FOCAL: X-ray optics for accurate spectroscopy

Spectrochimica Acta Part B 59 (2004) 1535 – 1542 www.elsevier.com/locate/sab

FOCAL: X-ray optics for accurate spectroscopyB H.F. Beyera,*, Th. Stfhlkera, D. Banasb, D. Liesena, D. Protic´c, K. Beckerta, P. Bellera, J. Bojowaldc, F. Boscha, E. Ffrsterd, B. Franzkea, A. Gumberidzea, S. Hagmannh, J. Hoszowskae, P. Indelicatof, O. Kleppera, H.-J. Klugea, St. Kfnigd, Chr. Kozhuharova, X. Maa, B. Manilg, I. Mohosc, A. Orsˇic´-Muthiga, F. Noldena, U. Poppa, A. Simionovicie, D. Sierpowskib, U. Spillmanna, Z. Stachurab, M. Stecka, S. Tachenova, M. Trassinellif, A. Warczakb, O. Wehrhanf, E. Zieglere a GSI, Planckstraße 1, D-64291 Darmstadt, Germany Institute of Physics, Jagiellonian University, PL-30059 Cracow, Poland c FZ Ju¨lich, Institut fu¨r Kernphysik, Germany d Inst. fu¨r Optik und Quantenelektronik, F. Schiller-Universita¨t, D-07743 Jena, Germany e ESRF, F-38043 Grenoble, France f Lab. Kastler Brossel, Universite´ P. et M. Curie, F-75252 Paris Ce´dex 05, France g CIRIL-GANIL, rue Claude Bloche, F-14070 Caen, France h IKF, University of Frankfurt, D-60486, Frankfurt, Germany b

Received 26 September 2003; accepted 19 March 2004 Available online 11 September 2004

Abstract A crystal spectrometer has been constructed in the Focusing Compensated Asymmetric Laue geometry covering the energy range between 30 and 120 keV. We summarize the crystal optics and show the usefulness of the instrument for spectroscopy of stationary and fast moving X-ray sources. Results are reported from several tests employing a 169Yb gamma-ray source and the Lyman radiation of one-electron Au78+ ions travelling at a velocity corresponding to b=v/c oc0.44. D 2004 Published by Elsevier B.V. PACS: 32.30.Rj; 29.40.Wk; 29.40.Gx; 31.30.Jv Keywords: X-ray spectroscopy; X-ray optics; Fast-beam spectroscopy; Position-sensitive detectors

1. Introduction X-ray spectroscopy of K-shell transitions of very heavy one-electron ions like Au78+ or U91+ can be used to test the fundamental theory of bound electronic systems in the domain of strong electric fields. The inner electrons of atoms B This paper was presented at the International Congress on X-Ray Optics and Microanalysis (ICXOM XVII), held in Chamonix, Mont Blanc, France, 22-26 September 2003, and is published in the special issue of Spectrochimica Acta Part B, dedicated to that conference. * Corresponding author. GSI, Atomic Physics, Planckstrasse, Darmstadt 64291, Germany. Tel.: +496159712140; fax: +496159712901. E-mail address: [email protected] (H.F. Beyer).

0584-8547/$ - see front matter D 2004 Published by Elsevier B.V. doi:10.1016/j.sab.2004.03.023

with a high nuclear charge are exposed to such strong fields that a considerable part of their binding energy is determined by quantum-electrodynamic (QED) processes. Despite its great success for light systems, the QED theory is less well tested for electrons in strong fields. The spectroscopy of those unique systems available in accelerator-based experiments with their limited source strength was the motivation for the development of new X-ray optics suitable for the ~30–120keV energy range. The methods described in this publication can be transferred to all applications aiming at an accurate spectral measurement insensitive to the source topology. In the FOcusing Compensated Asymmetric Laue (FOCAL) geometry [1], a curved crystals with a small

