Electron impact double ionization of neon
M. Ford, J. Doering, J. Cooper, M. Coplan, J. Moore
To cite this version:
M. Ford, J. Doering, J. Cooper, M. Coplan, J. Moore. Electron impact double ionization of neon. Journal de Physique IV Colloque, 1993, 03 (C6), pp.C6-117-C6-123.
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JOURNAL DE PHYSIQUE IV
Colloque C6, supplkment au Journal de Physique 11, Volume 3, novembre 1993
Electron impact double ionization of neon
M.J. FORD. J.P. DOERING. J.W. COOPER*,M.A. COPLAN* and J.H. MOORE'
Johns Hopkins University,Baltimore, MD 21218, U S.A.
* University of Maryland, College Park, MD 20742, U S A .
Abstract: Electron-impactdouble ionization from the valence shell of neon has been measured
at an incident electron energy of 3662.5 eV. Double-coincidence (e, (3-1)e) measurements have
been made between the scattered electron and each of the ejected electrons in turn, ejected
energies were 10 eV and 90 eV, respectively, at ejection angles of 45, 60, 90, 120 and 135
degrees with respect to the incident electron beam. Absolute four-fold-differential crosssections have been derived from the measured data and can be interpreted in terms of a fast,
single-step, shake-off process.
1. INTRODUCTION
Double ionization of atoms by electron impact, or (e,3e), is a complex process because of the large
number of interactions that contribute to the cross-section. As far as the kinematics are concerned, it is
necessary to consider the interaction of the incident electron with the target in the initial state and the
scattered and ejected electrons with each other and the residual doubly-charged core in the final state. In
addition, the n-electron target state and (n-2)-electron ion state must be adequately represented and the
details of the collision mechanism responsible for the ejection of two electrons described. The nature of
the complexities provides both the motivation for, and difficulty of, studying double ionization.
By a suitable choice of kinematic conditions and targets it is possible to isolate the different
interactions and thereby work toward an overall understanding of the mechanism of double ionization.
For example, final-state interactions among the scattered and ejected electrons are best studied for
helium near threshold. On the other hand, the electronic structure of the target is best studied at high
incident electron energies and high energies for the scattered and ejected electrons in order to minimize
the interactions among the electrons involved in the collision.
We have begun an (e,3e) project for the purpose of investigating the electronic structure of atomic
targets with particular emphasis on atoms such as magnesium with highly correlated valence electrons.
In the high energy limit where the incident, scattered and ejected electrons can be represented by plane
waves, the (e,3e) cross section is directly related to the square of the double Fourier transform of the
wave function of the target atom projected onto the state for the residual ion. This factor depends in a
sensitive way on correlation effects among the target electrons and thus has the potential for providing
rather direct information on the collective motion of atomic electrons.
Because double ionization has a small probability compared with single ionization, (e,3e) crosssections are very small. The required fully-differential cross-section measurements with complete
determination of the energies and vector momenta of the incident, scattered and ejected electrons have
only recently been done by Lahmam-Bennani and co-workers [I, 21. In those experiments the ejected
electrons had low energies, and the results were interpreted in terms of final-state angular correlations.
We have designed and built a spectrometer that can measure (e,3e) cross sections at several angles
simultaneously. Because high energies are necessary to study the electronic structure of the target this is
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1993611
JOURNAL DE PHYSIQUE IV
118
a crucial consideration since the cross-sections are significantly smaller than for the lower energy
regime.
