J. Rasch

Gauge discrepancies in calculations of on helium

We have studied the dependency and sensitivity of the triple differential cross section (TDCS) for on He with respect to the gauge formulation that one employs to represent the TDCS. This analysis has been performed using a variety of analytic initial- and final-state wavefunctions. It was found that the TDCS is very sensitive to the representation of the final-state wavefunction in all geometries and all formulations of the TDCS. When the detected electrons are of unequal energy the TDCS is also sensitive to the initial-state wavefunction. The predictions using all combinations of initial- and final-channel wavefunctions are gauge dependent and vary enormously in absolute size.

Triple differential cross sections for the electron-impact ionization of argon and neon

Cross sections have been measured for the electron-impact ionization of argon and neon in a coplanar symmetric geometry. Results are presented for impact energies of 115.8, 85.8 and 50 eV for argon and 50 eV for neon. A comparison is made with distorted-wave Born approximation calculations which include initial channel polarization and final channel post-collisional interactions. The lowest-energy argon data appear to indicate that polarization effects are very significant, and, in order to explore this, additional measurements have been performed in the coplanar constant geometry.

First and second Born calculations of (e, 2e) excitation-ionization of helium

We report detailed calculations of the first Born triple-differential cross section for (e, 2e) excitation-ionization of ground state He to He+ (n = 2). These are in accord with the very recent work of Kheifets et al (1999 J. Phys. B: At. Mol. Opt. Phys. 32 L433) and confirm that the first Born amplitude is now known very accurately. We illustrate the sensitivity of the first Born cross section to the choice of initial and final state wavefunctions. We combine our accurate first Born amplitude with an estimate of the second Born term evaluated in the closure approximation. As in previous work (Marchalant et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 1141) we find that second-order effects are significant even up to energies as high as 5.5 keV. Agreement with experiment generally remains not very satisfactory.

On the use of analytic ansatz three–body wave functions in the study of (e, 2e) band related processes

We present a critical analysis of the analytic ansatz wave functions that have been proposed for use in the calculation of triple–differential cross–sections for the electron–impact ionization of atoms. We will first discuss, in detail, the mathematical background to these approximations, and we will give, for the first time, cross–sections for the electron–impact ionization of hydrogen using the most elaborate of these. We will show that they give generally unsatisfactory agreement with experiment. We will argue that this failure comes from an inability to model the crucial region where the three particles are close together. The analysis presented should be of value not only in the case of electron–impact ionization but also for a wide range of Coulombic three–body problems in atomic physics.

On the numerical evaluation of a class of integrals occurring in scattering problems

Abstract We consider integrals of the form ∫ R ∞ Xl ∫ ( k ∫ r ) Xl ∫ ( k ∫ r ) r − gl +1 dr , where Xl ∫ ( k ∫ r ) and Xl ∫ ( k ∫ r ) are Bessel or Coulomb wave functions. Integrals of this type occur in very many scattering calculations and it is frequently the case that a large number need to be evaluated to high accuracy and with great efficiency. In this paper we present a systematic study of the method available for this evaluation and show how they may be effectively dealt with.

Spin dependence of (e, 2e) collisions on lithium at 54.4 eV

We present results of experimental measurements and theoretical calculations for the spin asymmetry, ), of the triple differential cross section. Spin-polarized lithium atoms were ionized by spin-polarized electrons of 54.4 eV incident energy. The geometry was coplanar with one detector at a fixed angle ( or ). Three data sets were obtained for ratios of shared energy = 8.8, 2.4, and 1. For the most asymmetric set the convergent close-coupling method gives best agreement, whereas for the symmetric set the distorted-wave Born approximation seems to be in better agreement.

processes with positive-ion targets in coplanar symmetric geometry

We present results for the electron impact ionization of a sequence of hydrogenic ions and the first five ions in the He isoelectronic sequence. These are obtained in coplanar symmetric geometry for a wide range of energies, from near threshold into the intermediate range. We have concentrated the analysis on the role of the ion in the incident and final channel. All calculations are performed in a distorted-wave Born approximation (DWBA) which allows for elastic scattering in both the incident and final channels. The role of repulsion between the final state electrons is discussed in a simple model. Comparisons are also shown with DWBA calculations that include a polarization potential, and with a Coulomb-Born approximation.

An Explanation of the Structure Observed in Out-Of-Plane Symmetric Measurements on Helium

The study of (e,2e) processes on Helium at impact energies of 100eV and below has yielded a wealth of experimental data and has contributed greatly to the understanding of the Coulomb few body problem. The great advantage of coincidence measurements is that one can manipulate the geometry of the experiment to study delicate processes which yield striking structures in a particular arrangement, but are largely masked by stronger effects in virtually all other setups. Quite recently Murray1 identified a very strong structure in the ionization of Helium at an impact energy of 64.6eV in a very specific out of plane geometry. In this paper we will show that this structure is well represented in a Distorted Wave Born Approximation (DWBA) calculation and we will interpret it as an interference, that is to say a pure quantum, effect. We predict that similar structures will be present in the Triple Differential Cross Section (TDCS) for some targets but not for others.

The Normalisation of the Experimental Triple Differential Cross Section of Noble Gas Atoms in Extreme Asymmetric Geometry

Electron-electron coincidence experiments, usually known as (e,2e) experiments, are the most powerful tool to study the process of the electron impact ionizationl,2. Despite the extended activity in the field in the last years, the understanding of the process for targets heavier than H and He still presents many serious challenges for both, theoreticians and experimentalists alike. As far as the experiments are concerned, the challenge consists in (a) providing a large body of experimental data to explore the various zones of the Bethe surface3, (b) determining the absolute scale of the triple differential cross-section (TDCS).

On the numerical evaluation of six dimensional integrals occurring in scattering problems

We consider integrals of the from ∫ d3r0 tf(r0) ∫ d3ri V(r0, ri)g(ri), where tf(r0) and g(ri) are complex functions. Such integrals occur frequently in scattering theory problems where typically V(r0, ri) is the Coulomb potential xt/vbr0−rivb and g contains an exponentially decaying function. tf(r0) usually contains oscillatory functions and may or may not contain an exponentially decreasing one. In the former case standard techniques such as Monte Carlo integration can be used with reasonable accuracy, however, in the latter these methods fail due to the extremely large integration region required for the outer integral. We propose a numerical 6 Dimensional Integration Method (6DIME) which can be used for either situations. In the exponentially damped case it provides faster and more accurate results. However, this methods tackles for the very first time the far more difficult problem of the undamped case. The accuracy of this approach is tested against analytically solvable integrals that occur in scattering problems.