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asymmetry angle is employed. The X-ray source is placed on the convex side of the cylindrically curved crystal. Two simultaneous spectra appear symmetrically to the optical axis running through the crystals apex and pointing in the direction of the lattice planes used for the Bragg reflections. The ratio of the asymmetry angle to the radius of curvature determines the resolving power and the integrated reflectivity. Thus, to a large extent, resolution and detection efficiency can be adapted to the requirements of a given X-ray source. General features of FOCAL comprise a large useful wavelength range, high linearity, self alignment through double spectra and easy adaption to stationary and to fast moving sources. A FOCAL spectrometer has been constructed at GSI with a Si (220) crystal having a 2-m radius of curvature. The instrument was operated either in scanning mode using a moving slit assembly together with a solid state germanium detector or with a newly developed position-sensitive germanium strip detector. Extended tests of the instrument were run using a 169Yb gamma-ray source. The resulting performance figures are compared to analytical calculations and to numerical simulations. The spectrometer was used together with a Au79+ ion beam travelling at a velocity of 44% of the speed of light.

2. Crystal optics 2.1. General scheme Nearly perfect crystals of silicon or germanium are preferred in crystal spectrometers because of their long-term stability. Also their reflection properties can be well described by theory. In the symmetric Laue case, the lattice planes used for Bragg reflection are oriented perpendicular to the principal crystal surfaces. In a usual focusing geometry with a cylindrically bent crystal, there is a perfect cancellation of two effects: the variation of the Bragg angle and that of the lattice spacing across the thickness of a crystal. As a consequence, the reflection curves for the symmetric Laue case remain identical for bent and for flat crystals.

Fig. 1. Definition of the asymmetry angle v.

Fig. 2. Calculated reflection curves for the asymmetric Laue case. The example is for a t=1.5-mm-thick Si (220) crystal with a radius of curvature of 2 m, an X-ray energy of 63 keV and an asymmetry angle v=08, 18, 28 and 38, respectively.

In the asymmetric Laue case, characterized by the asymmetry angle v as defined in Fig. 1, this cancellation is no longer valid leading to the well-known broadening [2–4] of the reflection curves for bent crystals illustrated in Fig. 2. The example is calculated for a t=1.5-mm-thick Si (220) crystal with a radius of curvature of 2 m and for an X-ray energy of 63 keV relevant for the actual spectrometer that will be described in detail later. Because the maximum of the reflectivity does not drop very much for small asymmetry angles, this behavior can be used to trade off spectral resolving power for spectrometer efficiency. In applications using X-ray sources with broad spectral features or with natural line widths exceeding the intrinsic perfect crystal’s reflection width, a tremendous gain in measurement efficiency can be achieved making use of the increased integrated reflectivity in the asymmetric Laue case. The feature of a pre-selectable rocking-curve width is implemented in the FOCAL X-ray optics. For practical estimates, the width can be parameterized like Dh ¼ W

t vðdegÞ; R

ð1Þ

where W is a constant and t and R denote the crystal thickness and radius of curvature, respectively. For a Si (220) crystal, the constant W amounts to Wc0.034 rad. A schematic drawing of the FOCAL geometry is sketched in Fig. 3 showing the path for X-rays of two different wavelengths k 1 and k 2. There is an optical axis that runs through the curved crystal’s apex pointing in the same direction as the lattice planes tilted by the asymmetry angle v. The X-ray source is located on that axis on the convex side of the crystal. A polychromatic focus is formed on the optical axis the locus of which depends on the source-tocrystal separation. For practical alignment purposes, the crystal is tilted by the angle v relative to the optical axis which in our application was oriented horizontally in the laboratory. Note

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Fig. 3. Principle of the FOCAL geometry. The source is placed on an axis intersecting the crystal at its apex there pointing in the direction of the tilted crystal planes [1].

