Andris T. Stelbovics

Non-coplanar symmetric (e, 2e) momentum profile measurements for helium: an accurate test of helium wavefunctions

The 1200 eV non-coplanar symmetric (e, 2e) cross sections for helium leading to the n=1, 2 and 3 ion states were measured with a modified coincidence spectrometer using position-sensitive microchannel plate detectors. The ground-state momentum profiles (cross sections) are compared with the momentum distribution given by the Hartree-Fock wavefunction, the accurate correlated wavefunction of Joachain and Vanderpoorten (1970), and the momentum distribution derived from accurate Compton profile measurements by Lee (1977). Good agreement is obtained between theory and the (e, 2e) measurements, but the Compton momentum distribution is seriously in error at low momentum. The small discrepancy at high momenta between the present measurements and the plane-wave impulse approximation is completely explained by allowing for distortion of the continuum electron waves by the helium and ion potentials. The n=2 and 3 cross sections cannot be explained using the helium HF wavefunctions, but are well described by the accurate correlated JV wavefunction. The measured n=2 to n=1 cross section ratio discriminates between several accurate correlated helium ground-state wavefunctions.

An Auger photoelectron coincidence spectrometer

The feasibility of photoelectron Auger electron coincidence spectroscopy from solid surfaces has been demonstrated by Haak et al. [Ph. D. thesis, University of Groningen, The Netherlands, 1983; Phys. Rev. Lett. 41, 1825 (1978); Rev. Sci. Instrum. 55, 696 (1984)]. They were able to show the considerable power of the technique in deconvoluting the L23M45M45 line of Cu by finding those parts of the line that were due to a 2p3/2 hole and those which were due to a 2p1/2 hole. However, the technique is a difficult one, requiring two analyzers rather than one and complex coincidence electronics. Even then a single spectrum can take weeks to acquire. This initial work was followed up by Jensen et al. [Phys. Rev. Lett. 62, 71 (1989); Physical Electronics Conference abstract A‐5, July, 1988] using a synchrotron to provide the radiation and a means of getting very good timing resolution. They were able to acquire Cu spectra in 2–3 days using this system. We have constructed a set of electron analyzers specifically for this experiment. We used the ideas of Volkel and Sandner [J. Phys. E 16, 456 (1983)] to produce analyzers that have good angular acceptance, good energy resolution, and very good timing resolution. With this system we are able to measure coincidence line shapes, for elements with large enough cross section, within a few days using a standard laboratory dc x‐ray source.

Calculation of electron scattering on the He+ ion

We apply the convergent close-coupling method to the calculation of electron scattering on the ground state of He+ It is shown that the inclusion of the treatment of the continuum, even below the ionization threshold, significantly reduces the calculated 2S cross section. We generally find good agreement with the measurements of the 2S excitation cross section, though in the vicinity of a few eV near threshold our results are characteristically higher than the experiment Complete quantitative agreement is obtained with the measurement of the total ionization cross section from threshold to 700 eV.

Multiconfigurational two-centre convergent close-coupling approach to positron scattering on helium

The convergent close-coupling method with two-centre expansions has been developed to calculate positron scattering on helium. The method utilizes a multiconfigurational description of helium wavefunctions. Positronium formation is taken into account explicitly as electron capture into the positronium states. Direct-scattering, positronium-formation and breakup cross sections are calculated at all energies of practical relevance. Convergence in the calculated cross sections is demonstrated by increasing the basis size and orbital quantum number of the included states for each of the centres. Better agreement with experimental data is found when a multiconfigurational description is used for the helium wavefunctions in comparison with the recent frozen-core results.

Electron scattering from sodium at intermediate energies

A comprehensive comparison is made between theoretical calculations and experimental data for intermediate energy (>or=10 eV) electron scattering from sodium vapour. The theoretical predictions of coupled-channels calculations (including one, two or four channels) do not agree with experimental values of the differential cross sections for elastic scattering or the resonant 3s to 3p excitation. Increasingly more sophisticated calculations, incorporating electron correlations in the target states, and also including core-excited states in the close-coupling expansion, are done at a few selected energies in an attempt to isolate the cause of the discrepancies between theory and experiment. It is found that these more sophisticated calculations give essentially the same results as the two- and four-channel calculations using Hartree-Fock wavefunctions.

Coupled-channel integral-equation approach to antiproton–hydrogen collisions

A fully quantal integral-equation approach to ion–atom collisions is developed along the lines of the convergent close-coupling approach to electron–atom scattering. The approach starts from the exact three-body Schrodinger equation for the scattering wavefunction and leads to coupled-channel Lippmann–Schwinger equations for the transition amplitudes in the impact-parameter representation, with the relative motion of the heavy particles treated quantum mechanically. The method is applied to calculate antiproton collisions with atomic hydrogen. Integrated total, excitation and ionization cross sections are calculated in the energy range from 1 keV to 1 MeV.

Direct solution of the three-dimensional Lippmann–Schwinger equation

A standard technique for solving three-dimensional momentum-space integral equations in scattering theory is their transformation into one-dimensional equations in terms of partial waves. However, for some scattering systems where a large number of partial waves contribute this technique is not efficient. In this work we explore the alternative approach of solving these equations directly without partial-wave expansion. For illustrative purposes we adopt the coupled-channel approach and consider a well-studied static-exchange model of electron-hydrogen scattering.

Low-energy positron–helium convergent close coupling calculations

The convergent close coupling method has been applied to positron?helium scattering for energies below the positronium formation threshold (17.8?eV). Convergence is studied as a function of the Laguerre basis size. Rapid convergence to the accurate phase shifts given by Van Reeth and Humberston (1999 J.?Phys.?B:?At.?Mol.?Opt.?Phys.?32 3651?67) is demonstrated. The resultant cross sections are in excellent agreement with the experimental data of Stein et al (1978 Phys.?Rev.?A?17?1600?8) and Mizogawa et al (1985 Phys.?Rev.?A 31 2171?9).

Iteratively-coupled propagating exterior complex scaling method for electron–hydrogen collisions

A newly-derived iterative coupling procedure for the propagating exterior complex scaling (PECS) method is used to efficiently calculate the electron-impact wavefunctions for atomic hydrogen. An overview of this method is given along with methods for extracting scattering cross sections. Differential scattering cross sections at 30 eV are presented for the electron-impact excitation to the n = 1, 2, 3 and 4 final states, for both PECS and convergent close coupling (CCC), which are in excellent agreement with each other and with experiment. PECS results are presented at 27.2 eV and 30 eV for symmetric and asymmetric energy-sharing triple differential cross sections, which are in excellent agreement with CCC and exterior complex scaling calculations, and with experimental data. At these intermediate energies, the efficiency of the PECS method with iterative coupling has allowed highly accurate partial-wave solutions of the full Schrodinger equation, for L ≤ 50 and a large number of coupled angular momentum states, to be obtained with minimal computing resources.

The convergent close-coupling method for a Coulomb three-body problem

The close-coupling method relies on the reformulation of the Schrodinger equation into an infinite set of coupled-channel equations by expanding over the complete set of target states. The difficulty in applying this approach is that the continuum channels are known to be very important in the intermediate-energy region and coupling to them must be included with little approximation. We discuss the application of the convergent close-coupling (CCC) method which allows the continuum to be treated in a systematic manner via the use of square-integrable states. The CCC method utilizes an expansion of the target in a complete set of orthogonal L2 functions which form a basis for the underlying Hilbert space. The utility of the method relies on being able to demonstrate convergence in the scattering amplitudes of interest as the basis size is increased.