PROJECTILE CHARGE EFFECTS
IN MULTIPLE IONIZATION OF ARGON
BY POSITRON AND ELECTRON IMPACT
A. C. F. Santos, A. Hasan and R. D. DuBois
Department of Physics, University of Missouri - Rolla
MO 65409, USA.
Abstract. Differential single- and multiple-ionization cross section ratios have been measured for 750 eV positron
and electron impact on argon as a function of the projectile energy-loss from threshold up to 85% of the initial
projectile energy. In addition, differential multiple ionization cross section ratios have been obtained for 500 eV
electron impact as a function of both the scattering angle and projectile energy loss. The differential singleionization cross sections obtained with positrons and electrons are found to have the same shape, i.e., the same
energy loss dependence, in agreement with distorted wave Born predictions. The differential double- and tripleionization cross sections obtained by electron impact, however, are systematically larger than those obtained with
positron impact. This charge effect has been attributed to the quantal interference between the mechanisms leading
to double ionization.
ejection the cross sections for positron impact exceed those
for electron impact by an order of magnitude.
INTRODUCTION
Single and multiple ionization of atoms and molecules
has been a subject of interest for decades1-5. At sufficiently
high projectile velocities, single ionization is well described
by first order theories such as the first Born
Approximation. At lower velocities, however, deviations
from perturbative theories arise. Also the mass and charge
of the projectile can influence which channels participate
and what theoretical approximation can be applied. On the
other hand, the study of multiple ionization is a tougher
task; theoretically due to the presence of many bodies in the
continuum, all interacting by the long range Coulomb field,
and experimentally due to the inherent experimental
difficulties. However, such information is important since
comparisons of electron and positron impact data can be
used to elucidate these complex many-body interactions
and provide information about electron correlation, for
example, e+ projectiles are distinguishable from the ejected
electron. Another important difference is that the
repulsive/attractive Coulomb field switches when the
projectile charge is changed.
Several important studies have also been performed by
the University of London group4-6. For instance, they
measured the energy distributions of positrons and
electrons scattered at angles around 0o in coincidence with
Ar+ ions at 100, 150 and 250 eV. Very similar distributions
for both projectiles were found except in the region when
the outgoing velocities of the scattered projectile and the
ionized electron were equal.
This paper compares single and multiple differential
ionization fractions resulting from electron and positron
impact on argon, as a function of projectile energy loss and
scattering angle. The processes studied can be represented
as
e ± ( E ) + Ar → e ± ( E − ∆E , ∆θ ) + Ar q + + qe − . (1)
In the case of electron impact, the projectile and the
ejected electron are indistinguishable, however, the fastest
of the electrons in the continuum is attributed to be the
scattered projectile. For 750 eV electron and positron
impact the horizontal and vertical acceptance angles were
approximately ± 22o; for 500 eV electron impact, an
improved angular resolution was used where horizontal and
vertical angles were ± 6.5o and ± 22o, respectively.
To date, few differential studies for positron impact
have been performed. Notable work includes the studies of
Schmitt et al.3 who determined doubly differential
ionization cross sections for 100 eV positron and electron
impact on argon atoms by energy- and angle- resolved
measurements. They found that at small angles of electron
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195
projectile charge on multiple ionization. Differential single
and double ionization cross section fractions for 750 eV e+
and e- impact as a function of the projectile energy loss are
presented in Fig. 2. The data are for projectiles scattered
into forward vertical angles between ± 22o. The relative
percent yields were obtained from
EXPERIMENTAL
Collimated e+ and e- beams are delivered by a 22Na
source coupled to a tungsten-mesh moderator. After
crossing a gas jet at right angles, the beams are energy and
angle analyzed by a modified cylindrical spectrometer and
recorded by a position sensitive microchannel plate
detector housed at the focal plane of the spectrometer.
