Convergent calculations of double ionization of helium: From(γ,2e)to(e,3e

Abstract

The first absolute ͑e ,3e͒ measurements, by Lahmam-Bennani et al. [Phys. Rev. A 59, 3548 (1999) When attempting calculations of complex collision processes we have found it important to utilize a formalism where convergence of the results can be tested by substantial variation of as many of the input parameters as possible. The goal is to develop a predictive theory whose outcomes can be relied upon on scientific merit irrespective of agreement with experiment or other theory. The convergent close-coupling (CCC) method [1] was developed with this idea in mind. The total wave function is expanded utilizing a complete Laguerre basis and so greater accuracy is ensured with increasing basis size. In the Coulomb three-body problems, such as e-H scattering, once convergence is reached there is no freedom left to alter the results. Hence, when there is disagreement with experiment as discussed in Ref. Whereas in e-H calculations convergence considerations relate primarily to the usage of the Laguerre basis, in ͑␥ ,2e͒ calculations there is additional consideration of convergence with respect to the description of the initial state. In the more complicated Coulomb four-body problem that is electronimpact double ionization of helium ͑e ,3e͒ there are further considerations of convergence with respect to the Born approximation order used to treat the case of a fast projectile. It is these issues that are of interest to us presently.The physics of the He ͑e ,3e͒ reaction in the very fast projectile mode where the incident electron has an order of magnitude or more energy than the two "slow" ejected electrons is quite similar to the case of ͑␥ ,2e͒. In both cases the initial and final atomic states are three-body problems of the He 2+ nucleus interacting with the two slow electrons. The application of the CCC method to ͑e ,3e͒ process under these kinematical conditions is straightforward and expected to produce results as accurate as those for ͑␥ ,2e͒. However, the first Born CCC result of ͑e ,3e͒ on He at 5.6 keV incident energy [8] was found significantly lower in magnitude (by factors of ϳ3 and ϳ12 for 10 and 4 eV ejected electrons, respectively) as compared with absolute measurements of Lahmam-Bennani et al. [9]. Such a strong disagreement could only be attributed to deviation from the first Born regime since the treatment of the initial and final states was the same in the CCC ͑␥ ,2e͒ and ͑e ,3e͒ calculations. Some indications of that followed from the work of Berakdar [10] who reported good agreement with the absolute measurements [9] on the basis of a lowest-order implementation of a Faddeev-type approach. These calculations differed significantly for electron or positron impact (by about a factor of 2), thus apparently invalidating the first Born approximation.This conclusion, however, was challenged by the recent work of Jones and Madison [11] who managed to get good agreement, both in shape and magnitude, with the experiment of within the first Born model.

Convergent close-coupling calculations of two-photon double ionization of helium

“…The reduced matrix elements entering Equation (8), in the length gauge, have been worked out in an earlier paper on the second Born treatment of the electron impact ionization-excitation and double ionization of He (Kheifets 2004).…”

“…As the result of this procedure, we end up with evaluation of the monopole and quadrupole matrix elements between the correlated ground state and the CCC final state. This procedure has been worked out in an earlier paper on the second Born treatment of the electron impact ionizationexcitation and double ionization of He (Kheifets 2004).…”

Strong suppression of positron-induced double ionization of helium at low-to-intermediate velocities

“…Schultz and Olson [13] used the classical trajectory Monte Carlo (CTMC) method to calculate the single-ionization cross section of positronhelium collision at intermediate velocities. The second-order Born model was proposed by Kheifets [14] to describe the simultaneous ionization excitation and double ionization of He impacted by positron at velocity of 12 a.u. Simonovic [15] used the classical Newtonian method to calculate the double-ionization cross section of positron-helium impact near the threshold.…”

Ground and excited states for exotic three-body atomic systems

“…All these trial wave functions have separate, and possibly complementary, purposes: obtain very accurate mean quantities (including the energy), search for a solution as formal as possible, or useful for applications such as collision studies. For the latter, it is useful to remind that the evaluation differential cross sections for processes such as double ionization by electron or photon impact [26][27][28][29][30][31][32] involve multi-dimensional numerical integrations; moreover, for calculations within the second Born approximation, a complete orthogonal set of wave functions is necessary. The use of bound wave functions with a very large number of terms (first group) can be prohibitive, even with modern computer facilities [26].…”