Our first experiments have been performed on neon where only two of the possible three electrons
have been detected in coincidence--the so called (e, (3-1)e) experiment [3,4]. The experiment has been
performed under conditions where the energy lost by the incident electron is unequally shared between
the ejected electrons, the recent results of Duguet et al. [3] suggest that the cross-section is relatively
large within this regime. The fast scattered electron was detected in the forward direction (€la = 0') with
an energy Ea = 3500 eV. The incident-electronenergy was fixed at 3662.5 eV which, after taking into
account the energy required to remove two p-shell electrons from neon (62.52 eV), leaves an excess
energy of 100 eV to be shared between the two ejected electrons. It is important to note that the
detection of only two of the three continuum electrons means that the final state of the residual ion is not
well defined. In addition to double ionization with the ejection of 10 eV and 90 eV electrons, there is
the possibility of triple ionization (only when detecting the 10 eV electron) and double ionization with
excitation of the doubly charged residual ion (possible for both the detection of the 10 eV and 90 eV
electrons). We believe these latter two cases to be improbable because they require three electron
processes that have cross sections an order of magnitude less than the two electron process that results in
double ionization with the residual ion in the ground state. In two separate experiments the two electrons
ejected in the collision were in turn detected in coincidence with the scattered electron at ejection angles
8b = 45, 60, 90, 120 and 135 degrees with respect to the incident-beam direction. Ejected-electron
energies were Eb = 90 eV and 10 eV. The measured cross-section is integrated over the ejection angle of
the third, unobserved, electron and is four-fold-differential(4DCS) with respect to two energies and two
solid angles. The experiments were undertaken in order to gain experience with the spectrometer and
electronics and obtain calibration data, and have allowed us to estimate the absolute value of the 4DCS
for double-ionization in neon over a limited range of experimental conditions.
2. EXPERIMENTAL
ALKALINE EARTH METAL SOURCE
\
CTED ELECTRO
CTED ELECTRON ANALY
LECTRON GUN
ELECTRON MULTIPLIE
Fig 1. Schematic diagram of the (e,3e) apparatus.
Figure 1 shows a schematic diagram of the (e,3e) apparatus. A gas cell was used in the present neon
measurements in place of the alkaline-earth-metal source, and only two multipliers were used in each
ejected analyser. Each of the ejected multipliers subtended a solid angle of approximately 0.05
+
steradians and accepted electrons over an angular range of approximately 12O. The analysers were
operated at a constant fractional resolution of 3.8%. The primary analyser was set at 0' relative to the
incident beam and was o erated at a resolution of approximately 4 eV and an acceptance solid angle of
approximately 2.4 x 10- steradians, corresponding to a maximum scattering angle of 0.5'. The small
magnitude of the cross-sections being measured necessitated the use of modest energy and angular
resolutions, but, as noted by Duguet et al. [3] this should not degrade the angular information obtained
since no sharp structure is expected. Signal-to-noise in the experiment is comparatively poor and so it
was necessary to operate at low incident beam currents of approximately 16 nA. Fluctuations in the
incident beam current were less than 10%. The gas cell was operated at a constant pressure of
approximately 1 mtorr.
The relatively large resolution employed results in the measured double-ionization cross-sections
containing a contribution from single-ionization events. Accordingly a similar procedure was employed
to that described by Duguet et al. [3] in order to extract the double-ionization cross-section from the
data. The coincidence resolution function of the apparatus was determined by measuring the binding
energy spectrum of neon between the 2p and 2s main single-ionization lines. Two Voight profiles were
fitted to this data to give the analytic form of the resolution function. The entire binding energy spectrum
was then compared to a convolution of the resolution function with the single-ionization spectrum of
neon determined in photoionization experiments [5, 61. Binding energy spectra were generated by
varying the incident energy keeping all other parameters fixed. A best fit of the convoluted spectrum to
the measured binding energy spectrum below the double-ionization threshold was obtained by varying
the intensities of the 2p and 2s main lines whilst keeping the relative intensities of the satellite lines
fixed. Figure 2 shows the resolution function, and convoluted and measured spectra. The coincidence
rate is plotted as a function of incident beam energy relative to the 2p single ionization threshold. Above
the double ionization threshold the difference between the measured and convoluted data directly
represents the magnitude of the double-ionization cross-section. For Eb = 90 eV and Bb = 45' (the last
data point) it can be seen that the measured cross-section contains approximately 20% single ionization.
The contribution of single ionization to the cross-sections measured at Eb = 10 eV was estimated to be
less than 5 % using a convolution of the photoionization spectrum [5, 61 and the resolution function
measured at Eb = 96 eV; the resolution function at 10 eV is narrower and so the single-ionization
contribution could be neglected.