N q+
f
Projectiles having different energies are focused to
different horizontal positions of the detector. One can
investigate different projectile energy-loss ranges by setting
the inner and outer spectrometer voltages, VIN and VOUT ,
respectively (see Fig. 1). In addition, angular information
about the scattered projectiles is contained on the vertical
positions. The argon gas flow is kept constant by a flow
controller and monitored by a thermocouple. Typical
operating conditions gave a chamber pressure of 1-2 × 10-5
Torr. The singly and multiply charged recoil ions are
extracted from interaction region by a weak (10 V/cm)
electric field and separated according to their mass-tocharge ratio by a time-of-flight spectrometer. Finally, the
recoil ions created by projectiles in the interaction region
impinge onto another position sensitive microchannel plate
detector. The recoil signals provide time marks for the start
of a time-to-digital converter (TDC). Fig.1 shows
schematically the experimental apparatus.
=
3
∑N
i =1
ε q+
(2)
i+
ε i+
where f q+ is the charge-state fraction of q times ionized
argon, ε q+ is the microchannel plate detection efficiency
for the ion Arq+, and N q+ is the number of scattered
positrons or electrons in coincidence with the Arq+ recoil
ions. The target gas pressure was kept low enough to
guarantee single collision conditions. The same projectile
detection efficiencies were assumed for positron and
electron impact.
The single ionization cross sections for both positron and
electron impact (not shown) were found to have the same
energy loss dependence, as expected, and to be in good
agreement with theoretical calculations using distorted
wave Born calculations9, since the cross section for
positronium formation is expected to be negligible at this
energy. As seen in Fig. 2, the contributions of single
ionization of argon by electron and positron impact
decrease slowly and monotonically as a function of the
PS M C P
TD C
q+
0
10
PS M C P
gas needle
-1
V IN
Fraction
TO F
V+
Incidentbeam
V-
10
-2
10
VO UT
Figure 1. Schematic of the experimental set-up showing beam
trajectories. The modified cylindrical spectrometer is used to
collect and focus a wide range of horizontal scattering energies
onto the projectile detector, a 50 mm diameter microchannel plate
mounted in chevron configuration. By changing the spectrometer
voltages, VIN and VOUT, different projectile energy loss ranges are
accessed.
-3
10
0
100
200
300
400
500
600
700
Energy-Loss (eV)
projectile energy-loss.
Figure 2. Fractions of single and double ionization of argon as a
function of the projectile energy loss for 750 eV positron and
electron impact on argon. Data are for projectiles scattered into
horizontal and vertical angles between ± 22o. The solid lines show
double photoionization fractions from Holland et al. [10]. Closed
circles: single ionization by electron impact; open circles: single
ionization by positron impact; closed triangles: double ionization
EXPERIMENTAL METHOD
The main scope of the present article is to study multiple
ionization processes and, particularly the role played by the
196
by electron impact; open triangles: double ionization by positron
impact.
eV, the amount of double photoionization is slightly larger
than the corresponding amount for 500 eV electron impact.
The fraction of triple ionization presents an even faster rise
and stays constant at about 7% at higher energy losses.
The fractions of double ionization increase rapidly for
the first 100 eV and continue increasing more slowly up to
250 eV (Fig. 2). For large energy-loss, they are
approximately constant for both projectiles. The relative
amount of double ionization is systematically larger for
electrons than for positron impact. At higher projectile
energy-losses, the amount of double ionization is roughly
30% for electrons and 20% for positrons. Fig. 2 also
presents the double ionization fraction by photoionization
from ref. [10]. The sharp increase in the photon data above
248 eV is due to the opening of the L shell.
0
10
Fraction
-1
In the case of argon triple ionization, a huge difference
is observed in Fig. 3 between positron and electron impact
in both shape and magnitude. The threshold for removing
three electrons from the M-shell in argon is 84.1 eV. For
positron impact, triple ionization was not observed below
200 eV, only a steep rise after the L shell is opened. For
electron impact, triple ionization is clearly observable
below the L-shell threshold. This can perhaps be attributed
to the detection of ionized electrons, which did not occur in
our positron study since scattered projectiles are detected.
