Exploring the Helium (e,2e) Differential Cross Section at 64.6eV with Symmetric Scattering Angles and Unequal Outgoing Electron Energies.

Page constructed by Andrew Murray

This Page has last been updated on the 20th January, 1999.

Look at the (e,2e) Computer Controlled Spectrometer Hardware

Look at the Symmetric (e,2e) Data collected by this spectrometer

Look at the Symmetric data parameterisation

Look at the Data where the Ion is left in an Excited State

Look at results in the Perpendicular Plane from 10eV to 80ev above the first Helium I.P.

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Low energy and threshold helium (e,2e) angular correlation experiments in which the scattering process is investigated over a wide range of geometries, for example the results that have been published in

have provided the most detailed and rigorous tests of current electron impact ionisation theories, since an adequate description of the scattering process tolerates few approximations and simplifications. In these energy regions the complexities of

Figure 1. The Experimental Geometry for asymmetric energies, where the scattered and ionised electrons do not take equal energy away from the reaction.

Previous low energy (e,2e) experiments were conducted from coplanar geometry to the perpendicular plane geometry at incident energies from 1eV to 50eV above the helium ionisation threshold at 24.6eV. The outgoing electrons were selected to have equal energy and the same scattering angle x with respect to the projection of the incident electron trajectory onto the detection plane spanned by the electron analysers.

Note that a common point exists at x = 90° for all gun angles y.

In the experiments described here the gun angle y has again been varied from coplanar geometry (y = 0°) to the perpendicular geometry (y = 90°) and the scattering angles x are again symmetric (as shown in figure 1), but the symmetry of the outgoing electron energies has been relaxed.

The incident electron energy has been set to 64.6eV, and the detected electron energies have been selected to range from the symmetric energy sharing, in which each electron carries 20eV away from the reaction, to highly asymmetric sharing in which the electron energies are 5eV and 35eV.

The previous fully symmetric experiments show the existence of a very deep minimum in the (e,2e) differential cross section at Einc = 64.6eV, y = 67.5° and x = 70°. Deconvolution of the experimental results using an estimated angular response function indicated that this dip is five or more orders of magnitude smaller than the maximum differential cross section at this energy. The dip is less pronounced at other incident energies where the excess energy is equally shared.

One purpose of the experiments described here was to investigate the dependence of the dip on the symmetry of the outgoing electron energies.

The spectrometer is a fully computer controlled and real-time computer optimised (e,2e) coincidence spectrometer.

The optimisation software monitors and controls

The spectrometer is maintained at its optimum working condition during data accumulation, with automatic adjustment for any long term drifts. Typical operating conditions were as follows:

The computer optimises the spectrometer at regular intervals as the analysers sweep around the detection plane using a modified simplex technique. Full details of the spectrometer may be found in

An additional check of the apparatus has been made to verify that the measured differential cross section is unchanged when the detected energies E1 and E2 are exchanged.

Figure 2a. The DCS at 64.6eV Incident Energy for the asymmetric energy configuration E1 = 5eV, E2 = 35eV and Symmetric Geometry

Figure 2b. The DCS at 64.6eV Incident Energy for the asymmetric energy configuration E1 = 10eV, E2 = 30eV and Symmetric Geometry

Figure 2c. The DCS at 64.6eV Incident Energy for the asymmetric energy configuration E1 = 15eV, E2 = 25eV and Symmetric Geometry

Figure 2d. The DCS at 64.6eV Incident Energy for the symmetric energy configuration E1 = 20eV, E2 = 20eV and Symmetric Geometry

Figures 2(a) - (d) show the helium (e,2e) differential cross sections obtained for the four selected energy pairs.

Six gun angles y were chosen,

All the results have been placed on the same absolute logarithmic scale which has been normalised with an uncertainty of ±44% at the common point (x = 90°) to the results of

using a technique which is described elsewhere.

At gun angles less than 70° the analyser angular range is constrained to be between x = 35° and x = 125° by the presence of

At higher gun angles the angular range is limited only by the physical size of the analysers.

A trend that can be noticed in the data is that the differential cross section becomes more isotropic as the energy asymmetry increases. Another feature is that the differential cross section at the relative normalisation point (x = 90°) does not change markedly with increasing asymmetry, being lowest at 2.2 x 10E-3 a.u. for symmetric energy sharing and increasing monotonically to 4.3 x 10E-3 a.u. for the most asymmetric sharing.

The forward and backward scatter peaks in the coplanar differential cross section tend to move to lower values of x as the energy asymmetry is increased, the forward peak lying outside the range of measured angles for energy sharing of 10/30eV and 5/35eV. This tendency does not exist for gun angles of 45° and higher.

For all energy sharing the forward scatter peak evolves into the lower angle peak in the perpendicular plane, while the backscatter peak evolves into the central peak.

In the perpendicular plane the central peak becomes broader as the asymmetry increases, and the side peaks become less distinct, almost disappearing at the highest asymmetry. As discussed elsewhere, the side peaks near x = 45° and 135° are thought to arise from a double scattering process in which the incident electron scatters elastically from the nucleus and then collides with the valence electron in a quasi-free interaction. If the two electrons emerge from this reaction in the perpendicular plane then they have an angle of approximately 90° to each other, as observed.

The peak at x = 90° can arise either from collision with a valence electron whose momentum is equal in magnitude but opposite in direction to the incident electron, or via multiple collision processes due to long range Coulombic interactions between the outgoing electrons, as becomes increasingly important in the threshold region.

Figure 3. The (e,2e) differential cross-section at a gun angle y of 67.5°, showing the evolution of the dip as a function of the energy sharing of the detected electrons.

Figure 4. Variation of the minimum of the dip shown in figure 3 as a function of the energy difference (E1 - E2) when the experimental angular function is deconvolved from the data.

The existence of the sharp dip at y = 67.5°, x = 70° and E1 = E2 has been noted previously. Figure 3 shows how the energy sharing affects the shape of the differential cross section for the four different detection energy pairs, and figure 4 shows the dependence on the energy sharing of the minimum differential cross section at the dip, deconvoluted as described elsewhere. The estimated width w of the experimental angular response function is 8°.

For asymmetric energy sharing the deconvolved cross section at the minimum is insensitive to the width of the estimated experimental angular function, the deconvolved cross section being almost unchanged from the measured cross section. As the degree of asymmetry decreases this sensitivity correspondingly increases, until for symmetric energy sharing the calculated deconvolved differential cross section changes by two orders of magnitude compared to the measured cross section.