Differential energy measurement between He- and Li-like uranium intra-shell transitions

Abstract

We present the first clear identification and highly accurate measurement of
the intra-shell transition $1s2p\, ^3P_2 \to 1s2s\, ^3S_1$ of He-like uranium
performed via X-ray spectroscopy. The present experiment has been conducted at
the gas-jet target of the ESR storage ring in GSI (Darmstadt, Germany) where a
Bragg spectrometer, with a bent germanium crystal, and a Ge(i) detector were
mounted. Using the ESR deceleration capabilities, we performed a differential
measurement between the $1s2p\, ^3P_2 \to 1s2s\, ^3S_1$ He-like U transition
energy, at 4510 eV, and the $1s^22p\ ^2P_{3/2} \to 1s^22s\, ^2S_{1/2}$ Li-like
U transition energy, at 4460 eV. By a proper choice of the ion velocities, the
X-ray energies from the He- and Li-like ions could be measured, in the
laboratory frame, at the same photon energy. This allowed for a drastic
reduction of the experimental systematic uncertainties, principally due to the
Doppler effect, and for a comparison with the theory without the uncertainties
arising from one-photon QED predictions and nuclear size corrections.

Full text

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arXiv:1106.4155v1 [physics.atom-ph] 21 Jun 2011
Differential energy measurement between He- and
Li-like uranium intra-shell transitions
M. Trassinelli1, A. Kumar2, H.F. Beyer3, P. Indelicato4, R. M¨ artin3,5,
R. Reuschl1, Y.S. Kozhedub6, C. Brandau3, H. Br¨ auning3, S. Geyer3,
A. Gumberidze7, S. Hess3, P. Jagodzinski8, C. Kozhuharov3,
D. Liesen3, U. Spillmann3, S. Trotsenko9, G. Weber3,5,
D.F.A. Winters3,5, Th. St¨ ohlker3,5,9
1Institut des NanoSciences de Paris; CNRS; Univ. Pierre et Marie Curie - Paris 6, Paris,
France
2Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai, India
3GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, Darmstadt, Germany
4Laboratoire Kastler Brossel,´Ecole Normale Sup´ erieure; CNRS; Univ. Pierre et Marie Curie -
Paris 6, Paris, France
5Physikalisches Institut, Univ. Heidelberg, Heidelberg, Germany
6Department of Physics, St. Petersburg State Univ., St. Petersburg, Russia
7ExtreMe Matter Institue, Darmstadt, Germany
8Institute of Physics, Jan Kochanowski Univ., Kielce, Poland
9Helmholtz-Institut Jena, Jena, Germany
E-mail: martino.trassinelli@insp.jussieu.fr
Abstract.
intra-shell transition 1s2p3P2 → 1s2s3S1 of He-like uranium performed via X-ray spectroscopy.
The present experiment has been conducted at the gas-jet target of the ESR storage ring in GSI
(Darmstadt, Germany) where a Bragg spectrometer, with a bent germanium crystal, and a Ge(i)
detector were mounted. Using the ESR deceleration capabilities, we performed a differential
measurement between the 1s2p3P2 → 1s2s3S1 He-like U transition energy, at 4510 eV, and the
1s22p2P3/2→ 1s22s2S1/2Li-like U transition energy, at 4460 eV. By a proper choice of the ion
velocities, the X-ray energies from the He- and Li-like ions could be measured, in the laboratory
frame, at the same photon energy. This allowed for a drastic reduction of the experimental
systematic uncertainties, principally due to the Doppler effect, and for a comparison with the
theory without the uncertainties arising from one-photon QED predictions and nuclear size
corrections.
We present the first clear identification and highly accurate measurement of the
1. Introduction
Heliumlike heavy ion spectroscopy represents an unique probe of relativistic and Quantum
Electrodynamics (QED) effects on the electron-electron interaction in the domain of strong fields.
As compared to a one-electron and many-electron ions, these ions are the simplest multibody
systems where theory can make predictions in a rigorous way. Here we present the first clear
identification of the intra-shell transition 1s2p3P2 → 1s2s3S1 of He-like uranium performed
via X-ray spectroscopy.In addition, using the deceleration capabilities of the ESR storage
ring, we performed a differential measurement between this transition and the analog transition

