Crespo López-Urrutia, J.

Draganic, I.

DuBois, R.

Shevelko, V.

Ullrich, J.

Zou, Y.

English

MPG.PuRe

High precision wavelength measurements of QED−sensitive forbidden transitions in highly charged argon ionsI. Dragani?1?, J. R. Crespo López−Urrutia1, R. DuBois2, S.Fritzsche3, V. M.Shabaev1,4, R. Soria Orts1,I. I. Tupitsyn1,4, Y. Zou5 and J. Ullrich11Max−Planck Institut für Kernphysik, Saupfercheckweg 1, D−69117 Heidelberg, Germany2University of Missouri−Rolla, Physics Building, Rolla, MO 65409−0640, USA3Department of Physics, University of Kassel, Heinrich−Plett−St. 40, D−34132 Kassel, Germany4St. Petersburg State University, Oulianovskaya 1, Petrodvorets, St. Petersburg 198504, Russia5Applied Ion Beam Physics Lab, Fudan University, Shanghai 200433, P. R. ChinaWe present the results of an experimental study of magnetic dipole (M1)transitions in highly charged argon ions ( Ar X, Ar XI, Ar XIV, Ar XV) in the visiblespectral range. Their wavelengths were determined with for highly charged ionsunprecedented accuracy up to the sub−ppm level using an electron beam ion trap, andwere compared with theoretical calculations. The QED contributions, calculated inthis work, are found to be four orders of magnitude larger than the experimental errorfor the Be−like and B−like transitions, and are absolutely indispensable to bringtheory and experiment to a good agreement. This method shows a great potential forthe study of QED effects in relativistic few−electron systems.  PACS number(s): 31.15.Ar, 31.30.Jv, 32.10.Fn, 32.30.Jc, 32.70.JzForbidden transitions, which play a vital role in the temperature and densitydiagnostics of both laboratory [1] and astrophysical plasmas [2], were first identifiedin the solar corona by B. Edlén [3]. In more recent years, the major advances in usingspectral lines and, in particular, forbidden lines in the analysis of astrophysicalplasmas have been successfully transferred to the diagnostics of fusion plasmas, e.g.in tokamak devices. Argon, the element under study in this work, is often chosen forinjection into tokamaks for plasma diagnostic. Apart from these applications, precise? Present address: The Institute of Nuclear Sciences "Vin?a", Laboratory of Physics (010), P.O. Box522, 11001 Belgrade, Yugoslavia, e−mail address: draganic@rt270.vin.bg.ac.yu1wavelength measurements of magnetic dipole transitions (M1) in few−electron highlycharged ions can provide sensitive tests forab initio and semi−empirical theoreticalatomic structure calculations [4−10]. At present, no calculations can reproduce thewavelengths at the level of accuracy obtained in this work.Furthermore, theoretical calculations show QED contributions to the measuredtransitions energies as large as 0.3% of the total. The size of these effects, combinedwith the fact that four− and five−electron systems are becoming tractable forab initioQED calculations (see, e.g. Ref. [11]), as well as comparatively amenable to many−body atomic structure calculations, places these measurements among the mostsensitive to QED contributions in highly charged ions. Our experimental data canonly be correctly reproduced by including QED radiative corrections and, in fact, thebest agreement has been obtained in this way. In recent years, the full QED treatment of bound electrons has advancedstepwise from the hydrogenic systems to the Li−like sequence. The analytical andnumerical methods, developed during this process, can now be applied to the nextlevels of structural complexity. Nonetheless, the necessary calculations still present aformidable challenge. Here we demonstrate an experimental test with the highestsensitivity and potentially very small theoretical uncertainties in the electron−electroncorrelation field, which makes further refinem nt both worthwhile and rewarding.    We measured the wavelengths of the M1 transitions of Ar X2s2 2p5 2P3/2 −2P1/2, Ar XI 2s2 2p4 3P2 − 3P1, Ar XIV 2s2 2p 2P1/2 − 2P3/2, and Ar XV 2s 2p 3P1 −3P2. These measurements were done exploiting the very favourable conditions offeredby an electron beam ion trap (EBIT) for high−resolution spectroscopy studies onhighly charged ions. A good general reference to EBITs and their applications toatomic physics can be found in [12]. The argon lines have been previously studied byEdlén in 1982 [13] and 1983 [10,14], and, also with an EBIT, by Bieber t al. [15]. 