C. Dal Cappello

The second Born approximation for the single and double ionization of atoms by electrons and positrons

Recently, Lahmam-Bennani et al (2010 J. Phys. B: At. Mol. Opt. Phys. 43 105201) have shown that the second Born approximation is necessary to describe the experimental results of the double ionization of atoms and molecules. The second Born approximation needs a difficult triple numerical integration and often many authors find some controversial results. We now investigate, in greater detail, the application of the second Born approximation for the easier case: the ionization of atomic hydrogen by electrons. The ionization of atomic hydrogen allows us to check accurately this approximation because the wavefunctions describing the target are known exactly. Moreover, sophisticated models such as convergent close coupling (CCC) and the continuum distorted wave eikonal initial state (CDW-EIS) exist and give closer results leading to easier comparisons. We report accurate second Born results for differential cross sections for the ionization of atomic hydrogen using a basis including 100 discrete states, and another basis including 32 discrete states and pseudo-states. The results of the present method are compared with other calculations and experiment. The single ionization of helium is also investigated in order to answer an old controversy between two different theoretical results. Finally, an application of the second Born approximation to the double ionization of helium has been performed.

Triple differential cross sections for molecular hydrogen, both under Bethe ridge conditions and in the dipolar regime. Experiments and theory

High-accuracy absolute triple differential cross sections for ionisation of molecular hydrogen by approximately 4 keV electron impact have been measured in a coplanar asymmetric arrangement. Ejected electron energies were Eb=20 and 100 eV, and momentum transfer values ranged from K=0.1 au (dipolar region) up to approximately 4 au (impulsive region). They are compared with calculations performed within the framework of the first Born approximation and the impulse approximation. A perturbation treatment developed up to second order where the distortion of the ejected electron trajectory is taken into account is in reasonable agreement with the experiments only under impulsive conditions (large K and Eb values), due to the slow convergence of the series development. The factorised first Born approximation where the ejected electron is described by an orthogonalised Coulomb wave is in general good agreement with the experiments. For this model, the length form is found to be better than the velocity form.

Dynamics of electron impact ionization of the outer and inner valence (1t2 and 2a1) molecular orbitals of CH4 at intermediate and large ion recoil momentum

The triply differential cross section has been measured for electron-impact ionization of the outer valence 1t2 and the inner valence 2a1 orbitals of methane using the (e,2e) technique with coplanar asymmetric kinematics. The measurements are performed at scattered electron energy of 500 eV, ejected electron energy of 12, 37 and 74 eV and for scattering angle of the fast outgoing electron of 6?. This kinematics is characterized by a target ion recoil momentum ranging from moderate (0.25 au) to very large (3.2 au) values. The results are compared with theoretical cross sections calculated using the 1CW and the BBK models recently extended to molecules. The experimental cross sections exhibit a very large recoil scattering, especially for the inner 2a1 molecular orbital, which is not predicted by the theory. The differences between experiment and theory are attributed to the very strong scattering from the ion, not properly accounted for by theory. This indicates the need for further theoretical developments as well as experimental investigations in order to correctly model the process of molecular ionization.

The electron-impact double ionization of atoms: an insight into the four-body Coulomb scattering dynamics

Abstract Over the past two decades impressive progress has been made in the theoretical and the experimental study of the multiple excitation and of the complete fragmentation of four-body Coulomb systems. The double ionization of atoms by charged particle impact is employed routinely to prepare and to explore the Coulomb four-body excited states (the two ionized electrons and the scattered charged projectile moving in the field of the residual ion). The spectrum of this four-body system can be determined experimentally by resolving simultaneously the momentum vectors of all particles. Such a multi-coincidence measurement entails however low counting rates which makes the experimental realization a challenging task. This work gives a brief overview on recent achievements in multi-detection techniques and outlines the various methods to carry out the double ionization experiments induced by electron impact. The advantages and the limits of the various experimental approaches are pointed out. On the theoretical side, serious difficulties are encountered which are prototypical for the theoretical treatment of many-body correlated systems: (A) With increasing number of interacting particles (and hence of degrees of freedom) a direct numerical evaluation of the four-body Greens function, which encompasses the entire spectrum of the system, becomes a challenge. (B) Due to the non-integrable character of interacting many particle systems, an analytical approach can only be approximate. In this report we discuss in details the various methods that have been put forward to deal with the four-body problem, including: perturbative many-body treatments (first and second order theories) and non-perturbative methods as well as pure numerical approaches. Due to the complicated structure of the four-particle continuum spectrum we present and discuss simple qualitative arguments to explain the main features (peaks and dips) that are observed in the experiments. The limitations of these simple methods are illustrated by contrasting the predictions with full numerical calculations and with experimental data. Future directions and possible applications are also discussed.