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Figure 1.
arrangement at the gas-jet target of the
ESR storage ring.
and a focusing Bragg spectrometer are
simultaneously viewing the X-ray source
defined by the overlap of the circulating ion
beam with the gas-jet.
Sketch of the experimental
A Ge(i) detector
1s2p 3P2 - 1s2s 3S1
Figure 2. The X-ray spectrum, originating from
43.57 MeV/u He-like uranium ions, as recorded by
the Ge(i) detector. The energies correspond to the
emitter frame. The inset shows a magnification of
the region around the3P2→3S1transition [1].
1s22p2P3/2→ 1s22s2S1/2of Li-like uranium. In this paper we will focus on some aspects of this
measurement and in particular on its outlooks. A more complete description of the experiment
can be found in Ref. [1].
2. Description of the experimental setup and data acquisition
The experiment was performed at the GSI experimental storage ring ESR in August 2007. Here,
a H-like uranium beam with up to ∼ 4×107ions was stored, cooled, and decelerated to an energy
of 43.57 MeV/u. Excited He-like ions were formed by electron capture during the interaction
of the ion beam with a supersonic nitrogen gas-jet target. At the selected velocity, electrons
are primarily captured into shells with principal quantum number of n ≤ 20, which efficiently
populate the n = 23P2state via cascade feeding. This state decays to the n = 23S1state via an
electric dipole (E1) intra-shell transition (branching ration 30%) with the emission of photons
of an energy close to 4.51 keV.
For the X-ray detection, we used a standard Ge(i) solid-state detector and a new Bragg
spectrometer specially designed for accurate spectroscopy of fast ions. The two instruments are
complementary: The Ge(i) detector has a high detection efficiency and covers a wide spectral
range with a moderate spectral resolving power. The focusing crystal spectrometer serves as an
accurate wavelength comparator in a narrow wavelength interval. The Ge(i) solid-state detector
and the Bragg crystal spectrometer were mounted under observation angles of 35◦and 90◦,
respectively. Both instruments were separated from the ultra-high vacuum of the gas-target
chamber by 100µm-thick beryllium windows transparent for the few keV X rays. A scheme of
the experimental setup is presented in Fig. 1. The crystal spectrometer [2] was mounted in
the Johann geometry in a fixed angle configuration allowing for the detection of X rays with a
Bragg angle Θ around 46.0◦. The spectrometer was equipped with a Ge(220) crystal cylindrically
bent, with a radius of curvature of R = 800 mm, and an X-ray CCD camera (Andor DO420), as
position sensitive detector, positioned on the Rowland circle (the focusing position of the Johann
spectrometer). The Rowland-circle plane of the spectrometer was placed perpendicular to the

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ion-beam direction. In such a configuration the spectral lines appear slanted in the image plane
of the spectrometer with their slope proportional to the ion-beam velocity. For a minimization of
the systematic effects due to the ion velocity and alignment uncertainties, the observation angle
θ = 90◦was chosen for the crystal spectrometer. The value of the ion velocity was selected such
that the photon energy, E in the ion frame, was Doppler-shifted to the value Elab= 4.3 keV in
the laboratory frame. This value of Elabwas chosen to have the He-like uranium spectral line
position on the CCD close to the position of the 8.6 keV Kα1,2lines of zinc, which were observed
in second order diffraction. The zinc lines were used to monitor the spectrometer stability and
they were produced by a commercial X-ray tube and a removable zinc plate between the target
chamber and the crystal. Additional information on the experimental setup can be found in
Ref. [1].
For the accurate energy measurement of the He-like intra-shell transition energy, the
1s22p2P3/2→ 1s22s2S1/2transition in Li-like U, which has an energy of 4459.37 ± 0.21 eV
[3, 4] was chosen as calibration line. Similar to the He-like system, the Li-like ions were obtained
by electron capture into He-like uranium ions. To match the energy of the He-like transition,
an energy of 32.63 MeV/u was selected to Doppler-shift the Li-like transition.
The data were acquired during a total period of about 4.5 days. Survey spectra were recorded
by the Ge(i) detector. Here the 23P2→ 23S1transition was easily identified close to the lines
originating from n′→ n transitions (see Fig. 2) with n = 3 − 4 [1]. The measurement with
the crystal spectrometer provided a much higher accuracy for the spectral line position. In this
case, the observable energy range, principally limited by the ion beam diameter and its distance
from the crystal, was in the order of 4308±40 eV. For the transition in He-like uranium, a total
number of about 300 counts in an effective acquisition time of ∼ 24 hours was accumulated. For
the Li-like ions, about 160 counts in ∼ 5 hours were recorded. These spectra are characterized
by a very low background drastically reduced only by the energy cuts and cluster analysis of the
CCD raw data.
High resolution energy spectra were obtained by projecting the transition lines from the
Bragg spectrometer CCD (Fig. 3 left) on the dispersion axis (the x-axis in the figure), after the
slope correction due to the Doppler effect (Fig. 3 right). We note that the shape of the lines
-150
-100
-50
0
50
100
0 200 400
x-axis (channels)
600 800 1000
y-axis (channels)
0
2
4
6
8
10
0 200400
x-axis (channels)
600 8001000
Counts
Figure 3. Left: Image of the He-like uranium intra-shell transitions on the Bragg spectrometer
position sensitive detector. The transition energy increases with increasing x-position. The
slightly negative slope of the line is due to the relativistic velocity of the fast ions. Right:
The corresponding high resolution energy spectrum from the projection on the dispersion axis
(x-axis) [1].