0
-3
10
50
100
150
200
250
300
Figure 4. Fractions of single and double ionization of argon as a
function of the projectile energy loss for 500 eV electron impact
on argon. Data are for projectiles scattered into horizontal and
vertical angles between ± 6 and 8o, respectively. The solid lines
show double photoionization fractions from Holland et al. [10].
Closed squares: single ionization; open circles: double ionization;
closed triangles: triple ionization.
Ar
-1
Fraction
0
Energy-Loss (eV)
10
DISCUSSION
Figures 3 and 4 show that double and triple ionization
cross sections fractions for electron impact are
systematically higher than the corresponding fraction for
positron impact, while the photoionization fractions are
intermediate between the positron and electron fractions.
McGuire11 suggested that the difference between the
double ionization cross sections for electron and proton
impact to be a charge effect due to the interference between
the so called two-step and shake-off processes resulting in
an interference term proportional to the third power of the
projectile charge.
-2
10
3+
Ar
L II, III
LI
-3
10
-2
10
3+
10
10
0
100
200
300
400
500
600
700
Energy-Loss (eV)
Figure 3. Fractions of triple ionization of argon as a function of
the projectile energy loss for 750 eV positrons and electrons
scattered into vertical angles between ± 22o. The dotted line
represents the fraction of triple photoionization of argon from ref.
[10]. The vertical lines indicate thresholds for single, double and
triple ionization as well as the thresholds for removing electrons
from the L shell.
Andersen et al.12 showed that the double ionization total
cross sections of helium for proton and antiproton impact
also depended upon the sign of the projectile charge.
Another explanation for the dependence of the double
ionization on the projectile charge was given by Olson13
using the classical trajectory Monte Carlo calculations as an
effect of the transient destabilization of the target due to the
difference in screening by the projectiles.
Figure 4 shows the results for single, double and triple
ionization of argon by 500 eV electron impact as a function
of the projectile energy-loss. Included is the fraction of
double photoionization of argon10. Generally speaking, the
amount of multiple ionization is smaller at 500 eV when
compared with 750 eV, as expected. The amount of double
ionization increases rapidly up to 130 eV and reaches a
plateau at about roughly 15%. Between 130 eV and 230
The contributions of the inner-shell ionization cross
sections cannot be neglected in the analysis of the multiple
ionization cross sections. Negative particles may be
197
expected to have larger inner-shell ionization cross sections
due to the static interaction with the nucleus9,11.
electron impact systematically exceed those for positron
impact. This effect has been attributed to the quantal
interference of the processes leading to multiple ionization.
0
10
ACKNOWLEDGMENTS
DDCS (arb. units)
This work is supported by National Science Foundation,
grant No. PHY0097902 and CNPq (Brazil).
REFERENCES
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10
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8
Angle (deg)
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Figure 5. Doubly differential cross sections (in arbitrary units)
for 500 eV electron impact on argon, in the final electron energy
range from 470-460 eV as a function of the electron scattering
angle. Single ionization: closed circles; double ionization (open
circles). The data were corrected by the recoil detection
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470 eV as a function of the scattering angle. The present
angular resolution is approximately 2o. Both the single and
double ionization cross sections decrease as a function of
the scattering angle. The ratio of double-to-single
ionization cross sections presented in Fig. 5 ranges from
roughly 1% at the larger angles (± 8o) to 1.6% near zero
degrees.
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CONCLUSIONS
13. R. E. Olson, Phys. Rev. A 36, 1519 (1987).
In conclusion, we have compared the multiple
ionization differential cross sections fractions for 750 eV e+
and e- impact on Ar as a function of projectile energy-loss.
Angular distributions of the projectiles have also been
measured for 500 eV electrons. The relative contribution
of multiple ionization increases with increasing projectile
energy loss. The double and triple ionization fractions for
198