The Astrophysical Journal, 729:76 (8pp), 2011 March 1 doi:10.1088/0004-637X/729/1/76
C
2011. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
STORAGE RING CROSS SECTION MEASUREMENTS FOR ELECTRON IMPACT IONIZATION
OF Fe
11+
FORMING Fe
12+
AND Fe
13+
M. Hahn
1
, D. Bernhardt
2
, M. Grieser
3
, C. Krantz
3
, M. Lestinsky
1
,A.M
¨
uller
2
, O. Novotn
´
y
1
, R. Repnow
3
,
S. Schippers
2
, A. Wolf
3
, and D. W. Savin
1
1
Columbia Astrophysics Laboratory, Columbia University, 550 West 120th, New York, NY 10027, USA
2
Institut f
¨
ur Atom- und Molek
¨
ulphysik, Justus-Liebig-Universit
¨
at Giessen, Leihgesterner Weg 217, 35392 Giessen, Germany
3
Max-Planck-Institut f
¨
ur Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
Received 2010 November 29; accepted 2011 January 10; published 2011 February 10
ABSTRACT
We report ionization cross section measurements for electron impact single ionization (EISI) of Fe
11+
forming Fe
12+
and electron impact double ionization (EIDI) of Fe
11+
forming Fe
13+
. The measurements cover the center-of-mass
energy range from approximately 230 eV to 2300 eV. The experiment was performed using the heavy-ion storage
ring TSR located at the Max-Planck-Institut f
¨
ur Kernphysik in Heidelberg, Germany. The storage ring approach
allows nearly all metastable levels to relax to the ground state before data collection begins. We find that the cross
section for single ionization is 30% smaller than was previously measured in a single-pass experiment using an ion
beam with an unknown metastable fraction. We also find some significant differences between our experimental
cross section for single ionization and recent distorted wave (DW) calculations. The DW Maxwellian EISI rate
coefficient for Fe
11+
forming Fe
12+
may be underestimated by as much as 25% at temperatures for which Fe
11+
is abundant in collisional ionization equilibrium. This is likely due to the absence of 3s excitation–autoionization
(EA) in the calculations. However, a precise measurement of the cross section due to this EA channel was not
possible because this process is not distinguishable experimentally from electron impact excitation of an n = 3
electron to levels of n 44 followed by field ionization in the charge state analyzer after the interaction region. Our
experimental results also indicate that the EIDI cross section is dominated by the indirect process in which direct
single ionization of an inner shell 2l electron is followed by autoionization, resulting in a net double ionization.
Key words: atomic data – atomic processes – methods: laboratory
1. INTRODUCTION
Collisionally ionized atomic plasmas are formed in a range
of astrophysical objects including stellar coronae, galaxies, and
supernova remnants. The charge state distribution (CSD) of
such plasmas is determined by a balance between electron
impact ionization (EII) and electron–ion recombination. The
CSD plays an important role in a wide range of spectroscopic
diagnostics used to infer electron temperature, electron density,
and elemental abundances (Brickhouse 1996; Landi & Landini
1999; Bryans et al. 2009). Most CSD calculations are carried
out under the assumption of collisional ionization equilibrium
(CIE) for conditions where the electron density is low (meaning
three body recombination is unimportant), radiation can be
ignored, and there is no dust. In this case, the ionization
and recombination rates are the same so that n
e
n
q
α
q
I
=
n
e
n
q+1
α
q+1
R
, where n
e
is the electron density, n
q
is the density
of ions of a particular element with charge q, α
q
I
is the rate
coefficient for ionization from q to q
+ 1, and α
q+1
R
is the
rate coefficient for recombination from q
+ 1toq. Rewriting
gives n
q+1
/n
q
= α
q
I
/α
q+1
R
, thus making clear the importance of
accurate ionization and recombination data to model the CSD
of a plasma.
For CIE, generally only electron impact single ionization
(EISI) needs be considered since for a given charge state
multiple ionization is significant only at temperatures so high
that the fractional abundance of that ion is negligible (Tendler
et al. 1984). Multiple-electron ionization, such as electron
impact double ionization (EIDI), needs be considered only
when modeling the CSD in dynamic systems where ions
are suddenly exposed to higher electron temperatures (M
¨
uller
1986). Examples of such non-equilibrium systems include solar
flares (Reale & Orlando 2008), supernova remnants (Patnaude
et al. 2009), and merging galaxy clusters (Akahori & Yoshikawa
2010).