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corresponding to the fast ion emission is slightly asymmetric. Such an asymmetry might be
caused by a non-uniform X-ray reflectivity of the crystal surface. After the experiment, a survey
of the crystal surface by the X-ray Optics Group from the Institute for Optics and Quantum
Electronics in Jena indeed revealed a non-uniformity.
3. Results and discussions
Starting from the Bragg law, the energy of the He-like U transition EHeis related to the energy
of the calibration line ELiby the simple formula
EHe≈ ELiγHe
γLi
?
1 +
∆x
D tanΘB
?
,
(1)
where ∆x = xHe− xLi denotes the distance between the He- and Li-like U line positions on
the CCD and D the distance between crystal and CCD. γHe = 1.04677 and γLi = 1.03503
are the Lorentz factors corresponding to the velocities of the stored H- and He-like ions,
respectively. Their values are determined by the accurately known voltages of the electron
cooler of the ESR [5]. From the experimental measurement of ∆x, using Eq. (1), the energy of
the 1s2p3P2→ 1s2s3S1transition was determined to be
EHe= 4509.71 ± 0.48stat± 0.86systeV,
(2)
The first uncertainty is statistical and the second one is due to the systematic uncertainties
(quadratically summed).Principal contributions to the last term are i) the asymmetric
response function of the spectrometer, ii) the calibration line and iii) the uncertainty of the
observation angle. All other contributions, due to the accuracy of the electron cooler voltage,
the crystal-detector distance, etc., are negligible. A more extended discussion on the systematic
uncertainties can be found in Ref. [6]. The systematic effect introduced by this asymmetry
has been estimated by comparing the results of the line position measurement obtained from
different approaches (median distribution, and a series of fit adjustments). This contribution
results to be the largest systematic uncertainty of 0.83 eV. The uncertainty of the observation
angle, equal to 0.04◦, contributes with 0.11 eV and it is due to the limited position accuracy of
the gas-jet position (±0.5 mm) combined with the Doppler shift of the ion emission. We note,
the use of the fast Li-like ion transition as calibration, instead of a stationary source, like the
Zn Kα lines, causes a reduction of such a systematic uncertainty from 0.9 to 0.1 eV [6].
The measured transition energy for He-like uranium agrees well with all more recent
theoretical predictions, which reflect different approaches:
configuration Dirac-Fock calculation with QED corrections included [1, 7], and 4509.86±0.07 eV,
from an ab initio calculation [1, 8, 9] and other older calculations [10, 11, 12] (see Fig. 4 (left)).
The accuracy of the present experiment, equal to 0.99 eV, is on the same order as the QED
effects on the electron-electron interaction, 0.76 eV for this transition, but is too large to be
sensitive to the two-loop QED effects that contributes with 0.20 eV [8, 9].
A more significant test of the electron-electron interaction in strong Coulomb fields, comes
from the comparison between the measured He- and Li-like transition energy difference and
the corresponding theoretical predictions. From the experimental side, the energy difference
eliminates the uncertainty contribution due to the calibration line (0.21 eV), whereas, from the
theoretical side, the systematic effects due to the one-electron QED and nuclear size uncertainties
are canceled out. In this case we find
4510.30 eV, using a multi-
EHe-Li= 50.34 ± 0.48stat± 0.84systeV.
(3)
In contrast to the absolute value of the transition energy, the difference carries an experimental
systematic uncertainty, peak asymmetry excluded,that is reduced from 0.24 to 0.11 eV, where

