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Low-temperature X-ray detectors for precise Lamb shift measurements on hydrogen-like heavy ions
Nuclear Instruments and Methods in Physics Research A 444 (2000) 488}491
Low-temperature X-ray detectors for precise Lamb shift measurements on hydrogen-like heavy ions A. Bleile , P. Egelhof *, H.-J. Kluge, U. Liebisch , D. McCammon, H.J. Meier , O. SebastiaH n , C.K. Stahle, M. Weber Institut fu( r Physik der Universita( t Mainz, D-55099 Mainz, Germany Gesellschaft fu( r Schwerionenforschung (GSI), D-64291 Darmstadt, Germany Department of Physics, University of Wisconsin, Madison, WI 53706, USA NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
Abstract The precise determination of the Lamb shift in heavy hydrogen-like ions provides a sensitive test of quantum electrodynamics in very strong Coulomb "elds, not accessible otherwise. For the investigation of the Lyman-a transitions in Pb> or U> with su$cient accuracy a high resolving calorimetric detector for hard X-rays (E)100 keV) is presently developed. The detector modules consist of arrays of silicon thermistors and of X-ray absorbers made of high Z material to optimize the absorption e$ciency. The detectors are housed in a specially designed He/He dilution refrigerator with a side arm which "ts to the geometry of the internal target of the storage ring ESR at GSI Darmstadt. The detector performance presently achieved is already close to ful"ll the demands of the Lamb shift experiment. For a prototype detector pixel with a 0.3 mm;66 lm Sn absorber an energy resolution of *E "75 eV is obtained for $5&+ 60 keV X-rays. 2000 Elsevier Science B.V. All rights reserved.
1. Motivation The precise experimental test of the theoretical predictions of quantum electrodynamics (QED) on corrections to the classical Coulomb interaction potential is still } at least for high Z systems } one of the outstanding and most challenging problems of atomic physics. In the hydrogen atom, or in hydrogen like ions, the QED corrections give rise to the so-called Lamb shift, which is a small deviation of the binding energies from those predicted by the relativistic Dirac}Coulomb energy (see Fig. 1). Whereas in light systems, where QED
* Corresponding author.
predictions were con"rmed to a high precision [1], the higher-order contributions are almost negligible, they increase strongly with higher Z. On the other hand, the theoretical predictions of QED, which are usually performed in series expansions in Za (a being the "ne structure constant), become most critical for the heaviest systems, where Za approaches values close to unity. Therefore, a precise determination of the Lamb shift in hydrogen like very heavy ions represents one of the most sensitive tests of QED in strong electromagnetic "elds, not accessible otherwise. The level scheme of the hydrogen-like U> ion is displayed in Fig. 1. The binding energy of the 1senergy level is about !132 keV, thus yielding transition energies for the Lyman-a lines of about
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 1 4 2 9 - 1
A. Bleile et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 488}491
489
2. Development of calorimetric detectors for hard X-rays To meet the experimental conditions required by the Lamb shift experiment the calorimetric detector should, among others [3], ful"ll the following constraints:
Fig. 1. Level scheme for hydrogen-like U> according to various atomic models. The numbers on the right indicate the electronic binding energies.
100 keV. The 1s Lamb shift is predicted to be ¸ "463 eV. To determine the 1s Lamb shift of heavy ions the transition energies of the Lyman-a transitions are to be measured with high accuracy and compared with theoretical predictions from the Dirac theory. Such experiments are performed at the experimental storage ring ESR of GSI Darmstadt [2]. A beam of bare U> ions is injected and interacts with an internal gas target. This may lead to the capture of one electron and to the population of a 2p state, which promptly decays to the 1s state. The emitted Lyman-a X-rays are detected by detectors surrounding the internal target. The latest experimental results on the Z"79 and 92 systems are compared with theoretical predictions in Ref. [2]. The experimental results agree well with the theoretical predictions, but the experimental errors ($13 eV) are about one order of magnitude larger than the theoretical ones ($1 eV). Thus, the experimental accuracy has to be improved considerably for a more stringent test of QED. One major contribution to the experimental error is the poor energy resolution of *E*500 eV obtained with Ge-detectors, which must be improved to at least *E)50}100 eV in order to reach an absolute accuracy of about dE"$1 eV in the determination of the center of gravity of the transition energy. This was the motivation for the design of a lowtemperature calorimetric detector for the present application.