Much work has been carried out in deriving the necessary
EII data (see the compilation by Dere 2007); however, sizable
discrepancies in the data exist even among the most recent com-
pilations (Bryans et al. 2009). Experimental EII measurements,
like those reported here, will help to resolve these differences.
These measurements can also be used to benchmark theory
enabling more accurate EII cross section calculations for ions
isoelectronic to those measured.
The difficulty of producing well characterized ground state
ion beams has been a major limitation for obtaining the accu-
rate EII data needed for CIE models. Most measurements of EII
have been performed in a single-pass geometry in which
metastable ions generally have not had enough time to radia-
tively relax to the ground state before the EII measurements
are performed. In this paper, we describe an experiment em-
ploying an ion storage ring. This arrangement allows the ions
to be stored long enough for typically all the metastable levels
to radiatively relax before data acquisition begins. This fact has
been exploited previously by Linkemann et al. (1995a, 1995b).
Here, we study ionization of Fe
11+
. This ion produces strong
spectral lines which can be used for plasma diagnostics and
instrument calibration (Del Zanna & Mason 2005). It is also a
particularly important ion for observations of the solar corona
(Moses et al. 1997; Brown et al. 2008).
EISI of Fe
11+
has already been the subject of some theoretical
and experimental work (Younger 1983; Pindzola et al. 1986;
1
The Astrophysical Journal, 729:76 (8pp), 2011 March 1 Hahn et al.
Gregory et al. 1987;Dere2007). Gregory et al. (1987) measured
the ionization cross section for Fe
11+
using a single-pass
experimental geometry. The EISI cross section measured by
that experiment was about 30% larger than that predicted by the
distorted wave (DW) calculations of Pindzola et al. (1986)or
Dere (2007). Gregory et al. (1987) compared their experimental
result to theoretical calculations for ionization from the ground
and metastable levels and concluded that the discrepancy was
due to a large metastable population in the ion beam in the
experiment. The measurements reported here, by being able to
generate nearly pure ground state ion beams, can resolve this
issue and also provide an excellent test case to compare crossed
beams experimental results with the storage ring technique.
Specifically, we study in detail EISI of P-like Fe
11+
forming
Si-like Fe
12+
over the electron–ion collision energy range of
230–2300 eV. This energy range includes the following direct
ionization channels:
e
−
+ Fe
11+
(2s
2
2p
6
3s
2
3p
3
)→
⎧
⎪
⎪
⎨
⎪
⎪
⎩
Fe
12+
(2s
2
2p
6
3s
2
3p
2
) + 2e
−
Fe
12+
(2s
2
2p
6
3s 3p
3
) + 2e
−
Fe
12+
(2s
2
2p
5
3s
2
3p
3
) + 2e
−
Fe
12+
(2s
1
2p
6
3s
2
3p
3
) + 2e
−
.
(1)
The energy thresholds for direct ionization are 330.79 eV from
the 3p subshell and 357.40 eV from the 3s subshell (Ralchenko
et al. 2008). Excitation–autoionization (EA) can also occur
starting at the ionization threshold of 330.79 eV through the
electron impact excitation of a 3s electron to an autoionizing
state. We are unaware of any theoretical work on this specific
EA channel for Fe
11+
.
Theoretical calculations have shown that EA is expected
to make an important contribution to the ionization cross
section above the excitation threshold for n = 2 electrons
at ≈710 eV (Pindzola et al. 1986). In that same energy
range resonant processes such as resonant excitation double
autoionization (REDA) and resonant excitation auto-double-
ionization (READI) are predicted in the cross section. These
occur through dielectronic capture when an ion forms an
excited state that subsequently decays by ejecting two electrons
(LaGattuta & Hahn 1981; Henry & Msezane 1982;M
¨
uller et al.
1988a, 1988b;M
¨
uller 2008). In the REDA process, the electrons
are released sequentially, whereas in READI the two electrons
are ejected simultaneously.
The theoretical energy thresholds for ionization of the 2p or
2s electrons are 1073 eV and 1199 eV, respectively (Kaastra
&Mewe1993). Ionization from the 2p subshell radiatively
stabilizes with a predicted probability of 1.1% and from the
2s with a probability of 8.0% (Kaastra & Mewe 1993). In both
cases, it is more likely that direct ionization of an n = 2 electron
will be followed by autoionization giving a net double ionization
to form Fe
13+
. Thus, ionization of an inner shell electron is
expected to be a very small contribution to the total single
ionization cross section, but it can be significant for double
ionization (M
¨
uller & Frodl 1980).