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4508.5
4509.0
4509.5
4510.0
4510.5
4511.0
EHe (eV)
Drake 1988
Chen 1993
Plante 1994
Artemyev 2005
Kozhedub 2008
Indelicato 2008
This work
49.0
49.5
50.0
50.5
51.0
51.5
52.0
EHe-Li (eV)
Kozhedub 2008
without 2e QED
Kozhedub 2008
Indelicato 2008
This work
Figure 4.
U intra-shell transition energy (left) and its relative measurement with respect to the Li-like
transition (right). In these figures the reference of the different predictions are: Drake 1988 [10],
Chen 1993 [11], Plante 1994 [12], Artmyev 2005 [9], Kozhedub 2008 [8] and Indelicato 2008 [7].
Comparison between our result and different theory approaches for the He-like
in practice only the observation angle accuracy contributes. This value is in agreement with
the theoretical predictions: 49.96 eV [1, 7] and 50.30 ± 0.03 eV [1, 8, 9] where the QED
effects on the electron-electron interaction contribute with 1.66 eV. For a visual comparison
see Fig. 4 (right), where the role of the two-electron QED effect is presented. As in the absolute
transition energy, the accuracy of the present experiment is on the edge to be sensitive to
QED effects. However, in future experiments, improved and verified analyzer crystals together
with an extended acquisition time will allow for more stringent tests of the two-electron QED
contributions in heavy highly charged ions. A more extended discussion on the possible outlooks
is presented in the next section.
4. Potential improvements
From the analysis of the different uncertainty contributions, possible improvements of the present
experiment can be clearly inferred. As presented in the previous section, the main source of
accuracy limitation is due to the quality of the Germanium crystal employed for the Bragg
spectrometer. A new crystal carefully selected and X-ray optically characterized could allow to
eliminate completely such a systematic effect. In the relative measurement, the second largest
contribution of the systematic uncertainties comes from the alignment accuracy of the crystal
spectrometer with respect to the gas-jet position. This uncertainty can be reduced considerably
by the use of two twin Bragg spectrometers at observation angles of +90◦and −90◦. An accuracy
better than 0.01◦could be achieved on the alignment of the two spectrometer with respect to
each other. In this case, the position of the gas-jet with respect to the spectrometers axis can
be used for compensation by comparing the energy measurement from each spectrometer. A
reduction of the uncertainty from 0.11 eV to about 0.02 eV can be expected. The use of a second
spectrometer will also improve the statistical uncertainty. A larger crystal radius of curvature
will enhance the spectrometer dispersion implying a reduction of instrumental efficiency that
can be compensated by a larger position sensitive detector area, limited to 26.6×6.6 mm2in the
present experiment. Finally, the simplest improvement can come by a longer acquisition time
that, we remember, was limited in the present experiment to only 4.5 days. A reduction of the
statistical uncertainty from 0.5 to 0.1 eV can be expected.
With these upgrades, a future experiment could provide a critical test of the theoretical

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predictions for the interaction between bound electrons in the presences of a strong Coulomb
field where, in particular, the QED contributions could be accurately measured. In the present
experiment we limited to compare He- and Li-like heavy ions. In the future, this study could be
extended to additional atomic systems, like Be- and B-like ions, applying the same experimental
technique strongly based on the Doppler tuning of the X-ray energy in the laboratory frame.
5. Conclusions
In summary, we report the first clear identification of the 1s2p3P2→ 1s2s3S1transition in He-
like uranium. In addition we measured the transition energy of such a transition with a relative
uncertainty of 2 × 10−4, which is currently the most accurate test of many-body and QED
contributions in excited levels of very heavy He-like ions. Differential measurements between
different charge states of the same fast ion pave the way for increased sensitivity via the reduction
of the systematic uncertainty in both the experimental and the theoretical side. We also discuss
several possible improvements that can be applied to the present experiment to perform more
stringent tests on QED and relativistic effects in few-electrons heavy highly charged ions.
Acknowledgments
We thank V. Shabaev, A.N. Artemyev and A. Surzhykov for interesting discussions and
theoretical support. We thank O. Wehrhan, H. Marschner and E. F¨ orster for the characterization
of the spectrometer crystal. The close collaboration and support by the members of the
ESR team, the A. von Humboldt Foundation (M.T.), the DAAD (A.K., No.: A/05/52927)
and I3 EURONS (EC contract no.506065) are gratefully acknowledged.
partially supported by Helmholtz Alliance HA216/EMMI. Institut des Nanosciences de Paris
and Laboratoire Kastler Brossel are Unit´ e Mixte de Recherche du CNRS n◦7588 and n◦8552,
respectively.
This work was
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