that the cylinder axis of the crystal does not run through the optical axis. Through this measure, the X-ray spectra appear symmetrically on both sides of the optical axis. Thus, the asymmetry appears fully compensated—hence, the C in the acronym FOCAL. Monochromatic X-rays are reflected from a small area on the crystal and are focused on the Rowland circle indicated in Fig. 3. The footprint on the crystal is substantially larger than the corresponding rocking-curve width which is the cause for the improved light collection over the flat-crystal case. Because the Bragg angles are small, typically a few degrees, it is not necessary for the detectors to exactly follow the Rowland circle. Instead, they may be placed on a straight line as shown in Fig. 4. Out-of-plane X-rays are well accommodated by the curved crystal and can lead to an appreciable astigmatic height of the spectral lines as illustrated in the threedimensional visualization of the spectrometer arrangement of Fig. 5. As known from other dispersive instruments, there is a slight curvature in the two-dimensional intensity pattern in the detector plane (see Fig. 6). In case of a fast-beam Xray source, an additional complication is imposed by the Doppler effect. In order to adapt the X-ray optics to the angular-dependent emission pattern, it is essential to have the rotation of the crystal as shown in Fig. 5, i.e. the direction of dispersion (the coordinate x) forms a right angle with the velocity vector of the ion beam. The line of sight being at 908 relative to the ion-beam direction bears some advantages in aligning the apparatus but other observation angles can also be realized.

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Fig. 5. Orientation of the FOCAL spectrometer relative to the fast ion beam.

2.2. Some approximate formulae An extended mathematical description of the geometry has been given previously [1]. Here, we summarize some approximate formulae for the most important parameters necessary to set up the apparatus. As already shown in Fig. 4, the scale for the wavelength k is linked to the (vertical) coordinate x via the simple relation xc

R k; 2d

ð2Þ

where R denotes the crystal’s radius of curvature and d its lattice spacing. The linear dispersion simply is R/2d. The approximation as well as the ones to follow hold for small Bragg angles. For a source-to-crystal separation s, the footprints on the crystal are located at a distance tx c

Rs k R þ s 2d

ð3Þ

away from the centre of the crystal. The distance of the polychromatic focus from the crystal can be approximated by fc

Rs : R þ 2s

ð4Þ

A summary of the actual design parameters used for the realization of the FOCAL spectrometer at GSI is given in Table 1.

3. Technical layout 3.1. X-ray sources

Fig. 4. Schematics of the spectrometer arrangement for scanning mode or using a position sensitive X-ray detector.

For the current tests, we are using gamma-ray sources of 169Yb with a half life of 32 days. They were prepared starting with an isotopically enriched sample of Ytterbium oxide containing 25 mg of the 168Yb isotope. The form of the sample was a thin tablet of 5 mm diameter sealed in a small capsule of pure aluminum. The sample was neutron

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Fig. 6. Intensity pattern in the detector plane calculated through numerical simulation for (a) a stationary and (b) for a fast-beam source. Note the difference in the scales.

activated in the nuclear reactor at the Institut fqr Kernchemie in Mainz. With this procedure, sources of 169 Yb with an initial activity of about 5108 Bq could be produced. The radioactive probe was mounted inside a massive block of Tungsten alloy serving as a radiation shield.

Table 1 Design parameters of the FOCAL spectrometer X-ray energy range Wavelength range Calibration source Reference energy Beam velocity b Crystal Crystal dimension Reflection plane 2d spacing Asymmetry angle Bending radius Bragg angle h B Source diameter

30–120 keV 40–10 pm 169 Yb 63.12077 keV 0.4433 Silicon 401201.5 mm3 220 384.031 pm 28 2m 2.938 5 mm