EIDI of Fe
11+
forming Al-like Fe
13+
was also measured over
the same energy range of 230–2300 eV. The energy threshold
for EIDI through direct ionization is 691.83 eV (Ralchenko
et al. 2008). As discussed above, double ionization can also
occur through single ionization of an inner shell electron with
subsequent autoionization. Other indirect processes such as EA
and resonant processes analogous to those expected for single
ionization may also occur in the double ionization cross section
(M
¨
uller et al. 1988b).
The rest of this paper is organized as follows. In Section 2,we
describe the experimental setup. The data analysis is presented
in Section 3 and uncertainties in Section 4. Experimental results
and comparison to theory are presented for single ionization in
Section 5 and for double ionization in Section 6. A summary is
given in Section 7.
2. EXPERIMENTAL SETUP
EII measurements were performed at the TSR heavy-ion stor-
age ring of the Max-Plank-Institut f
¨
ur Kernphysik in Heidelberg,
Germany. The experiments basically followed the procedure
of previous experiments (Kilgus et al. 1992; Linkemann
et al. 1995a; Kenntner et al. 1995; Schippers et al. 2001;
Lestinsky et al. 2009). Details related specifically to ionization
are described in Hahn et al. (2010). Here, we describe additional
aspects relevant to the present work.
The TSR facility is equipped with two separate electron–ion-
merged beams sections. For the results presented here the
electron beam commonly referred to as the Cooler (Steck
et al. 1990; Pastuszka 1996) was used as a probe beam for
electron–ion collision studies at tunable relative energies. The
second electron beam device is known as the Target (Sprenger
et al. 2004). This device was operated as an electron cooler with
the energy fixed at what is referred to as the cooling energy (Poth
1990). Fixing the Target electron beam energy allowed the ion
beam to be cooled continuously. This inhibits expansion of the
beam due to warming and counteracts the drag force, both of
which arise as the electron energy of the probe beam is varied
during measurement.
A beam of 150 MeV
56
Fe
11+
ions was injected into TSR in
a series of five pulses spaced 0.8 s apart. The ion beam was
merged with the two electron beams described above. Initially,
both the Cooler and Target electron beams were set to the space-
charge-corrected cooling energy of 1460 eV. The center-of-mass
energy spread is limited by the Cooler electron temperature,
which can be described by a flattened Maxwellian distribution
with temperatures in the perpendicular and parallel directions of
typically k
B
T
⊥
= 13.5 meV and k
B
T
= 180 μeV (Kilgus et al.
1992; Schippers et al. 2001). During measurement, the average
ion current was 1–2 μA.
A delay of 2–3 s followed the last injection pulse before
data collection began. This allowed Fe
11+
metastable states to
decay. To estimate the metastable fraction during measurement,
we modeled the level populations as a function of storage
time starting from a Boltzmann distribution with temperature
750 eV, corresponding to the approximate collision energy of
the electrons in the stripping foil as the ions pass through the foil
in the accelerator. The energy levels and Einstein coefficients
of Ralchenko et al. (2008) were used for the calculation. The
longest lived metastable level was the
2
D
5/2
level within the
ground configuration, which has a lifetime of about 0.5s
(Ralchenko et al. 2008). The metastable fraction of the ion beam
at the end of the initial cooling cycle is estimated to be <0.5%.
Products of ionizing electron–ion collisions formed in the
Cooler were separated from the Fe
11+
parent beam by the
first dipole magnet downstream of the interaction section.
Recombination and ionization were measured simultaneously
using separate detectors on opposite sides of the parent ion
beam. The detectors were positioned for maximum signal
collection by stepping each unit horizontally and vertically in
small increments across each product beam. Single or double
ionization events were detected by positioning the ionization
detector to intercept either the Fe
12+
or Fe
13+
product beam.
2
The Astrophysical Journal, 729:76 (8pp), 2011 March 1 Hahn et al.
The ionization detector employs a channel electron multiplier
(CEM;Rinnetal.1982; Linkemann et al. 1995b). A suitable
CEM discriminator level was determined by measuring the total
pulse height distribution. The level was set so that the detection
efficiency of ionization events was essentially unity.