E a relative energy resolution of *E/E)1;10\ for E "50}100 keV, A E a total detection e$ciency (including detector solid angle) of *10\}10\, which may be reached with a photopeak e$ciency of *30% and an active detector area of *100 mm. The detector modules for the present experiment are designed on the basis of silicon microcalorimeters which were developed by the Madison/Goddard groups [4] for astrophysical applications at lower X-ray energies (E )6 keV). A The detector pixels consist of silicon thermistors, made from a wafer of silicon containing an implanted thermistor and of X-ray absorbers glued on the top of the thermistors by means of an epoxy varnish. Thermistor arrays [4], consisting of 36 pixels each, are provided from the collaborating groups from Madison and Goddard. The "nal detector concept foresees three calorimeter arrays, the active area of 1 pixel being about 1 mm. For the Lamb shift measurement the experimental setup was optimized with respect to energy resolution and detection e$ciency for hard X-rays at the experimental area of the storage ring ESR. In order to reach su$cient photopeak e$ciency, the absorber should be a high Z material and should have a volume of <*1 mm;40 lm. Absorber materials under investigation are Sn, HgTe and Re. To obtain a reasonable detection solid angle the detector arrays have to be located as close as possible to the interaction zone at the internal target of the ESR. To realize this concept a special He/He-dilution refrigerator with a side arm which "ts to the internal target geometry was designed in cooperation with Oxford Instruments. A schematic view of the system is displayed in Fig. 2. The detector arrays are mounted on the cold "nger at the end of the side arm and can be irradiated through a system of aluminum-coated mylar windows. In order to suppress low-frequency
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A. Bleile et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 488}491
with the ampli"ers are tensioned. The cryostat is prepared to read out a total of 100 detector channels, 10 channels being equipped and tested at present. In agreement with the speci"cations the cryostat reaches a base temperature of 11.5 mK, and a cooling power of 400 lW at 11.5 K. The operating temperature of the detectors may be chosen between ¹"50 and 100 mK. The "rst ampli"er stage consists of cooled FETs, operated at a temperature of about 125 K, which have the purpose to reduce the relatively high imFig. 2. Schematic view of the side arm of the He/He dilution refrigerator (for details see text).
Fig. 4. Signal due to a 60 keV photon obtained for a detector with a 0.3 mm;66 lm Sn absorber at an operating temperature of 62 mK.
Fig. 3. Noise spectra for di!erent samples of two modi"cations (A, D) of FETs of the type INTERFET NJ14AL obtained at a temperature of ¹"125 K (upper part). In the lower part of the "gure the temperature dependence of the noise spectrum for a FET of modi"cation D is displayed.
microphonics the "rst ampli"er stage was positioned close to the detectors inside the side arm of the cryostat, and all wires connecting the detectors
Fig. 5. Dependence of the signal amplitude on an external magnetic "eld for a detector with a 1;0.3 mm;66 lm Sn absorber.
A. Bleile et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 488}491
491
Fig. 6. Energy spectrum obtained with a calorimetric detector at an operating temperature of 62 mK with a 0.3 mm;66 lm Sn absorber for 59.6 keV photons. An energy resolution of *E "75 eV for the photopeak (right side) and of *E "71 eV for the $5&+ $5&+ K -escape lines (left side) is obtained. a
pedance of the detectors. It turned out that special care had to be taken to select low-noise FETs and to determine their optimum operating temperature. Therefore many samples of various modi"cations of the type INTERFET NJ14AL were systematically tested. As illustrated in Fig. 3 (upper part) pronounced di!erences in the noise spectra were obtained. Finally, a reasonable number of FETs with su$ciently small noise at low frequencies could be selected. In the lower part of Fig. 3 the temperature dependence of the FET noise spectrum is displayed. An optimum was found for a FET temperature of about 125 K.