Source-crystal separation Fast source Calibration source

600 mm 300 mm

Reflection curve Width Height

50 Arad 0.92

Footprint on crystal 600 mm 300 mm

F23.6 mm F13.3 mm

Spectral line Location Spatial width Energetic width

F102.3 mm 100 Am 60 eV

Crystal efficiency (100 mm detector width) Energy dispersion

26108 1.63 mm/keV

3.2. Background suppression and shielding The whole spectrometer has been placed inside an enclosure fabricated of 15-mm-thick sheets of Lead with a low gamma-ray activity. This way X-rays of not localized origin are prevented from hitting the X-ray detectors. As seen from Fig. 4, the X-ray optical design is very suggestive for placing shielding blocks along the spectrometer preventing stray radiation produced near the source from entering the detector area. We put shielding blocks immediately before and after the crystal aligned with the optical axis. At the polychromatic line focus, a horizontal slit is positioned allowing only Bragg-reflected X-rays entering the rear part of the spectrometer enclosure containing the detector. Additional ways of backgroundsuppression concern the X-ray detector and its electronics to be discussed later. 3.3. The curved crystal Realizing a crystal bending device, we are following a pure momentum-bender philosophy. Because severe constraints, usually prevailing at high-power synchrotron radiation [5], are absent the design can be simple. A slab of silicon with the dimensions 120401.5 mm3 was prepared as to use the 220 planes for the asymmetric Laue case with an asymmetry angle of v=28. There is still a remaining degree of freedom for choosing the crystal orientation which can be used to minimize the anticlastic curvature. The actual crystallographic orientation chosen is shown in Fig. 7. At its short ends, the crystal is glued into stainlesssteel mounting plates. By way of a rigid lever arm, a suitable torque is applied by a micrometer screw. The lever arm is allowed to slide longitudinally as to avoid any unwanted horizontal forces that would lead to a deviation from the desired cylindrical shape. At the BM05 Optics Beamline of the ESRF in Grenoble, the curvature of the crystal was measured using narrow

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that the slit aperture does not define the X-ray optical path and its use is solely background reduction. 3.5. Scanning mode

Fig. 7. Crystallographic orientation used for the analyzer crystal.

beams of 60 keV synchrotron radiation. Mapping the crystal with 14 vertical traces each 2-mm apart yielded the result shown in Fig. 8. Besides fluctuations of the local bending radius in the order of F2%, the average synclastic radius measured is 2020 mm close to the nominal radius of 2000 mm. A test utilizing reflections of laser light on the crystal surface yielded a radius of 2016 mm agreeing with the former value well within the estimated measurement uncertainty of about 5%. Theoretically, the ratio of the anticlastic to the synclastic radius R ac/R equals the Poisson ratio R s13 ¼ Rac s33

ð5Þ

solely determined by the respective components s ij of the tensor of elastic compliance [6]. For the present case, the Poisson ratio amounts to 0.068 leading to R acc30 m. The negative sign indicates that the anticlastic bending is opposite to the principal bending. A few specimen of silicon crystals with the same orientation as shown in Fig. 7 were checked by laser-light reflection to yield estimates of the anticlastic radius between 26 and 32 m. This amount of anticlastic bending is uncritical for the present Laue case with small Bragg angles.

Near the focal plane, a vertical linear stage of 1 m length was installed which could accurately move a platform in the vertical direction. In one case, this platform carried a horizontally aligned slit with a conventional, intrinsic germanium, Ge(i) detector behind it. The b0Q position of the detector slit was aligned with an optical telescope to the spectrometer axis defined in Fig. 3. Step scanning of the upper and lower X-ray spectra was achieved by a stepper motor drive plus an accurate incremental length encoder with position increments down to below 1 Am. 3.6. The position-sensitive germanium detector Alternatively, the scanner platform could also carry a position-sensitive X-ray detector which was parked in a spectral region of interest for a measurement. This germanium strip detector was developed by Protic´ et al. [7] at the Forschungszentrum Jqlich. A structure of 200 strips has been realized on a block of pure germanium with dimensions 4723.44.1 mm3 by etching 35-Am-wide grooves through the boron implanted front contact. A common 0.6-mm-thick Li-diffused rear contact was used. Each strip was connected to a chargesensitive preamplifier situated outside the detector vacuum. For the present tests, only 64 strips out of the 200 were read out covering 16 mm along the dispersion direction. For an individual strip, an energy width of 1.8 keV was observed at an X-ray energy of 60 keV. Time spectra for coincidences between neighboring strips showed a width of about 70 ns. Both the energy and time resolution helped to further reduce X-ray background by setting suitable energy and time windows.

3.4. Polychromatic focus An adjustable slit assembly made of tungsten alloy was mounted on the carriage of a linear stage and aligned with the optical axis of the spectrometer. The range of travel of 0.5 m accommodates all positions of the polychromatic focus when changing the position of the source. For the two most relevant source positions, 300 and 600 mm as measured from the crystal, Eq. (4) yields f=230 and 375 mm, respectively. As a matter of fact, this slit mechanism was a very helpful alignment tool. For instance, observing the intensity of a spectral line in the detector as a function of slit width and of slit position served in determining the actual X-ray paths. After completing alignment, the slit was positioned to the line focus and a width of 6 mm was chosen for most of the measurements. For this setting, we were sure

Fig. 8. Curvature measurements performed with synchrotron radiation. The local radius of curvature is mapped in 14 vertical traces over the crystal surface.