Data acquisition began after the injection and initial cooling
cycle already described. During data collection the relative
energy between the probe electron beam and the ion beam was
varied. Each energy scan consists of ∼250–700 pairs of steps,
one step at the measurement energy and the other at a fixed
reference energy. The total duration of each step was 12–35 ms.
There was a delay of 5–20 ms at the beginning of each energy
step before data were collected in order to allow the power
supply to settle at the new voltage. Data were collected for the
remaining 5–15 ms of each step.
The laboratory electron energies were always chosen to be
higher than the cooling energy and fell between 4000 and
8000 eV. Each energy scan covered a range of 80–2000 V
in the laboratory frame. A fast high-voltage amplifier with a
dynamic range of ±1000 V was used to quickly switch voltages
for the energy scans. This high-voltage amplifier was used in
combination with a slower power supply to lift the fast amplifier
into the voltage range desired for the energy scan, during which
the slower power supply maintained a constant voltage.
The number of pairs of steps in the scan and the range of the
energy scan were chosen to balance the desired energy resolution
against the lifetime of the ion beam during measurement, which
was about 18 s. The energy scans used fell into three broad
categories. Low-resolution overview scans, covering the entire
2000 V range permitted by the fast amplifier, revealed the
general shape of the cross section. Medium resolution scans,
covering an ≈330 eV laboratory energy range, were used to
capture major features of the cross section, such as EA, and to
fill in the details in the overview scan. Finally, high-resolution
scans, covering a range of ≈80 eV in the laboratory frame,
were used to resolve even finer details such as resonances. The
medium and high-resolution scans were normalized to the low-
resolution scans to correct for ion current measurement offsets
as described in Section 4.
In between every two measurement steps, a reference step was
used to estimate the background by measuring the count rate at a
fixed reference energy. For single ionization measurements the
reference energy was set below the EISI threshold for energy
scans up to a center-of-mass energy of about 950 eV. In this case,
the single ionization count rate at the reference energy was only
due to single electron stripping (SES) off the residual gas. In the
case of double ionization, energy scans extending to 1400 eV
were performed with the reference below the EIDI threshold
so that the count rate at reference was due only to double
electron stripping (DES). At energies above 950 (1400) eV,
the limited dynamic range of the fast high-voltage amplifier
prevented us from setting the reference point below the single
(double) ionization threshold. For these higher energies, the
reference point was set to an energy where the cross section had
already been determined from lower energy scans. For all data
runs, the background count rate due to stripping at the reference
energy was corrected to better represent the background at the
measurement energy using the method discussed in the next
section.
Cycles of ion injection, cooling, and energy scan were
repeated for ∼1 hr to improve the statistical accuracy. After
many cycles, the process was repeated for a new energy range.
Energy ranges were chosen to maintain at least 50% overlap
with other scans for high statistical accuracy and to correct
for systematic offsets due to fluctuations in the ion current
measurement calibration.
3. DATA ANALYSIS
The data analysis follows the procedure described in Hahn
et al. (2010). To review briefly, the cross section for single
ionization σ
I
versus energy is obtained from the measured
ionization rate coefficients
σ
I
v
rel
, which are averaged over the
velocity spread
v
rel
of the experiment. Because the center-
of-mass energy spread is very small,
v
rel
v
rel
and the
cross sections can be calculated by dividing the averaged rate
coefficients by the relative velocities. The cross section for single
ionization, in terms of measured quantities, is therefore (see
Appendix A)
σ
I
(E
m
) =
1
v
rel
R
m
I
(E
m
) − R
b
I
(E
m
)
[1 − β
i
β
e
(E
m
)]n
m
e
N
m
i
L
+
σ
I
v
rel
(E
r
)
n
r
e
n
m
e
[1 − β
i
β
e
(E
r
)]
[1 − β
i
β
e
(E
m
)]
. (2)
Here R
m
I
(E
m
) denotes the total single ionization count rate
at the measurement step; R
b
I
(E
m
) denotes the background
single ionization count rate at the measurement step, which
is proportional to the count rate at the reference step R
r
I
(E
r
) as
described in Hahn et al. (2010); L = 1.5 m is the length of the
interaction region for the probe beam; the factor
(1 − β
i
β
e
) is a
relativistic correction where β
i
and β
e
are the ion and electron
velocities normalized by the speed of light, v
i
/c and v
e
/c,
respectively; and E
m
and E
r
are the center-of-mass energies at
measurement and reference, respectively. The electron density
n
e
is of the order of 10
7
cm
−3
and is calculated from the
measured electron current and the geometry of the probe beam
(Kilgus et al. 1992). The total number of stored ions per unit
length N
i
is calculated from the measured ion current. The EISI
rate at the reference energy
σ
I
v
rel
(E
r
) is included in order
to remove the EISI contribution to the background count rate
R
b
I
when the reference energy is above the EISI threshold. The
factor n
r
e
/n
m
e
accounts for the different electron densities at
reference and measurement. The EIDI cross section σ
DI
can
be calculated in the same manner as the EISI cross section by
replacing the single ionization count rates in Equation (2) with
the analogous double ionization rates and the term
σ
I
v
rel
(E
r
)
by the equivalent double ionization term
σ
DI
v
rel
(E
r
).
