Asymptotic behavior of the Coulomb three-body scattered wave

Abstract

Asymptotic forms of the scattered wave for a system of three arbitrary charged particles valid in all domains relevant to breakup are derived. The derivations are based on the relationship between the total wave function of a breakup process in a three-body system with Coulomb interactions and the wave function of the process of scattering of all three particles of the system in the continuum. The results are free from amplitude-phase ambiguity problems associated with previously known forms. A similar technique is used to obtain asymptotic forms of the three-body Coulomb Green's function.

Theory of Electron Impact Ionization of Atoms

“…The ionization amplitude T is as defined according to Eq. (1) (see [16,17]) and therefore unambiguous. We emphasize that ⌽ c + , the continuum part of the asymptotic wave function, is valid in all asymptotic domains specified above.…”

“…We begin by noting that the full ambiguity-free asymptotic form of the total scattering wave function ⌽ + valid in all asymptotic domains as R → ϱ has been given recently [16,17]. In the present paper we ignore the threebody correlation effects.…”

“…In part because of this it has been impossible to define the ionization amplitude in a divergence-free manner. The full and unambiguous asymptotic forms of the three-body scattered wave function has been given recently [16,17]. This allowed us to obtain an integral representation for the ionization amplitude which is free of ambiguity and divergence problems [14].…”

“…This naturally requires knowledge of the partial waves of the asymptotic wave functions. The partial-wave expansion of the asymptotic wave function is developed for both the incident- [18,19] and scattered-wave [16,17] asymptotic forms of the three-body wave functions. Though we deal here with the e-H system, the formalism presented is general.…”

Various problems in electron-atom collision theory

“…Peterkop's [4] formulation suffers from the fact that the phase of the ionisation amplitude cannot be uniquely defined, yet a formal solution of the problem must yield a unique amplitude of a specified magnitude and phase. Accordingly these issues have been carefully reanalysed by Kadyrov et al [5] and Kadyrov et al [6]. Briefly, the correct boundary conditions for all kinematical arrangements leading to ionisation have been determined.…”