Effective-momenta approach for the four-body Coulomb problem

Abstract

We propose approximate separable solutions for the Schr\"odinger equation corresponding to the four-body Coulomb problem. By exploring several asymptotic limits, we find configurations where the nondiagonal terms of the Hamiltonian can be introduced in the two-body Coulomb-like distortion factors leading to modified momenta. The present effective momenta model is used to study the double ionization of He by ion impact at the fully differential level. Possible differences arising from proton and antiproton impact are explored at impact energies in the range 700 keV/amu--6 MeV/amu. The results are represented in terms of contour plots as a function of the electrons' emission angles, and the four-body dynamics for the double-ionization process is analyzed. Finally, we compare diverse representations for the fully differential cross section. A detailed interpretation of the features of the process is done by overlapping the recoil level lines over the contour plots. Ternary plots are tested as an alternative tool to explore the different physical mechanisms involved in the double emission process at the fully differential level.