High Resolution Recombination Measurements of Stored
Ions
M. Fogle*, N. Badnell†, N. Eklöw*, E. Lindroth*, S. Madzunkov*, T. Mohamed*,
R. Schuch*, and M. Tokman*
*
Department of Atomic Physics, Stockholm University, Alba Nova (SCFAB), SE106 91 Stockholm, Sweden
†
Department of Physics and Applied Physics, University of Strathclyde, G4 0NG Glasglow, UK
Abstract. The accuracy obtained in electron-ion recombination experiments at storage rings has reached a level which
allows strenuous tests of theoretical models and the ability to derive accurate, and useful, information for applications
such as plasma modeling and diagnostics. Here we present two such recombination experiments performed at the heavy
ion storage ring CRYRING. First, we investigated the possibility to derive a temperature dependent plasma rate
coefficient for Na-like Ni, which has been observed in emission lines from active solar regions and laboratory plasmas.
Second, we determined the 2s1/2-2p1/2 energy splitting in Li-like Kr. Such a highly charged ion exhibits large QED
contributions (~1.5 eV) which are difficult to represent in theoretically calculations. The experimental value for the
splitting was determined to within 8 meV while the theoretically determined value is only accurate to within 19 meV.
determine an accurate value for the 2s1/2-2p1/2 energy
splitting. In doing so, we also investigated the 2s Lamb
shift and quantum electrodynamical (QED) effects to a
higher precision than available theory. The QED
effects for such an ion are on the order of ~1.5 eV.
INTRODUCTION
Radiative recombination (RR) is a non-resonant
process in which a continuum electron is captured to a
bound state with the simultaneous emission of a
photon.
EXPERIMENT
Dielectronic recombination (DR) is a two-step
resonant process in which a continuum electron is
captured to some bound state while a target electron is
excited forming a doubly excited state. The subsequent
step involves the radiative de-excitation of this doubly
excited state to a singly excited state which lies below
the autoionization threshold.
The experiments discussed in this paper were
performed at the heavy ion storage ring CRYRING.
The ring is coupled with an electron cooler which also
serves as an electron target for recombination studies.
The ions are cooled by a velocity-matched electron
beam, i.e., zero center-of-mass (CM) energy between
the ions and electrons. DR resonances are investigated
by varying the electron gun cathode potential causing a
non-zero CM energy which can be controllably
scanned over an energy range of interest. Charge
changed recombined ions are then detected with a
unity efficiency surface barrier detector after the first
dipole magnet downstream from the cooler.
The study of electron-ion recombination plays an
important role in many aspects of physics. In the case
of Na-like Ni, there have been many observations of
emission lines of this ion from plasmas, e.g., the solar
corona [1] and tokamak fusion devices [2]. The
recombination rate coefficients are therefore of
interest, especially in a temperature dependent format
where they are more readily applicable. Moreover,
applications to atomic structure are also of interest
with regards to recombination, since DR deals with
doubly excited states. In this study, we were able to
Data analysis involves corrections for space charge
effects inside the interaction region of the cooler and
drag force effects on the ion energy as the cathode
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
156
Rate Coefficient [cm3 s-1]
Rate Coefficient x 10-9 [cm3 s-1]
6
5
4
3
2
1
0
1
2
3
4
5
6
10-8
10-9
Energy [eV]
FIGURE 1. Comparison of AUTOSTRUCTURE (solid
curve) and RMBPT (dashed) calculations for the low energy
resonances of Ni17+. These are the first and strongest DR
resonances for this ion corresponding to the resonances
3p3/210l and 3p1/211l, respectively from zero energy.
10-5
10-4
10-3
10-2
10-1
Energy [eV]
FIGURE 2. The RR spectrum from Ni17+. The experimental
data is fit with the rate coefficient derived from Kramers’
theory with an effective charge of 22.
potential is ramped. From these corrections, the CM
energy scale can be determined. The final task is to
convert the number of recorded counts to a rate
coefficient which is primarily dependent on the
number of stored ions, the ring circumference, the
electron cooler interaction length, and the electron
density.
Na-like Ni
n=50. Such an effect is inherent to the experiment and
does not represent what would occur in a “natural”
plasma. For this reason, we have chosen to extrapolate
the rate at the series limits with the
AUTOSTRUCTURE code [4]. This essentially
provides a no-field rate coefficient which can then be
used to determine the plasma rate coefficients.
AUTOSTRUCTURE has been used in many studies of
recombination [5], particularly those concerned with
plasma recombination rate coefficients, such as for
astrophysical plasmas. It is based on a many-body
Breit-Pauli description of the ion. If one compares
such a calculation to a more elaborate method of the
many-body problem, such as relativistic many-body
perturbation theory (RMBPT) [6], one can see, from a
comparison of the lower energy region (0-6 eV) in Fig.
1, that this method describes this particular ion very
well.
The primary goal of this experiment was to
determine the temperature dependent plasma
recombination rate coefficient. The spontaneous RR
rate and DR resonances were investigated up to the
3p1/2 and 3p3/2 series limits, at 38.7 and 42.5 eV
respectively. Resonances are denoted 3pjnl, where 3pj
indicates an excitation from 3s1/2 to 3pj and nl is the
quantum state for the recombined electron. Due to
ionization of Rydberg states in the v×B field as the ion
traverses the dipole magnet, the rate at the series limits
is truncated. We estimate that this cutoff occurs at
The experimental data in the RR region, as seen in
Fig. 2, exhibits a rate enhancement that is typical to
storage ring experiments. The source of this rate is the
topic of much investigation, but it is thought to be
linked to fields in the cooler interaction region. From
studies of bare ions [7], it has been observed that this
enhancement does not effect the energy region above
~1 meV and theory agrees perfectly. For this reason,
we have fit the experimental data with the rate
coefficient derived from the Kramers’ cross section [8]
with an effective charge of 22, as advocated by [9].