For all measurements, the electron and ion beams also interact
in the merging and demerging sections on either side of the
straight section in which the electron probe and ion beam co-
propagate. In these sections, the ion and electron beams meet at
an angle causing the relative velocity to be greater than when
the beams are collinear. These toroidal effects are accounted
for using the method of Lampert et al. (1996) to correct an
overestimate of the cross section of ≈20%.
The total ionization detector signal at the measurement energy
is made up of EISI or EIDI plus a stripping background.
We estimate the background R
b
I
using the rate measured at a
reference energy where σ
I
or σ
DI
is either zero or known from
previous measurements so that the stripping rate can be inferred.
For EIDI the background is primarily due to DES, analogous to
the situation in the EISI measurement where the background is
due to SES. For the double ionization measurement, it is possible
for the combination of SES plus EISI in sequence to contribute
to the background, thereby introducing an energy dependence
3
The Astrophysical Journal, 729:76 (8pp), 2011 March 1 Hahn et al.
that cannot be accounted for by measuring the count rate at
the fixed reference energy. However, the expected rate for this
multiple collision process was estimated based on the measured
EISI and SES count rates to be at most about 10
−6
times the rate
of DES. Thus, multiple collisions are extremely rare and can be
ignored in the analysis.
The background rate R
b
I
is proportional to the SES or DES
cross section, the number of ions, and the residual gas density
of the vacuum. The stripping cross sections depend only on v
i
,
which remains constant throughout the measurement. However,
the ion beam decays during the measurement, so there is a
slight difference in ion number related to the time delay between
the measurement step and the reference step. Additionally, the
residual gas density can vary systematically with energy in a
way that seems to be related to the probe beam electron current.
This can also introduce a systematic distortion of the cross
section as a function of energy. Taken all together we expect
that R
b
I
(E
m
) = R
b
I
(E
r
).
We correct for both of the above systematic errors in our
analysis using the method described in Hahn et al. (2010). The
end result of the correction procedure is to adjust the shape
of the cross section by about 3%. The correction uses the
recombination signal at high energies as a proxy for the pressure
to correct the reference count rate so that it better reflects the
true background rate at measurement. This works because at
high energies the recombination signal is dominated by single
electron capture (SEC), which depends on residual gas density
and ion current in the same way that SES and DES do. The
electron capture signal can therefore be used to detect relative
differences in pressure and ion current between the reference
and measurement steps. The analysis of the recombination
data shows that dielectronic recombination (DR) of Fe
11+
contributes less than 10% of the total recombination signal
above the ionization threshold. This measured DR component
is subtracted from the total recombination signal in order to use
only the SEC signal for the correction.
When the reference energy is greater than the ionization
threshold the above procedure has to be modified. It is possible
to account for the decay of the ion beam using direct measure-
ments of the ion current. The ion beam decays exponentially
with a characteristic decay time measured to be ≈18 s. The time
between the measurement and reference steps was about 20 ms.
Therefore, the expected difference between the measured refer-
ence rate and the actual background rate from stripping at the
measurement step due to the decay of the ion beam is only 0.2%.
The effect of the energy-dependent pressure variation was not
corrected for scans where the reference energy is above the ion-
ization threshold. Based on the size of the correction applied
to the low energy scans, we estimate that not correcting single
ionization scans above 950 eV or double ionization scans above
1400 eV introduces a distortion of about 3% in those energy
ranges.