3. Performance of prototype detectors The detector performance presently achieved is already close to ful"ll the demands of the Lamb shift experiment. The best results were obtained with Sn as absorber material. The signal obtained for a detector with a 0.3 mm;66 lm Sn absorber at an operating temperature of 62 mK for a 60 keV photon is displayed in Fig. 4. The dominating thermal time constant is q"5.9 ms. The dependence of the signal amplitude on an external magnetic "eld is displayed in Fig. 5. A reduction of the amplitude by about 2% is obtained for relatively low magnetic "eld strengths above 45 G. A similar, but more pronounced e!ect, namely a reduction of the
signal amplitude by about 45% at slightly lower magnetic "eld, was observed for a detector with a Re-absorber. These unwanted e!ects are interpreted as due to the existence of an intermediate state of a type 1 superconductor with a drastic "eld ampli"cation due to the special probe geometry. A careful shielding of the detectors against external magnetic "elds is therefore essential for a stable operation of the present detectors. The energy spectrum, again obtained for a detector with a 0.3 mm;66 lm Sn absorber for 59.6 keV photons, provided by an Am source, is displayed in Fig. 6. For the photopeak at 59.6 keV an energy resolution of *E "75 eV is ob$5&+ tained, whereas for the K -escape lines, appearing a at E"34.4 keV, a resolution of *E "71 eV $5&+ was measured. These results may be compared to the theoretical limit of the energy resolution for a conventional semiconductor detector which is about *E+380 eV for 60 keV photons.
References [1] M. Weitz et al., Phys. Rev. Lett. 68 (1992) 1120. [2] H.F. Beyer, T. StoK hlker, in: E. Zavattini, B. Akalov, C. Rizzo (Eds.), Frontier Tests of QED and Physics of the Vacuum, Heron Press, So"a, 1998, p. 354. [3] P. Egelhof et al., Nucl. Instr. and Meth. A 326 (1993) 157. [4] C.K. Stahle et al., Nucl. Instr. and Meth. A 370 (1996) 173.
SECTION X.
Low-temperature X-ray detectors for precise Lamb shift measurements on hydrogen-like heavy ions A. Bleile , P. Egelhof *, H.-J. Kluge, U. Liebisch , D. McCammon, H.J. Meier , O. SebastiaH n , C.K. Stahle, M. Weber Institut fu( r Physik der Universita( t Mainz, D-55099 Mainz, Germany Gesellschaft fu( r Schwerionenforschung (GSI), D-64291 Darmstadt, Germany Department of Physics, University of Wisconsin, Madison, WI 53706, USA NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
Abstract The precise determination of the Lamb shift in heavy hydrogen-like ions provides a sensitive test of quantum electrodynamics in very strong Coulomb "elds, not accessible otherwise. For the investigation of the Lyman-a transitions in Pb> or U> with su$cient accuracy a high resolving calorimetric detector for hard X-rays (E)100 keV) is presently developed. The detector modules consist of arrays of silicon thermistors and of X-ray absorbers made of high Z material to optimize the absorption e$ciency. The detectors are housed in a specially designed He/He dilution refrigerator with a side arm which "ts to the geometry of the internal target of the storage ring ESR at GSI Darmstadt. The detector performance presently achieved is already close to ful"ll the demands of the Lamb shift experiment. For a prototype detector pixel with a 0.3 mm;66 lm Sn absorber an energy resolution of *E "75 eV is obtained for $5&+ 60 keV X-rays. 2000 Elsevier Science B.V. All rights reserved.
