Convergent Close-Coupling Approach to Electron-Atom Collisions

It was with great pleasure and honour to accept the invitation to make a presentation at the symposium celebrating the life-long work of Aaron Temkin and Richard Drachman. The work of Aaron Temkin was particularly influential on our own during the development of the CCC method for electron-atom collisions. There are a number of key problems that need to be dealt with when developing a general computational approach to such collisions. Traditionally, the electron energy range was subdivided into the low, intermediate, and high energies. At the low energies only a finite number of channels are open and variational or close-coupling techniques could be used to obtain accurate results. At high energies an infinite number of discrete channels and the target continuum are open, but perturbative techniques are able to yield accurate results. However, at the intermediate energies perturbative techniques fail and computational approaches need to be found for treating the infinite number of open channels. In addition, there are also problems associated with the identical nature of electrons and the difficulty of implementing the boundary conditions for ionization processes. The beauty of the Temkin-Poet model of electron-hydrogen scattering is that it simplifies the full computational problem by neglecting any non-zero orbital angular momenta in the partial-wave expansion, without loosing the complexity associated with the above-mentioned problems. The unique nature of the problem allowed for accurate solution leading to benchmark results which could then be used to test the much more general approaches to electron-atom collision problems. The immense value of the Temkin-Poet model is readily summarised by the fact that the initial papers of Temkin and Poet have been collectively cited around 250 times to date and are still being cited in present times. Many of the citations came from our own work during the course of the development of the CCC method, which we now describe

Two-center convergent close-coupling calculations for positron-lithium collisions

We report on two-center convergent close-coupling calculations of positron-lithium collisions. The target is treated as one active electron interacting with an inert ion core. The positronium formation channels are taken into account explicitly utilizing both negative- and positive-energy Laguerre-based states. A large number of channels and high partial waves are used to ensure the convergence of the cross sections. We find the Ramsauer-Townsend minimum in total and elastic cross sections at an impact energy E of about 0.0016 eV. As found previously forH and He, the contributions to the breakup cross section from both the Li and the Ps centers become the same as the threshold is approached

Surface-integral formulation of scattering theory

We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surface integrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions

Antihydrogen Formation via Antiproton Scattering with Excited Positronium

Use of CCC method to calculate for the first time very accurate cross sections for Hbar formation in antiiproton-Ps collisions close to threshold for a numebr of excited Ps states. Discovery of novel 1/E behaviour for the cross ections near thresold for excited states

Coherent Excitation of the Singlet-triplet Mixed 1s4f State of Helium

In this paper, we present a detailed theoretical description for the coherent electron-impact excitation, the subsequent time evolution, and the cascading decay process of the singlet-triplet mixed 1s4f state of helium. The excitation amplitude and phase of each sublevel of this state are related to measurable coincidence intensities and polarizations of the emitted photons. It is found that the intensity and polarization of the emitted photons are time modulated due to the singlet and triplet mixing in the 1s4f state

On-shell approach to three-body scattering

146 leaves : ill. ; 30 cm.Thesis (Ph.D.) -- University of Adelaide, Dept. of Mathematical Physics, 197

Convergent Close-Coupling Approach to Electron-Atom Collisions

The convergent close-coupling (CCC) method was developed in order to resolve the long-standing discrepancy between two consistent experiments and all available theories for 2p excitation of atomic hydrogen [1] . The method was unable to resolve this discrepancy, but subsequent experiments [2,3] found much more in favor of theory than the previous experiments. There have been a number of reviews of the applications of the CCC theory with the most recent one being by Bray et al. [4] . The method has been extended to ionization [5], resulting in some controversy [6,7] that required further explanation [8,9]. Our own confidence in the ability of the CCC method to reproduce electron— hydrogen fully differential ionization cross sections was shaken by the less than satisfactory agreement with experiment [10] . However, this turned out to be primarily due to insufficient computational resources available at the time [11]. Consequently, we are now confident that the CCC method is able to solve the e—H, γ—He, and e—He (within the frozen-core model) collision systems at all energies with one or two outgoing electrons. We shall attempt to explain here the underlying foundations as clearly as possible. The example of the S-wave model will be used to demonstrate the method. A published program is available that shows the workings of the method discussed here [12] . We will finish by concentrating on the application of the method to fully differential ionization processes

The application of propagating exterior complex scaling to atomic collisions

© Cambridge University Press 2013.Introduction The accurate solution of the Schrödinger equation (SE) for electron-impact collisions leading to discrete elastic and inelastic scattering progressed rapidly with the increase in computing power from the 1970s. A review of the principal methods, including second Born, distorted wave, R-matrix, intermediate-energy R-matrix, pseudo-state close coupling and optical model is given in [1]. However, electron impact collisions leading to ionization on even the simplest atom, hydrogen, were by comparison poorly described; significant progress dates only from the early 1990s when Bray and Stelbovics [2] developed a technique called convergent close coupling (CCC). In this approach they used an in-principle complete set of functions to approximate the hydrogenic target states, both bound and continuous, and used the coupled channels formalism to expand the scattering wave function in these discretized states, reducing the solution of the SE to a set of coupled linear equations in a single co-ordinate. The method was tested in a non-trivial model [3] and shown to provide convergent cross sections not only for discrete elastic and inelastic processes but also for the total ionization cross section. Shortly thereafter the method was applied to the full collision problem from atomic hydrogen and one of the major achievements of the method was that it yielded essentially complete agreement with the (then) recent experiment for total ionization cross section [4]. In the following years, the method was applied to other atoms with considerable success; the range of applications of CCC are covered in the review of Bray et al. [5]