture. These are the boundary-corrected continuum intermediate state (BCIS) [8, 41] and the Born distorted wave (BDW) [49, 50] methods.

Theory

If further Ei

Illustrations

Method

MeV: Q

Discussion and conclusion