4. UNCERTAINTIES
The statistical uncertainty on the cross section is not the same
for all energies. For single ionization, the statistical uncertainty
is about 10% at 400 eV and drops to 1% by 700 eV as the
number of counts increases with the increasing ionization cross
section. The statistical uncertainty remains at that level until
1400 eV, where it grows to ≈3%, because at such high energies
the cross section is relatively featureless and we performed only
a few low-resolution energy scans. The double ionization cross
section was measured with a few low-resolution scans, and
the cross section is much smaller than for single ionization.
Consequently, the statistical uncertainties for those results are
≈5% on average, with larger uncertainties below 1000 eV where
the cross section and corresponding count rates are very small.
There is a systematic error due to the uncertainty in the stored
ion current measurement. Here the ion current was measured
non-destructively using a beam profile monitor (BPM; Hochadel
et al. 1994). The absolute calibration of this instrument depends
on the residual gas pressure and any electronic drifts. The
calibration drifts with a timescale that appears to be one to
several hours. To correct for the drift of the BPM calibration,
we performed an initial calibration of the BPM. This calibration
was seen to be stable over a 3 hr period. During this time
period, we performed a long range energy scan, which covered
the energy range of 260–950 eV. This scan gives an accurate
measurement for the shape of the cross section as a function
of energy. For all other data runs, we adjusted the ion current
calibration in order to produce agreement with this long energy
range scan. This normalization is possible because all other
quantities were measured much more accurately than the ion
current, so we can attribute discontinuities between the energy
scans, which overlap in energy range by 50% and so should
give identical results, as being caused by shifts in the ion current
calibration. Thus, the details of the cross section can be filled in
without introducing distortions to the shape of the curve from the
normalization. Finally, we quantified the systematic uncertainty
in the magnitude of the cross section by repeating the analysis
of the low-resolution scans using high and low estimates for
the BPM calibration. We estimate the average 1σ systematic
uncertainty from the ion current measurement to be about 12%.
Other sources of systematic error were small compared to that
from the ion current measurement. In the earlier measurements
of Hahn et al. (2010), the ion beam was not cooled during
measurement and the expansion of the ion beam introduced
additional systematic errors. These included possible loss of
detection efficiency due to ions far from the center of the
beam not hitting the detectors and uncertainties in the toroidal
corrections due to the slight differences in the path length
through the merging and demerging sections of the interaction
region experienced by ions at different transverse locations
within the expanded beam. In the present experiment, beam
profile measurements using the BPM showed that constant
cooling limited the ion beam width to ≈1 mm. Since the width
was small compared with the size of the particle detectors,
the signal loss due to the finite width of the ion beam was
insignificant. Similarly, the systematic uncertainty due to the
transverse size of the beam in the merging and demerging
sections was also negligible. The uncertainty on the electron
density is about 3% (Lestinsky et al. 2009). All uncertainties
are summarized in Table 1.
5. RESULTS FOR SINGLE IONIZATION
The EISI ionization cross section for Fe
11+
forming Fe
12+
is shown in Figure 1. The dotted curves in the figure indicate
the 1σ systematic uncertainty due to the ion current calibration.
The figure also shows the experimental results of Gregory et al.
(1987), the fit to that data used in the CIE calculations of Arnaud
& Raymond (1992), and the Flexible Atomic Code (FAC) DW
calculation of Dere (2007).
Figure 1 shows that the crossed beams measurement of
Gregory et al. (1987) is about 30% larger than the current
measurement. This is well outside the uncertainties of either
experiment, which supports the hypothesis that the earlier
4
The Astrophysical Journal, 729:76 (8pp), 2011 March 1 Hahn et al.
Table 1
Sources of Uncertainty
Source Estimated 1σ Uncertainty
Ion current measurement 12%
Electron density 3%
Detection efficiency 3%
Interaction length spread
a
<0.1%
Counting statistics 1%–10%
Background correction
b
0%–3%
Quadrature sum 13%–16%
Notes.
a
Although negligible, this uncertainties is listed here for
comparison with the similar experiment of Hahn et al.
(2010) where the expansion of the ion beam introduced
small additional uncertainties. In the present experiment,
continuous cooling of the ion beam inhibited beam expansion
making these measurements more precise.
b
The 3% uncertainty applies to data for E>950 eV for
single ionization and E>1400 eV for double ionization
where the background correction could not be applied.
measurement had a significant metastable population in the ion
beam. Consequently, CSD calculations that relied on those data
are likely to be inaccurate (e.g., Arnaud & Raymond 1992;
Mazzotta et al. 1998). A recent CSD calculation by Bryans et al.