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4. Performance tests 4.1. Scanned spectra The 169Yb source emits a rich spectrum of gamma-ray and X-ray lines. Part of this spectrum is shown in Fig. 9 as a result of scanning lower and upper reflections from the silicon crystal. Both spectra appear very symmetric to the optical axis in the region F(100–130 mm). The scanned x coordinate is proportional to the wavelength scale also included in the figure. For calibration, we used the Tm and Yb Ka1,2 doublets and the 63.121-keV gamma-ray line. For an accurate alignment of the curved crystal, the symmetry feature can be used. In a first step, the crystal was optically aligned and tilted by the asymmetry angle v=28. Then, in a second step, the crystal was finely tuned as to force the measured spectra to be very symmetric. This procedure allows the crystal to be aligned more accurately than the corresponding uncertainty of the asymmetry angle known beforehand. 4.1.1. Detection efficiency The spectrometer efficiency was measured by comparing the registered X-ray event rates with and without the crystal in place. In the first case, the detector slit is positioned to the centre of an isolated spectral line with the slit opened wide enough to catch the whole line intensity. In the second case, a well-defined aperture was used in front of the detector allowing to determine the solid angle. In Fig. 10, two measurement points near 50 and 63 keV are compared to numerical calculations with the procedures described in Ref. [1]. Surprisingly, the measured efficiency was higher than the calculated one—9 versus 6108 at 63 keV. Of course, the efficiency depends on the size of the detector installed. For scanning, a 50-mm-wide detector was used, whereas the strip detector has a width of 23.4 mm. The efficiency numbers given here, as the one contained in Table 1 are normalized to a width of 100 mm.

Fig. 10. Calculated spectrometer efficiency (curve) compared with measured data points.

4.1.2. Line width The line widths observed in the scanned spectra were derived by fitting Voigt profiles to the spectral lines. Comparing to numerical predictions would allow to judge the validity of the theoretical assumptions made in the beginning. In Table 2, calculated and estimated line widths are listed at 50.7 and at 63.1 keV, respectively. All contributions from the crystal diffraction are subsumed in the line bRocking curveQ. Only the K Xray line at 50.7 has an appreciable natural width of C K c30 eV. There is also a substantial broadening introduced by the finite width of the scanner slit of about 50 Am. In total, observed and predicted widths nicely agree for both lines. 4.2. Spectra obtained with the position-sensitive detector 4.2.1. Stationary source The same spectral range, 19–25 pm, that was covered by scanning, see Fig. 9, was also measured with the germanium strip detector. Because the latter is only 16 mm wide, spectra

Fig. 9. X-ray spectra of a 169Yb source recorded by scanning a Ge(i) detector over a lower and upper portion along the dispersive direction of the spectrometer. The width of the slit in front of the detector was approximately 50 Am.

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Table 2 Estimated and observed line widths in eV Energy

50.7 keV

63.1 keV

Rocking curve Natural width Slit width (50 Am)

40 30 20

55 – 31

Total estimated Observed

65 69

86 84

were taken in two steps with the germanium strip detector placed at two different positions. The joined spectrum is displayed in Fig. 11. The most evident feature is a very low background. This can be mainly attributed to the smaller detector volume of a single strip. Even the very weak feature of the Yb-Kh2 line near 20.3 pm, hardly discernible by scanning, is clearly visible. Additionally, the measurement speed is boosted up by measuring an extended spectral range simultaneously. Both the conventional and the strip detector have a high detection efficiency for 50–60 keV X-rays. So the gain in measurement speed is approximately given by the number of strips used simultaneously, in the present case 64. 4.2.2. Fast-beam source The FOCAL spectrometer carefully aligned with the aid of the stationary source was tested in a beamtime at the ESR storage ring. There, a beam of completely stripped Au79+ ions were stored at a velocity b=v/c o=0.4433. K X-ray lines of hydrogen-like Au78+ were induced following charge exchange in a crossed jet of argon atoms. For a general view of the arrangement, see Fig. 5. X rays were measured in coincidence with those particles that have lost one unit of charge and that are registered in a particle detector after the next dipole magnet of the storage ring. After setting suitable time and energy windows in the data acquisition software, the spectrum of Fig. 12 was obtained showing clearly the Lyman-a doublet of one-