1
Q
J
100-
0
=
8
%
8
2
4
3
2
I
~ e ~ '
lo:
1;
J/:Y- -
\
.:
Oel
- 2p
-- - - 2s
2%-
"""""""" """""'"
0.01-' " '
-10
0
10
20
30
40
50
60
Incident Energy Relative to Ne 2p Threshold (eV)
Fig 2. Binding Energy spectrum for neon. Ea = 3500 eV, Oa = 0°, Eb = 90 eV, 8b = 45'. Solid circles
are the experimental data. Broken curve is the resolution function determined from measurements of 2p
and 2s ionization in neon. Solid Curve is a convolution of the resolution function with the
photoionization spectrum for single ionization fitted to the experimental data; this represents the single
ionization contribution.
JOURNAL DE PHYSIQUE IV
3. RESULTS AND DISCUSSION
Ejected Electron Angle Relative to
Incident Electron Beam
Ejected Electron Angle Relative to
Incident Electron Beam
Fig 3. Four-fold-differential cross-sections for valence shell double ionization of neon by 3662.5 eV
electrons, plotted as a ratio to the 2p single ionization triple differential cross-section for the same
ejected electron energy. Ea = 3500 eV, Oa = 0".
Angular distribution measurements must account for anisotropies in the apparatus as well as
differences in detector efficie~ces.Magnetic fields within the vacuum chamber have been reduced to
the level of less than a milligauss with a double mapetic shield in order to eliminate distortion of the
electron trajectories, and uniform detector efficienes have been attained by accelerating the ejected
electrons to 100 eV at the front surfaces of the detectors. Moreover, the tiple-differential cross-sections
(TDCS) for 2p single ionization can be extracted from the measured binding energy spectra for Eb = 90
eV and 10 eV: in figure 2 the number of coincidence counts at 0 eV give the 2u TDCS at 45" for
Eb = 90 eV. Since both the single- and double-ionization cross-sections were measured in a single
experimental run with the analysers set to the same conditions they will be on the same relative scale and
subject to the same angular calibration. Dividing the double-ionization cross-sections by the
corresponding single-ionization cross-sections effectively eliminates variations in the angular response
of the instrument. Figure 3 shows the 4DCS for double ionization plotted in the above manner.
The data of figure 3 for Eb = 90 eV is practically isotropic while that for Eb = 10 eV shows a distinct
peak in the backward direction. The fact that the single- and double-ionization cross-sections for Eb = 90
eV show the same angular dependence, suggests that in the double-ionizing collision under
investigation, where the electrons are ejected at 90 eV and 10 eV, respectively, the faster electron is
ejected in a 'single-ionization like' collision. It is difficult to draw any conclusions regarding the 10 eV
electron from the data of figure 3 without knowing the form of the single ionization cross-section.
Provided that the momentum transfer is small enough, the TDCS for single ionization should be well
described by the photoionization angular distribution
In the present experiment, with an acceptance angle of 0.5' for the primary analyser, the momentum
transfer for single ionization ranges from 0.07 to 0.16 a.u. for Eb = 10 eV, and 0.25 to 0.29 a.u. for
Eb = 90 eV. On the other hand the direction of the momentum-transfer vector ranges from 0' to 61' for
Eb = 10 eV and 0" to 29" for Eb = 90 eV relative to the incident electron beam. Since both the crosssection and transmission of the primary analyser decrease relatively rapidly with increasing scattering
angle, it can be anticipated that the observed TDCS is dominated by collisions where the incident
electron is scattered very close to the forward direction. In eqn (I), 8 may be taken as the angle of the
ejected electron relative to the incident beam. In order to test this model for the single-ionization crosssections, the TDCS has been compared to the photoionization angular distributions calculated from eqn
(1). The result is shown in figure 4, where again data for Eb = 90 eV have been divided by data for Eb =
10 eV. We have assumed that the precautions that have been taken with stray magnetic fields and
detector efficiences for electrons of different energies are sufficient to eliminate any differences in
angular response with electron energy. Values used for the asymmetry parameter were 0.5 for Eb = 10
eV, and 1.0 for Eb = 90 eV [7]. The calculated ratio has been normalized to the data at 0b = 90'.
