A Self-Consistent Model for Positronium Formation from Helium Atoms

Abstract

The differential and total cross sections for electron capture by positrons from helium atoms are calculated using a first-order distorted wave theory satisfying the Coulomb boundary conditions. In this formalism a parametric potential is used to describe the electron screening in a consistent and realistic manner. The present procedure is self consistent because (i) it satisfies the correct boundary conditions and post-prior symmetry, and (ii) the potential and the electron binding energies appearing in the transition amplitude are consistent with the wave functions describing the collision system. The results are compared with the other theories and with the available experimental measurements. At the considered range of collision energies, the results agree reasonably well with recent experiments and theories.

Comparative study of the three- and four-body boundary-corrected Born approximations for positronium formation

“…For the considered rearrangement collisions, the post and prior forms of the differential cross sections (DCS) are given by [24] σ…”

“…The integral forms of I 2 (ζ ) and I 3 (ζ ) are the same as that of I 1 (ζ ), except that 1/R T , in the expression for I 1 (ζ ), should be replaced by 1/r T and 1/r P , respectively. Following the method which has been explained in detail in [24] and [34], these six-dimensional integrals can be reduced to one-dimensional integrals as…”

“…Prior CB1-4B Prior CB1-3B CCO [20] DWA [21] CCC [22] DWB1B [24] Caradonna et al [11] Figure 8. Present TCS for positronium formation from helium atoms are compared with the CCO [20], DWA [21], CCC [22] and DWB1B [24] theories. Symbols are the same as in figure 7.…”

“…Subsequently, the majority of the theoretical studies that have investigated the positron-atom collisions have employed such three-body models. For example, the threebody versions of the distorted-wave approach [13], the firstorder target continuum distorted-wave theory [14] and the Coulomb-Born distorted-wave approximation (CBDW-3B) [24] have been applied to calculate the cross section for positronium formation in the collision of positron with various targets at moderate and high impact energies. However, sometimes it becomes important to consider inter-electron correlation effects which originate from pure Coulombic interactions between active electrons in multielectron collisional systems.…”

K-shell single-electron capture in collision of fast protons with multi-electron atoms

“…The second way to preserve the post-prior equivalence, is to adopt the parameterization by Green, Sellin, and Zachor which is useful to determine atomic CBDW-3B(post) CBDW-3B(prior) DSPB [7] CDW-3B [17] Exp. Data [16] p-C quantities with a good approximation and which has been successful in various collision calculations [34][35][36]. However, as is generally accepted and our results show, for the asymmetric three-body rearrangement collisions with Z T > Z P , the prior form of the amplitude would be preferred since the expansions in terms of the weaker perturbation U might be expected to converge more rapidly [37].…”