For the Kr33+ experiment, a similar cathode
scanning scheme was employed, however an
alternative technique [3] was used to account for space
charge and drag force effects. Using this technique, we
improved the measurement accuracy of the 2p1/215l
DR resonances from 30 meV to 8 meV.
RESULTS AND DISCUSSION
157
Rate Coefficient x 10-9 [cm3 s-1]
3
-1
Rate Coefficient [cm s ]
10-10
10
-11
10
6 x10
10
4
5
Temperature [K]
10
6
12
Exp.
10
QED
screening
H-like QED correction (~1.73 eV)
8
6
4
2
0
3.7 3.8 3.9
-9
4.6
4.8
5.0
5.2
5.4
5.6
Energy [eV]
FIGURE 4. The 2p1/215l resonances of Kr33+. The solid
curve is the result of a RMBPT calculation with the
consideration of QED. The H-like QED contribution and
screening effect are shown by the arrow lines. The QED
uncertainty is shown by the vertical bar pair labeled “QED”.
The experimental uncertainty is shown by the vertical bar
pair labeled “Exp.”.
4
2
0
1
10
100
rate coefficients can be seen in the upper part if Fig. 3.
As a comparison, a calculation based on the Burgess
formula [10] was made. The result of this calculation
is also included in Fig. 3.
Energy [eV]
FIGURE 3. (upper) Temperature dependent plasma
recombination rate coefficients. The RR rate coefficient is
represented by the thin solid line. The extrapolated no-field
DR rate coefficient is represented by the thick solid line
while the dashed-dotted line represents the experimental
truncated rate coefficients. A Burgess formula calculation is
included for comparison, represented by the dashed line.
(lower) The DR resonances in the energy range investigated.
The extrapolated AUTOSTRUCTURE results are
represented by the solid line. A log scale, with 1 eV ≈ 104 K,
has been used to given an idea of how the resonances
contribute to the plasma rate coefficients.
Li-like Kr
Since QED contributions scale as Z4, it is easily
seen that highly charge ions can have sizeable QED
contributions to energy levels. Accurate values for the
H-like QED contribution can be made, however, in the
case of many electron systems, such as Kr33+, a
screening effect due to electron-electron correlation
must be taken into account. Since the experimental
data for QED contributions is sparse for such heavy,
many electron systems, these values are usually scaled
from nearby, similar ions [11].
We have used this fit in determining the plasma rate
coefficient for RR as it is unknown if such
enhancement effects can be regarded in the same
manner for natural plasmas.
The bottom section of Fig. 3 illustrates the DR
resonances in the energy range investigated. These
resonances, as well as the RR fit, were convoluted
with Maxwellian temperature distributions for electron
temperatures ranging from 103-107 K. These
distributions take the form,
P ( E , Te ) =
π
 −E 
2 E 1/ 2

exp
(k BTe ) 3 / 2
 k BTe 
1/ 2
In this experiment [3], we have measured the
2p1/215l DR resonances of Li-like Kr. These are the
lowest in energy and strongest resonances, thus aiding
in the statistical evaluation and fitting of the resonance
peaks. Figure 4 shows the resonances in this energy
range. The theoretical solid curve was calculated with
RMBPT utilizing the complex rotation method. QED
contributions are then added to the result of the
calculation. The size of the H-like QED contribution
(~1.73 eV) and screening (~0.20 eV) are also indicated
in the figure. The QED uncertainty, as shown by the
vertical bar pair labeled “QED”, is 0.019 eV. This,
again, is primarily from the uncertainty in the scaling
method used to determine the screening. By a more
(1)
where E is the energy, i.e., the resonance energy, and
Te is the electron temperature. The resulting plasma
158
2s1/2-2p1/2 energy splitting. The accuracy of the
experiment (8 meV) exceeds that obtained by theory
(19 meV) and thus opens the door to testing theoretical
methods of incorporating QED contributions.
elaborate experimental method, than is normally used
for such experiments, we were able to achieve an
experimental uncertainty, indicated by the vertical bar
pair labeled “Exp.”, of only 0.008 eV. This then
allowed us to make a precise determination of the
energy of the large resonances peak at 5.37 eV and
furthermore to extract the 2s1/2-2p1/2 energy splitting,
which has an accuracy greater than that available from
theoretical methods! The 2s1/2-2p1/2 energy splitting is
determined by the expression,
E ( 2 s1 2 − 2 p1 2 ) = Ee + E (15l ) + Ecorr
ACKNOWLEDGMENTS
The authors would like to thank the staff of Manne
Siegbahn Laboratory for their efforts in the operation
of CRYRING. This work was supported by the
National Research Council and the Knut and Alice
Wallenberg Foundation. T.M. would like to thank the
Egyptian government for financial support.
(2)
where Ee is the electron energy, i.e., the energy of a
resonance on the energy scale in Fig. 4, E(15l) is the
energy of the electron in the 15l state, and Ecorr
constitutes the corrections for correlation between the
Rydberg and excited electrons and the polarization of
the core electrons. These last two terms can be
calculated precisely, i.e., with more precision than the
experimental determination of the resonance peak. We
have determined the 2s1/2-2p1/2 energy splitting to be
71.243(8) eV where theoretical prediction is
71.248(19) eV.
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CONCLUSION
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159