1. Motivation The precise experimental test of the theoretical predictions of quantum electrodynamics (QED) on corrections to the classical Coulomb interaction potential is still } at least for high Z systems } one of the outstanding and most challenging problems of atomic physics. In the hydrogen atom, or in hydrogen like ions, the QED corrections give rise to the so-called Lamb shift, which is a small deviation of the binding energies from those predicted by the relativistic Dirac}Coulomb energy (see Fig. 1). Whereas in light systems, where QED
* Corresponding author.
predictions were con"rmed to a high precision [1], the higher-order contributions are almost negligible, they increase strongly with higher Z. On the other hand, the theoretical predictions of QED, which are usually performed in series expansions in Za (a being the "ne structure constant), become most critical for the heaviest systems, where Za approaches values close to unity. Therefore, a precise determination of the Lamb shift in hydrogen like very heavy ions represents one of the most sensitive tests of QED in strong electromagnetic "elds, not accessible otherwise. The level scheme of the hydrogen-like U> ion is displayed in Fig. 1. The binding energy of the 1senergy level is about !132 keV, thus yielding transition energies for the Lyman-a lines of about
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 1 4 2 9 - 1
A. Bleile et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 488}491
489
2. Development of calorimetric detectors for hard X-rays To meet the experimental conditions required by the Lamb shift experiment the calorimetric detector should, among others [3], ful"ll the following constraints:
Fig. 1. Level scheme for hydrogen-like U> according to various atomic models. The numbers on the right indicate the electronic binding energies.
100 keV. The 1s Lamb shift is predicted to be ¸ "463 eV. To determine the 1s Lamb shift of heavy ions the transition energies of the Lyman-a transitions are to be measured with high accuracy and compared with theoretical predictions from the Dirac theory. Such experiments are performed at the experimental storage ring ESR of GSI Darmstadt [2]. A beam of bare U> ions is injected and interacts with an internal gas target. This may lead to the capture of one electron and to the population of a 2p state, which promptly decays to the 1s state. The emitted Lyman-a X-rays are detected by detectors surrounding the internal target. The latest experimental results on the Z"79 and 92 systems are compared with theoretical predictions in Ref. [2]. The experimental results agree well with the theoretical predictions, but the experimental errors ($13 eV) are about one order of magnitude larger than the theoretical ones ($1 eV). Thus, the experimental accuracy has to be improved considerably for a more stringent test of QED. One major contribution to the experimental error is the poor energy resolution of *E*500 eV obtained with Ge-detectors, which must be improved to at least *E)50}100 eV in order to reach an absolute accuracy of about dE"$1 eV in the determination of the center of gravity of the transition energy. This was the motivation for the design of a lowtemperature calorimetric detector for the present application.
E a relative energy resolution of *E/E)1;10\ for E "50}100 keV, A E a total detection e$ciency (including detector solid angle) of *10\}10\, which may be reached with a photopeak e$ciency of *30% and an active detector area of *100 mm. The detector modules for the present experiment are designed on the basis of silicon microcalorimeters which were developed by the Madison/Goddard groups [4] for astrophysical applications at lower X-ray energies (E )6 keV). A The detector pixels consist of silicon thermistors, made from a wafer of silicon containing an implanted thermistor and of X-ray absorbers glued on the top of the thermistors by means of an epoxy varnish. Thermistor arrays [4], consisting of 36 pixels each, are provided from the collaborating groups from Madison and Goddard. The "nal detector concept foresees three calorimeter arrays, the active area of 1 pixel being about 1 mm. For the Lamb shift measurement the experimental setup was optimized with respect to energy resolution and detection e$ciency for hard X-rays at the experimental area of the storage ring ESR. In order to reach su$cient photopeak e$ciency, the absorber should be a high Z material and should have a volume of <*1 mm;40 lm. Absorber materials under investigation are Sn, HgTe and Re. To obtain a reasonable detection solid angle the detector arrays have to be located as close as possible to the interaction zone at the internal target of the ESR. To realize this concept a special He/He-dilution refrigerator with a side arm which "ts to the internal target geometry was designed in cooperation with Oxford Instruments. A schematic view of the system is displayed in Fig. 2. The detector arrays are mounted on the cold "nger at the end of the side arm and can be irradiated through a system of aluminum-coated mylar windows. In order to suppress low-frequency
SECTION X.