0.04
40
60
80
100
120
140
Ejected Electron Angle Relative to
Incident Electron Beam
Fig 4. The triple differentialcross-section for single ionization from the 2p shell of neon. Data have been
plotted as the ratio of the cross-section for Eb = 90 eV to the cross-section for Eb = 10 eV. Ea = 3500
eV, Oa = 0'. The solid circles are the experimental data. The solid line is the calculated ratio using eqn
(1).
122
JOURNAL DE PHYSIQUE IV
Within the experimental error, good agreement can be seen between the measured TDCS for single
ionization and the calculated photoionization angular distribution, implying that the average momentum
transfer is small and close to the forward direction in the observed collisions.
Ejected Electron Angle Relative to
Incident Electron Beam
Ejected Electron Angle Relative to
Incident Electron Beam
Figure 5. Absolute four-fold-differentialcross-sections for double ionization of neon by 3662.5 eV
electrons. Ea = 3500 eV, ea = 0". Solid circles are the experimental data. Solid curve for Eb = 90 eV is
photoionization angular distribution calculated from eqn (1).
Assuming now that the single-ionization cross-sections are adequately described by the
photoionization angular distribution in eqn (I), the 4DCS for double ionization can be extracted from the
data of figure 3. These are shown in figure 5. The absolute scale has been determined by calculating the
absolute TDCS from the equation given by Erhardt et al. [8] relating the TDCS under conditions of high
impact energy and low momentum transfer to the photoionization angular distribution of eqn (1). Values
for the total photoionization cross-section of 3.5 Mb and 8.94 Mb for Eb = 90 eV and 10 eV,
respectively, were used in the calculation [9]. The appropriate choice of momentum transfer is not a
trivial matter, especially for Eb = 10 eV where the range is quite large. In light of the data in figure 4 and
the above discussion it has been assumed that zero angle scattering dominates the measured.TDCS,
consequently values of 0.25 a.u. and 0.07 a.u. for the momentum transfer at 90 eV and 10 eV,
respectively, were used in the calculation; the absolute value of the TDCS for Eb = 10 eV is reduced by
a factor of approximately four if a value of 0.16 a.u. is used. From the relatively large uncertainties in
calculating the TDCS, the absolute 4DCS values are accurate to within an order of magnitude.The
momentum transferred in the double-ionizing collision can range from 0.37 to 0.39 a.u. with a maximum
angle of 21' relative to the incident electron beam. The absolute values of the 4DCS for neon are
approximately one order of magnitude smaller than the corresponding values for argon measured by
Duguet et a1 . [ 191. This may not be surprising in light of the double-differential cross-sections for
single ionization reported by Opal et al. [lo], where the values for argon and neon also differ by an
order of magnitude. The similarity in shape between the 4DCS for Eb = 90 eV and the photoionization
angular distribution for single-ionization can clearly be seen. For Eb = 10 eV there is a pronounced peak
in the backward direction. This would seem to imply that the double-ionization process has not taken
place simply as a two-step shake-off process with the faster electron being ejected in a 'single-ionizationlike' collision and the slower electron ejected in a subsequent relaxation of the remaining ion. If this
were the case the 4DCS for Eb = 10 eV would be isotropic. Rather, the ionization occurs in a single step
with the faster electron ejected in a 'single-ionization-like' process and the slower electron
simultaneously shaken-off. It is unclear why the observed 4DCS for the slower electron peaks at
approximately 120'.
4. CONCLUSION
The double-ionization process in neon investigated under the present kinematics may well contain
information regarding the electron-electron correlation in the target atom, and has the great advantage of
being in a regime where the cross-sections are relatively large. The observed 4DCS suggest that the
double-ionization mechanism is a non-adiabatic shake-off process.
Triple coincidence measurements of the five-fold-differential cross-section under similar kinematics
are required in order to put the above analysis on a firmer footing. Data from such an experiment are not
subject to contamination by single-ionization as in the present experiment. Although the errors reported
in the present data have tried to reflect the uncertainty in the convolution process used to subtract the
single-ionization contribution, it is rather difficult to verify the accuracy of such a procedure with the
current results.
ACKNOWLEDGMENTS
This work is supported by NSF grant number PHY-91-07337
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