2In the present work, we developed a new approach for precise wavelengthdeterminations, obtaining accuraciesup to sub−ppm level. Error sources fromstatistics, calibration line uncertainties, cut−off of high order of calibration functions,collision and Doppler broadening, Zeemand Stark effects, as well as detectorimperfections and temperature drifts during the measurements were carefully takeninto account.The experiment was performed on the FreEBIT device (now H−EBIT atMPI−K Heidelberg) at the University of Freiburg. The energy of the electron beamused for ionization was set to Ebeam=1010 eV, with moderate beam currents of 45−50mA. Argon was introduced into the trap region through a three−stage differentiallypumped gas injection system. All workingand adjustment parameters of EBIT werekept stable during the measurements.Photons in the visible range were transmitted from the trap through 2 pairs ofquartz lenses with the help of three mirrors to the entrance slit of a JY TRIAX 550spectrograph equipped with a cryogenic CCD camera (2000x800 pixels on a 30x12mm2 chip) with a high quantum efficiency (40% −90%). Detector noise levels areextremely low. The entrance slit of the spectrograph was set to 50 ?m as acompromise between line intensity and resolution. The individual exposure time waschosen to obtain at least about 1500 counts for weak lines and up to 100 000 countsfor strong lines (from a few minutes to one hour). The pixels located on the central 2mm stripe on the detector were vertically binned (200 pixels)i. e., in the non−dispersive direction. Coma and othernon−paraxial aberrations, which can causedeviations from the ideal line profile were thus extremely reduced. A typical result fora coronal line is shown in Fig.1. Lines from highly charged ions are typically threetimes broader (i.e., about 0.1 nm) than calibration lines (around 0.3 nm) due to theDoppler broadening caused by the thermal motion of the trapped ions. Calibration3spectra containing several well known lines were recorded before and after eachexposure. A diffuse reflector (illuminated with appropriate spectral lamps) was placedat the position of an intermediate real image of the trapped ions. With this choice, thepositioning of the reflector became uncritical, as tests showed. For each newexposure, the grating was slightly rotated. A new exposure, with its correspondingcalibrations, was then recorded. The entire process was repeated as many as thirtytimes for each forbidden line. In this way, the statistical limitations posed by too fewpixels illuminated across the width of a spectral line were overcome. Non−lineardetector response effects for the individual pixels or other flaws became negligible asthe sampled line profile contains several hundred individual data points times 200pixels. One can imagine each pixel as an individual "exit slit", and the proceduredescribed here as the recording of the spectrum with many single detectors by slowlyrotating the grating. Each spectrum was evaluated by fitting individual Gaussian functions to eachof the calibration lines to determine their positions, plotting them versus theirrecommended wavelengths, and using a least−square−algorithm to obtain a second−degree polynomial for the dispersion function. Since the deviation from lineardispersion for this type of spectrograph is small, a quadratic function already providesa very good approximation to the real dispersion. Figure 2 shows the deviation fromthe dispersion function fitted by linear, second, and third order of polynomialfunctions. As it can be seen, the difference between the third and the second orderpolynomial dispersion functions is not obvious and almost purely statistical. Theeffect of deviations of the line profile from the ideal Gaussian shape was checked byvarying the intervals around the line center for the fitting procedure. This was done inorder to take into account background, scattered light, Zeeman effect, comaaberration and so on, which could affect the line shape. Within reasonable fitting4intervals, average centroid shifts of about 0.004 pixel, or 3.5·10−5 nm were observed,well below the statistical uncertainty. In this