(2009) used the EISI cross section from the FAC calculation of
Dere (2007). Figure 1 shows that this calculation is closer to the
present experimental results, but significant differences remain.
In the low energy range from the ionization threshold at
approximately 330 eV up to about 690 eV, a comparison of
our experimental results and theory indicate that the ionization
cross section is dominated by direct ionization. However, the
experimental cross section increases faster near the threshold
than predicted by the calculations. There are two related effects
that can account for the faster than expected increase. The cross
section may be enhanced due to electron impact excitation
of 3s electrons to states that relax by autoionization. This
ionization mechanism has also been suggested for other P-like
ions (Gregory et al. 1983; Mueller et al. 1985; Yamada et al.
1988). Based on an estimate using the LANL Atomic Code suite
(Magee et al. 1995
4
), this mechanism is energetically possible
for excitation to n 8 and is sufficient to account for the
increased cross section if the branching ratio for autoionization
compared to radiative stabilization is large enough. However,
we are unaware of any published data for either EA from
3s excitation or the relevant branching ratio. There is also
a systematic effect from field ionization that could partially
account for the discrepancy. The magnetic fields in TSR cause
electric fields in the rest frame of the ions. If a collision
excites an electron to a high enough n level, it can be field-
ionized by the motional electric field generated in the first
dipole magnet downstream of the interaction region (Schippers
et al. 2001). Here the semi-classical onset for field ionization
is n>44. Excitation of a 3p electron to n>44 can lead to
field ionization that systematically increases the measured cross
section. Excitation of a 3s electron to n>44 also leads to
field ionization in the experiment, but we expect these states
primarily to ionize through EA even in the absence of external
fields. While the effect of these processes on the cross section
is most obvious near the ionization threshold, they also increase
the measured ionization cross section for all higher energies.
4
See also http://aphysics2.lanl.gov/tempweb/
Figure 1. EISI cross section for Fe
11+
forming Fe
12+
is shown here. The filled
circles indicate the experimental values and the error bars at selected points
illustrate the 1σ statistical uncertainty. The dotted curves show the 1σ range of
systematic uncertainty from the calibration of the ion current measurement. The
diamonds display the experimental results of Gregory et al. (1987)andafitto
that data that was used in the CIE calculations of Arnaud & Raymond (1992)is
indicated by a dashed line. The distorted wave calculation of Dere (2007)using
the FAC code is denoted by the solid curve.
The relative importance of EA versus field ionization can
be estimated from the dependence of the excitation cross
section on the n to which the electron is excited. In the Bethe
approximation, the electron impact excitation cross section for
dipole allowed transitions from level i to level j is given by (Van
Regemorter 1962)
σ
exc,ij
=
8π
√
3
I
H
EE
ij
f
ij
gπa
2
0
, (3)
where E is the electron collision energy and
E
ij
is the thresh-
old energy for the transition, both measured in Rydbergs, I
H
is
one Rydberg, f
ij
is the oscillator strength, g is a Gaunt factor,
and a
0
is the Bohr radius. For large n, the excitation energy
E
ij
is approximately constant and equal to the ionization en-
ergy. Thus, for a given collision energy σ
exc,ij
∝ f
ij
.Forlarge
n, the oscillator strength falls off as 1/n
3
(Bethe & Salpeter
1957). Therefore, the ratio of the cross section for excitation
to field-ionizing levels relative to autoionizing levels is approx-
imately
(2
∞
n=44
1/n
3
)/(
∞
n=8
1/n
3
) = 0.06. The factor of
two roughly accounts for the fact that excitation of either a 3s
or a 3p electron can lead to field ionization but only excitation
of 3s can lead to autoionization. This estimate suggests that the
systematic contribution to the measured ionization cross section
from field ionization is small relative to EA, on the order of a
few percent only, but detailed calculations taking into account
the branching ratios are needed to confirm this.
From the threshold behavior of the cross section near
700 eV (Figure 2), we infer that EA of n = 2 electrons
makes up about 25% of the total cross section at high energies.
Pindzola et al. (1986) predict EA from 2p → 3p excitations
at 709.3 eV and from 2p → 3d excitations at 763.8eV.This
roughly corresponds with the experimentally observed increase
in the cross section beginning at ≈690 eV. The experimentally
measured EA from n = 2 excitations could also be system-
atically enhanced by field ionization, which inhibits radiative
stabilization for excitation to n>44, but this effect should be
very small since such states are expected to autoionize even
5
