Coplanar Doubly-Symmetric Helium (e,2e) Measurements with Excitation of the Residual Ion.
Page constructed and updated 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 Perpendicular Plane measurements from 10eV to 80eV above the Helium I.P.
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As noted on previous pages, (e,2e) experiments which measure the angular correlations between scattered and ionised electrons following a collision provide a rigorous test of theories of electron impact ionisation of atoms. See for example,
These experiments have almost always been concerned with ionisation in which the residual ion is left in its ground state, and have principally been carried out in either coplanar geometry or in perpendicular plane geometry. The incident electron energy ranges widely from near threshold to many keV above threshold, allowing different theoretical approximations to be investigated.
In contrast to these direct ionisation experiments, only a few coincidence studies have been concerned with processes in which the ion, invariably He+ is left in an excited valence state :
e + He Þ He+ * + e + e
These studies have almost all been carried out at incident electron energies in excess of 650eV. The earliest experiments for example as given in
were concerned with structure studies, using momentum distributions derived from non-coplanar (e,2e) measurements to discriminate between different theoretical correlated wavefunctions of the helium ground state.
More recently, high energy coplanar experiments as discussed in
have probed the dynamics of the simultaneous ionisation and excitation process.
These experiments have been of the glancing type, with one of the outgoing electrons carrying away most of the energy and being deflected in the forward direction. The measurements show a marked contrast to those for direct ionisation, with the backscatter peak being larger than the forward scatter peak.
Theoretical models for these asymmetric geometries are only beginning to be developed as seen in
and these models indicate the importance of initial state correlations in the atom and final state correlations between the ejected electron in the continuum and the excited electron in the residual ion.
In this page results are presented for a coplanar non-glancing experiment at a much lower incident energy.
The excitation energy of the excited (n=2) electron in the He+ ion core is comparable to the kinetic energy of the detected electrons in this experiment, and so strong correlations between all three electrons in the final state might be expected.
Measurements are also presented for direct ionisation to the ionic ground state, where the energy of the detected electrons was selected to be the same as for ionisation with excitation. This allows a direct comparison to be made between the two processes, since the analyser efficiencies remained unchanged.
Labelling the ingoing and outgoing two electrons as e0, ea and eb respectively, the energy equation for this reaction may be written :
E0 = I.P. + Eex + Ea + Eb
where for helium the ionisation energy I.P. = 24.6 eV and the ionic excitation energy Eex = 0 eV and 40.7 eV for n = 1 and n = 2 respectively (see figure 1).
Figure 1. Energy Level Diagram for Helium direct and excited ionisation processes
In the present experiments the electrons ea and eb were chosen to have equal energy,
and were detected at equal azimuthal angles
Figure 2. The (e,2e) Experimental Geometry chosen to be in Coplnar Geometry with equal selection of energy for the scattered and ejected electrons.
The incident electron energy E0 was therefore
The doubly-symmetric differential cross-section (DCS) was obtained by varying the angle q and measuring the (e,2e) coincidence signal as a function of this angle. A particular "slice" of the five-fold differential cross-section d5s/dWadWbdEa was thus obtained, the polar co-ordinate f = (fa - fb) = 180° for coplanar geometry and the energy Ea = Eb being held constant as qa = qb = q was varied.
No attempt was made to distinguish between the 2S and 2P states as shown in figure 1.
In principle the differential cross-section arising from the 2P1/2,3/2 states could be separated from that for the 2S1/2 state with a triple coincidence between the outgoing electrons together with detection of the decay emission from the 2P states.
The ionic 2P substate populations and coherences could additionally be determined by measuring the angular distribution or polarisation of the emitted photons. Such an experiment would, however, be very difficult in practice due to the extremely low triple coincidence yields that would be obtained.
The spectrometer used to collect these results 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 during data accumulation, with frequent adjustment for any long term drifts. This is essential in experiments which require long data accumulation times such as the one described here.
Briefly,
The direct ionisation experiments carried out at 104.6eV incident energy were interleaved with the experiments where the ion was left in an excited state. The following experimental conditions were maintained over the long period of data accumulation necessary for these experiments :
The average coincidence counting rate for data accumulation to the ground ionic state varied from
By contrast, for ionisation with excitation, the average coincidence count rates varied from
These extremely low coincidence rates mean that the spectrometer must be stable for the very long times that data has to be accumulated to become statistically meaningful. If the spectrometer drifts over these times in energy, electron beam current , tuning conditions or gas density then the results are far more difficult to interpret. The use of the computer control to maintain the operating conditions at a stable point over the 2 months continuous accumulation time was essential for success of these experiments. Even with this sophisticated feedback control, there is evidence of variations in the cross sections obtained as seen in figures 3 & 4.
The data were normalised to each other, since the coincidence count rates C(E0,Ea) are given by
C(E0,Ea) = ea(Ea) eb(Ea) dWadWbdEcoinc
where
In these experiments, IF, r, ea(Ea), eb(Ea), dWa, dWb and dEcoinc were held constant for ionisation with and without excitation, whereas the electron beam diameter was focussed to a smaller diameter than viewed by the analysers.
The ratio of differential cross-sections for the two processes is therefore given by the ratio of observed coincidence count rates.
Figure 3. The DCS for ionisation and excitation of the ion plotted on a linear scale, normalised to unity at theta = 90 degrees. The data can be downloaded by linking to the figure.
Figure 4. The DCS for ionisation and excitation of the ion plotted on a logarithmic scale, normalised to unity at theta = 90 degrees. The data can be downloaded by linking to the figure.
Figures 3 and 4 show the normalised differential cross-sections plotted on linear and logarithmic scales in order to highlight the differences in the forward and backward scattering directions.
The direct ionisation result is almost identical in structure to that of Gélébart F and Tweed R J, J. Phys. B At. Mol. Opt. Phys. 23 L641(1990) at 100eV as expected, although the magnitude differs slightly because the incident energy is different.
A deep minimum is seen around 80°, followed by a backscatter peak around 135°.
It has been suggested that this results from elastic scattering of the incident electron through 180° from the atomic core followed by a quasi-free binary collision.
By contrast, the result for ionisation with excitation does not appear to exhibit this deep minimum or structure, although the very low measured coincidence counts at these angles make any definite conclusion difficult.
There is a slight structure observed at q ~ 60° for ionisation with excitation which does not appear for direct ionisation, and since these results were taken at the same time, this is not considered to be an instrumental effect.
Direct ionisation from a p-orbital exhibits structure in the cross-section with a splitting of the binary and backscatter peaks, a secondary peak appearing roughly at 50 - 60° in the forward lobe. It is perhaps not unreasonable to assume that analogously, excitation to the excited 2P state might exhibit similar structure.
The cross-section for excitation to the 2S ionic state would be expected to forward peak at approximately q = 45°, as in the direct ionisation process. A similar structure might be expected in a backscatter peak at approximately 120°, where the incident electron is initially scattered elastically by the atom prior to ionisation and excitation, and a suggestion of such a peak can be seen in figure 4.
Look at the (e,2e) Computer Controlled Spectrometer Hardware
Look at the Symmetric (e,2e) Data collected by this spectrometer
Look at the Perpendicular Plane measurements from 10eV to 80eV above the Helium I.P.
Link to the Atomic Molecular & Laser Manipulation Group Home Page
Link to the Manchester Physics & Astronomy Department Home Page