Double ionization of helium by fast electrons: use of correlated two electron wavefunctions

The mechanism for the simultaneous escape of two equivalent electrons from a noble gas atom is strongly related to interelectronic correlation. It is therefore necessary to use correlated wavefunctions to describe the system in its initial and final states. As a first step towards the study of other noble gases, the double ionization of the helium atom by fast electrons is studied in a first Born approximation approach by applying Hylleraas-type functions for the initial state and a correlated double-continuum wavefunction which satisfies the exact asymptotic boundary conditions for the final state of the two slow electrons.

Angular distributions in the double ionization of the noble gases by electron impact.

Electron-impact double ionization of noble gases is investigated theoretically for the case of high incident energies (5 keV). An ab initio calculation is made including partial correlation in the initial state as well as in the final state. The results of the calculations are compared with those of other theories and with the first available (e, 3e) experimental data on krypton 4p6.

Ab initio calculation of differential and total cross sections for the ionization of water vapor by protons

We present both differential and total cross sections for the direct ionization of water vapor by protons in the incident energy range 0.1-100 MeV. Different theoretical models are investigated within the framework of the Born approximation in order to evaluate the influence of each pairwise Coulomb interaction term among the ejected electron, the scattered proton, and the residual ionized target in the final state. In all these models, the ground state of the water molecule is described by means of an accurate molecular wave function proposed by Moccia [J. Chem. Phys. 40, 2186 (1964)]. The results of these full ab initio quantum-mechanical treatments are compared to experimental data. Good agreement is generally observed, showing that sophisticated Born models are sufficient to explain all the experimental data, including doubly differential, singly differential, and total cross sections.

Coincidence electron impact ionisation of helium: absolute experimental cross sections and comparison with first-order theories

Absolute triple differential cross sections (TDCS) for the ionisation of helium by 8 keV electron impact are measured in an asymmetric coplanar electron-electron coincidence experiment (e, 2e method). The angular distributions are made absolute by assuming a cylindrical symmetry about the momentum transfer direction, K, then integrating over all ejection angles and comparing with the corresponding double differential cross section. The latter is independently measured on an absolute scale in a separate experiment. The overall accuracy of the absolute TDCS is about 12%. Systematics in the behaviour of the binary and the recoil intensities as a function of scattering angle and ejection energy are shown. At small K values, the data are discussed in detail in relation to the optical limit (K to 0), and a new qualitative explanation is given for the shift of the recoil lobe axis from the -K direction.

Investigation of the (e, 2e) single ionization of He and Ar at large energy loss close to minimum momentum transfer

We report new coplanar (e, 2e) measurements for ionization of He and Ar under kinematics characterized by large energy transfer and close to minimum momentum transfer from the projectile to the target. These kinematics have remained rather unexplored to date due to the smallness of the corresponding cross sections. They could be investigated here thanks to the high sensitivity of our multi-collection spectrometer. The experimental results are used as a sensitive test of state-of-the-art available theoretical models for multi-electron atoms, namely the BBK and a hybrid DWBA+R-matrix (close coupling) models. An overall satisfactory agreement with experiment is obtained for the hybrid DWBA results for both targets. However, a close inspection of the remaining discrepancies calls for further refinement of the theory.

High-energy electron-impact spectroscopy: (e, 2e) models for absolute triple differential cross sections of neon

Various models based upon the binary encounter first Born approximation have been developed to test absolute (e, 2e) experimental cross sections of the neon atom. All models are shown to possess the same qualitative behaviour but vary widely in their order of magnitude. Except for the description of the recoil peak, the Coulomb-wave formalism with an adjustable screening parameter is found to give a satisfactory approach for the quantitative description of such experiments.