work, we can also neglect shifts of thecentral wavelength caused by Stark effect, below 10−7 nm, by collisions, 10−12nm, andby Paschen−Back effect, 10−6 nm, which were all estimated from standard formulae.Other possible sources of systematic deviations like temperature drift etc. are ruledout by our repeated calibration procedure. The main error sources together with theircontributions to the final uncertainties arelisted in Table 1. All random uncertainties(line centroid errors, standard deviations of wavelength calibration function) havebeen calculated as a "root sum of squares", whereas systematic calibration errors anduncertainties from calibration lines have been added linearly. Natural argon was used,which contains 40Ar almost exclusively (99.6%). As can be seen in Table 2, in comparison with other experiments, ourexperimental results for Ar9+ represent almost two orders of magnitude improvementin comparison with the previous most accurate data [19]. For Ar10+, Ar13+, and Ar14+,Bieberet al. have reported very accurate values [15]. Still, in our work the respectiveaccuracies have been improved by factors of five to thirty. At this level we have founddiscrepancies between our results and theirs for the lines of Ar13+ and Ar14+, 0.0059nm for Ar13+ and 0.015 nm for Ar14+ respectively. Therefore, we performed a second,completely independent measurement for Ar13+ after the Fre−EBIT had been movedto Heidelberg, and using a different set of calibration lines. The two results from ourindependent measurements agree with each other within error bars, giving usconfidence in our quoted error estimates.Our first theoretical approach has been the use of a series of multi−configuration Dirac−Fock (MCDF) computations. Effects from the core−polarizationand core−core correlations were considered and compared with the zero order5approximation. Both the experimental and theoretical results from this and otherworks are listed in Table 2. The theoretical results are at least two or three orders ofmagnitudes lower in accuracy. It is obviousthat semi−empirical calculations are inbetter agreement with our results. The wavelengths predicted by Kaufman et al [17],are 0.012 nm away from our experimental results for Ar9+ . The predictions by Edlénfor Ar10+, Ar13+, and Ar14+, are 0.09 nm, 0.06 nm and 0.02 nm, respectively, differentfrom our experimental wavelengths. The agreement forab initio MCDF calculationsis less satisfying, usually several tens of nm away from our experimental results. Theclosest wavelength, from MCDF calculation by Daset al. [5], deviates 0.06 nm fromour result of Ar13+. From our own MCDF calculations one can see that taking intoaccount the core−valence and core−core correlations does indeed improve thetheoretical value, even though the final results are still not satisfactory. A substantially enhanced agreement is reached when QED contributions aretaken into account. In this work, the large−scale configuration−interaction (CI)Dirack−Fock (DF) method was used to calulate the energies of the forbiddentransitions. The many−electron wave function with quantum numbersγ J wasexpanded in terms of a large number of the configuration state functions (CSFs) withthe same J. For the occupied shells the orbital basis was generated by themulticonfiguration DF method. The other one−electron states were obtained bysolving the Dirack−Fock−Sturm equations. The restricted active space method withsingle, double, and triple excitations was used to generate the set of CSFs. The totalnumber of CSFs was taken to be about 470 000 for Ar+13 and 150 000 for Ar+14 .TheQED contributions were evaluated by using the one−electron Lamb shift data takenfrom [25] with an effective nuclear charge number Zeff. For a given one−electronstate, Zeff was chosen to reproduce the related DF electron charged density at theCompton wavelength distance from the nucleus. In the case of Ar+14, our value for the6QED contribution agrees well with Sapirstein’s result presented in [9]. The results ofthe calculations are displayed in Table 3. They show excellent agreement with theexperimental results. Their estimated theoretical uncertainties are lower than those ofother ab initio calculations. In future, more elaborate evaluations of the