Fig. 11. Same spectrum as in Fig. 9 but obtained with the strip detector.

Fig. 12. The Lyman-a spectrum of fast hydrogen-like gold measured at the ESR storage ring. For comparison, the spectrum from the 169Yb source with the 63 keV gamma-ray line used for calibration is shown.

electron Au78+. Also shown in the figure is an overlaid calibration spectrum with the 63.121-keV gamma-ray line, scaled down by a factor of 140. Although the number of collected Lyman photons was low in this first test, it was demonstrated that it is feasible to record useful X-ray spectra with FOCAL in an accelerator environment with its limited source strength. The favorably low background level observed is attributed to the efficient shielding and suppression methods. The somewhat increased width seen in the Lyman lines is fully consistent with the expected slanting of the lines due to the Doppler effect. Our strip detector has a position resolution only in one direction. Therefore, the slanted image, such as calculated for Fig. 6b, is no longer parallel to the horizontally aligned strips of the detector. From the calculated slope of about 3%, it is expected that the intensity is spread over 0.7 mm for a 23-mm-wide detector. Hence, a foot width of about three strips can be expected and this is also observed. 4.2.3. Charge splitting It has been observed that a class of X-ray events exist that coincidentally appear in two neighboring strips. To study those effects, the detector was moved in steps small compared to the strip width. As a function of the detector position, the relative amount of coincidences markedly changed. Presumably, the maximum is reached when many photons hit the gap between strips and the charge is distributed between two neighboring channels. Such charge-splitting events are analyzed in Fig. 13 showing the pulse-height spectra for strip numbers 29 and 30. Whereas the individual distributions seen below channel number 500 are flat and nearly identical, there is a pronounced energy peak for the sum spectrum obtained by adding the pulse heights event by event. Also plotted in Fig. 13 is the intensity per strip when a condition is set to the sum peak. Events showing charge splitting now appear only in one strip. This feature could be

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Fig. 13. Left: Coincident spectra for strip numbers 29 and 30 and their sum spectrum obtained by summing event by event. Right: Position spectrum, full curve with and dashed curve without charge splitting.

used as a clue to interpolate position readout to a fraction of a strip width.

5. Conclusion The FOCAL X-ray optics have been analyzed and incorporated into a spectrometer which was tested with a stationary and with a fast beam source. It was demonstrated that measured efficiencies and line widths are close to the expected values. The feasibility of operating the instrument with a fast ion beam in an accelerator environment has been demonstrated. Background suppression appears to work very well with this kind of apparatus. Further directions of improvements mainly comprise larger detector areas, a two-dimensional position readout and sub strip-width position interpolation. The possibility of routinely incorporating a position sub division by using induced signals in neighboring strips is presently under investigation. Many spectroscopic applications could make use of the techniques introduced here. In particular, the test measurements presented mark a transition to new Lamb-shift measurements of higher accuracy than previously was possible.

Acknowledgments The excellent help from J.P. Vassalli of the ESRF crystal lab and from A. Rommeveaux of the ESRF Optics

Metrology lab is thankfully acknowledged. We thank T. Bigault and R. Hustache for their kind assistance at the optics beamline of the ESRF. We are indebted to N. Trautmann and W. Brqchle for preparing the radioactive samples. B. Lommel, B. Kindler and the crew of the GSI target lab helped with gluing the crystals. We thank W. Enders and H. Wesp for their technical assistance during spectrometer assembling. This research has been supported by a Marie Curie Fellowship of the European Community Programme IHP under contract number HPMT-CT-2000-00197.

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