Effective-momenta approach for the four-body Coulomb problem

Double ionization of helium by proton impact: A generalized-Sturmian approach

“…They also showed that the target bound-state description affects the FDCS palpably. The same authors further tackled the problem with an approach involving effective momenta [4]. In this second study, the obtained cross sections present structures that vary slowly with the ejection angles, a trend, to some degree, analogous to that observed for electron impact [16,18,27].…”

“…In this contribution we focus on proton-impact ionization of helium within the high-incident-energy regime for which the capture process can be disregarded. The most basic mechanisms which produce DI, called shake-off (SO), two-step-1 (TS1) and two-step-2 (TS2) [2], were studied with approximate descriptions of both the helium ground state and the double continuum [3,4]. The TS1 process implies a collision between the projectile and one of the target electrons, which subsequently impacts the other one, and both end up being ejected to the continuum.…”

“…The majority of previous works, both theoretical and experimental, discussed integrated cross sections [5][6][7][8][9][10]. To a lesser extent, fully differential cross sections (FDCS), which provide the most detailed information of the doubleionization process, have also been investigated experimentally and theoretically [3,4,11,12]. For the case of electron impact several FDCS measurements under different emission energies and momentum transfer regimes have been carried out by the Orsay and Heidelberg groups (restricted to fast projectiles; see Refs.…”

“…Here, we apply it to study the fast proton-helium double-ionization process: in chosen kinematical conditions we provide, within the FBA, benchmark FDCS with three goals in mind. First, we want to compare our FDCS with those presented in the recent theoretical investigations based on perturbative methods using approximate analytical three-body wave functions [4,12]. Second, we wish to identify the collisional processes and contrast them with those of the better-known electron-impact counterpart.…”

“…Section III, dedicated to the results, is divided in three subsections. The first one is devoted to a comparison of the GSF results with those obtained with the effective charges and effective momenta approaches [4,12]. Section III B contains the studies performed in the lowemission regimes (6 eV excess energy): we make a comparison with a preexisting result [4] in equal energy sharing; we then increase the momentum transfer to observe more prominent nondipolar effects.…”