490
A. Bleile et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 488}491
with the ampli"ers are tensioned. The cryostat is prepared to read out a total of 100 detector channels, 10 channels being equipped and tested at present. In agreement with the speci"cations the cryostat reaches a base temperature of 11.5 mK, and a cooling power of 400 lW at 11.5 K. The operating temperature of the detectors may be chosen between ¹"50 and 100 mK. The "rst ampli"er stage consists of cooled FETs, operated at a temperature of about 125 K, which have the purpose to reduce the relatively high imFig. 2. Schematic view of the side arm of the He/He dilution refrigerator (for details see text).
Fig. 4. Signal due to a 60 keV photon obtained for a detector with a 0.3 mm;66 lm Sn absorber at an operating temperature of 62 mK.
Fig. 3. Noise spectra for di!erent samples of two modi"cations (A, D) of FETs of the type INTERFET NJ14AL obtained at a temperature of ¹"125 K (upper part). In the lower part of the "gure the temperature dependence of the noise spectrum for a FET of modi"cation D is displayed.
microphonics the "rst ampli"er stage was positioned close to the detectors inside the side arm of the cryostat, and all wires connecting the detectors
Fig. 5. Dependence of the signal amplitude on an external magnetic "eld for a detector with a 1;0.3 mm;66 lm Sn absorber.
A. Bleile et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 488}491
491
Fig. 6. Energy spectrum obtained with a calorimetric detector at an operating temperature of 62 mK with a 0.3 mm;66 lm Sn absorber for 59.6 keV photons. An energy resolution of *E "75 eV for the photopeak (right side) and of *E "71 eV for the $5&+ $5&+ K -escape lines (left side) is obtained. a
pedance of the detectors. It turned out that special care had to be taken to select low-noise FETs and to determine their optimum operating temperature. Therefore many samples of various modi"cations of the type INTERFET NJ14AL were systematically tested. As illustrated in Fig. 3 (upper part) pronounced di!erences in the noise spectra were obtained. Finally, a reasonable number of FETs with su$ciently small noise at low frequencies could be selected. In the lower part of Fig. 3 the temperature dependence of the FET noise spectrum is displayed. An optimum was found for a FET temperature of about 125 K.
3. Performance of prototype detectors The detector performance presently achieved is already close to ful"ll the demands of the Lamb shift experiment. The best results were obtained with Sn as absorber material. The signal obtained for a detector with a 0.3 mm;66 lm Sn absorber at an operating temperature of 62 mK for a 60 keV photon is displayed in Fig. 4. The dominating thermal time constant is q"5.9 ms. The dependence of the signal amplitude on an external magnetic "eld is displayed in Fig. 5. A reduction of the amplitude by about 2% is obtained for relatively low magnetic "eld strengths above 45 G. A similar, but more pronounced e!ect, namely a reduction of the
signal amplitude by about 45% at slightly lower magnetic "eld, was observed for a detector with a Re-absorber. These unwanted e!ects are interpreted as due to the existence of an intermediate state of a type 1 superconductor with a drastic "eld ampli"cation due to the special probe geometry. A careful shielding of the detectors against external magnetic "elds is therefore essential for a stable operation of the present detectors. The energy spectrum, again obtained for a detector with a 0.3 mm;66 lm Sn absorber for 59.6 keV photons, provided by an Am source, is displayed in Fig. 6. For the photopeak at 59.6 keV an energy resolution of *E "75 eV is ob$5&+ tained, whereas for the K -escape lines, appearing a at E"34.4 keV, a resolution of *E "71 eV $5&+ was measured. These results may be compared to the theoretical limit of the energy resolution for a conventional semiconductor detector which is about *E+380 eV for 60 keV photons.
References [1] M. Weitz et al., Phys. Rev. Lett. 68 (1992) 1120. [2] H.F. Beyer, T. StoK hlker, in: E. Zavattini, B. Akalov, C. Rizzo (Eds.), Frontier Tests of QED and Physics of the Vacuum, Heron Press, So"a, 1998, p. 354. [3] P. Egelhof et al., Nucl. Instr. and Meth. A 326 (1993) 157. [4] C.K. Stahle et al., Nucl. Instr. and Meth. A 370 (1996) 173.
SECTION X.