A. Duguet

A comparative experimental and theoretical investigation of the electron-impact double ionization of He in the keV regime

We determine, both experimentally and theoretically, the fully resolved fivefold differential cross section (5DCS) of double ionization of helium by 5.6 keV electron impact. Symmetric energy sharing between the two ejected electrons is investigated at the excess energy of 8 and 20 eV with 0.22 and 0.24 au momentum transfer, respectively. Absolute 5DCS are determined by normalizing the experimental data to the well established single-ionization cross sections. The calculation is performed by using the convergent close-coupling method for the interaction between the two slow ejected electrons, together with the first Born approximation for the interaction of the fast incident electron with the atom. Experimental and theoretical 5DCS tend to agree in shape but disagree in magnitude by factors of three and 14 for the 20 and 8 eV excess energies, respectively. The small momentum transfer invites absolute comparison of the present electron-impact double-ionization results with the corresponding double-photoionization experiment and theory. Theoretically, the momentum transfer is sufficiently close to zero to show the scaling between the two scattering processes. This smallness of the momentum transfer also makes the calculated 5DCS nearly invariant with respect to simultaneous inversion of the momenta of the two ejected electrons.

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.

Bethe surface and Compton profile of NH3 obtained by 35 keV electron impact

Complete inelastic electron impact spectra have been obtained for NH3 for a momentum transfer range from 0.4 to 12.5 a.u. using 35 keV electrons. These spectra were converted to relative generalized oscillator strengths (GOS), were placed onto an absolute scale by the Bethe sum rule, and higher order sum rules were used to test the accuracy of the GOS. The Compton profile (CP) of NH3 was determined from the GOS by means of the impulse approximation (IA) and it was found that the CP’s were asymmetric and shifted in respect to the free electron theoretical CP. This Compton defect was analyzed in detail and was shown to be due to the failure of the IA. The area under the CP is discussed in terms of the x‐ray incoherent scattering factor and experimental results for the valence, inner shell, and total CP’s are compared to several theoretical profiles.

(e,2e) triple differential cross sections for the simultaneous ionization and excitation of helium

The authors present absolute triple differential cross sections (TDCS) measurements for ionization of helium leaving the ion in both n=1 and n=2 final states, obtained under asymmetric geometry at an incident energy approximately 5.5 keV and ejected electron energies of 5, 10 and 75 eV. The kinematics are chosen to correspond either to a constant ejection energy, or to a constant energy transfer to the target. Angular distributions are measured at both constant ejection angle ( theta a mode) and at constant scattering angle ( theta b mode). In the theta a mode experiments, the momentum transfer dependence of the n=2 triple differential generalized oscillator strength is investigated for the first time. In both modes, the n=2 angular distributions show several new features which are not present for the n=1 ones, and which tend to vanish as the ejected energy is increased. They are attributed to final state interactions between the ejected electron and the excited ion. Comparison with first-order theoretical models shows the inadequacy of a Coulomb wave representation of the ejected electron, while in the R-matrix formalism it is found that a five-state multichannel calculation qualitatively describes the shape (but not the amplitude) of the TDCS measured in the theta b mode. Comparison is also made with the photoionization in the dipolar limit where the momentum transfer approaches zero. When integrated over the ejection direction, the double differential generalized oscillator strength ratio for ionization to the n=1 and n=2 states is found to agree with an earlier first Born close coupling prediction.

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.

High‐energy electron impact spectrometer for absolute triple differential cross sections

A new high‐energy spectrometer for the coincident detection of both outgoing electrons in an electron impact ionization, or (e, 2e), experiment is described. The absolute triple differential cross section can be measured with this instrument to a precision of 10%. Selected results on rare gases are presented, demonstrating the ability of the spectrometer to either probe the target structure in impulsive or binary (e,2e) experiments, or to test the scattering mechanism in nonimpulsive conditions, both for valence or inner shells.

Absolute triple differential cross sections for the 3p ionisation of argon by electron impact

The triple differential cross sections for electron impact ionisation of argon on its 3p orbital are investigated for a primary electron energy near 8 keV. In a coplanar coincidence experiment, both ionisation electrons are analysed with respect to their energy and scattering angles. As in previous low-energy measurements, two lobes are found in the angular distribution of the slow ejected electron. The data are made absolute to an accuracy of better than 10%. This is done at high energy and large momentum transfer, K, by normalising to the impulse approximation Compton profile and assuming a cylindrical symmetry of the data about K. At high momentum transfer where the collision may be considered as a binary electron-electron process, the Ar 3p electron momentum distribution is determined and found to be in very good agreement with the Fourier transform of the Hartree-Fock-Clementi wavefunction.

High energy elastic and inelastic electron scattering by the NH3 molecule‐binding effect

From the measurement of high energy elastic and inelastic electron scattering by the NH3 molecule we find that molecular elastic scattering calculation agrees with experiment, but the independent atom model for molecular inelastic scattering does not reproduce the experiment, even when electron correlations are taken into account. This means that the inelastic scattering by molecules is strongly affected by the rearrangement of the charge densities during the bond formation.

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.

Differential cross sections for 35 keV electrons elastically scattered from NH3

High precision relative elastic differential cross sections d sigma /d Omega e for electrons scattered from ammonia are presented over a wide range of momentum transfer K. The effect of the bond formation is seen qualitatively through comparison with an independent-atom model (IAM) calculation, and the validity range of this IAM is clearly defined. Recent calculations using CNDO type wavefunctions, CI computations, and ab initio calculations within the Borne approximation are also compared with experiment and found to constitute a qualitative improvement over the IAM approximation. Tavards theorem is employed to estimate the exchange energy of the molecule.