electronicstructure will allow to extract QED information from the experimental results. In conclusion, highly precise experimental wavelengths of groundconfiguration M1 transitions of highly charged Ar ions were obtained in this work.The accuracy reached up to the 0.23 ppm level, 30 times higher than the previousrecord for this kind of transitions. To the best of our knowledge, these are also themost precise wavelength measurements for highly charged ions reported until now inany spectral range. Discrepancies betweenab initio calculations and experimentalresults are revealed, thus, calling on refined higher accurate modern relativisticatomic structure calculations. Inclusion of QED effects seems mandatory for asatisfactory agreement with the present experimental results.  We would like to thank Prof. V. P. Shevelko, Prof. I. Martinson, Dr. R.Hutton, and Dr. S. Huldt for helpful discussions. We gratefully acknowledge supportfrom the Deutsche Forschungsgemeinschaft (Leibniz Programm, also contract ULL166/2−1), Max−Planck−Institut für Kernphysik (MPI−K) in Heidelberg, DeutscheHochschulbauförderung and the University of Freiburg. One of the authors (YZ) isgrateful to the group of Prof. J. Ullrich (MPI−K) for their hospitality, and is partlysupported by the Natural Science Foundation of China (No. 0125520) and theChinese Educational ministry. VMS and IIT acknowledge the support from RFBR(Grants Nos 01−02−17248 and 00−03−33041) and from the program "RussianUniversities" (Grant No UR.01.01.072)7[1] R. W. P. McWhirter and H. P. Summers, App. At. Coll. Phys., Vol.2, 51 (1984).[2] A.H. Gabriel and C. Jordan, inCase Studies in Atomic Collisions Physics,edited by E. W.McDaniel and M. C. R. McDowell, (North Holand Press, 1972), Vol. 2, p. 209.[3] B. Edlén, Z. Astrophys. 22, 30 (1942).[4] K. N. Huang, Y. K. Kim, K. T. Cheng and J. P. Desclaus, Phys. Rev. Lett. 48, 1245 (1982).[5] D. P. Das, J. Hata and I. P. Grant, J. Phys. B 17, L1 (1984).[6] M. S. Safronova, W. R. Johnson and U. I. Safronova, Phys. Rev. A 54, 2850 (1996).[7] M. K. Aly, in The Solar Corona, edited by J.W. Evans (Academic Press, New York, 1963).[8] A. K. Bathia, U. Feldmann and J. F. Seely, At. Data. Nucl. Data Tab. 35, 453 (1996).[9] M. S. Safronova, W. R. Johnson and J. F. Safronova, Phys. Rev. A 53 , 4036 (1996).[10] B. Edlén, Phys. Scr. 28, 438 (1983).[11] V. M. Shabaev, Phys. Rep. 356, 119 (2002).[12] J. Gillaspy, in Trapping Highly Charged Ions: Fundamentals and Applications, (NOVAScience Publishers Inc., 2001).[13] B. Edlén, Phys. Scr. 26, 71 (1982).[14] B. Edlén, Phys. Scr. 28, 51 (1983).[15] D. J. Bieber, H. S. Margolis, P. K. Oxley and J. D. Silver, Phys. Scr. T73 , 64 (1997).[16] V. Kaufman and J. Sugar, J. Phys. Chem. Ref. Data Vol. 15, No 1, 321 (1986).[17] K. T. Cheng, Y. K. Kim and J. Desclaus, At. Data Nucl. Data Tab. 24, 111 (1979).[18] K. Butler and C. J. Zeippen, Astrophys. Supp. Ser. 108, 1 (1994).[19] J. T. Jefferies, Mem. Soc. R. Sci. Liege 17, 213 (1969).[20] G. Wlerick and C. Fehrenbach, inThe Solar Corona, edited by J.W. Evans (Academic Press,New York, 1963).[21] G. M. Nikolsky, R. A. Gulyaev and K. I. Nikolskaya, Solar Phys., 21 332 (1971).[22] B. Lyot and A. Dollfus, C. R. Acad. Sci. Paris 237, 855 (1953).[23] M. H. Prior, J. Opt. Soc. Am. B 4, 144 (1987).[24] C. Z. Dong, S. Fritzsche, B. Fricke and W. D. Sepp, Phys. Scr. T92, 294 (2001).[25] W.R. Johnson and G. Soff, At. Data and Nucl. Data Tables 33, 405 (1988).8434 436 438 440 442 444 446 4480200040006000800010000 Ar XIV  Intensity (counts)Wavelength (nm, air)441.0 441.510100100010000FWHM=0,106 nmy062 ± 3xc441.2606 ± 0.0006w 0.106 ± 0.001A 1044 ± 12 Fig. 19434 436 438 440 442 444 446 448−0.02−0.010.000.010.02Wavelength λ  (nm)(b)(a)  Linear fit  Polyn. 2nd degree  Polyn. 3rd degree  ∆λ (nm)434 436 438 440 442 444 446 448−0.0010.0000.001   ∆λ  (nm)Fig.210Table 1Source Contributions to wavelengthuncertainty (10−4 nm)   Ion Ar 9+ Ar 10+ Ar 13+ Ar 14+Line centroid determination 1.1 0.9 0.6 3.3Standard deviation of dispersionfunction1.1 1.6 0.2 0.9Calibration wavelength uncertainty 0.4 10 0.1 0.7Calibration systematic uncertainty 0.3 0.1 0.2 0.5Total 2 12 1 5Table 2Ion Transition Measured wavelength, (nm, air) Theoretical wavelength, (nm,air)This work Others ThisworkOthersAr +9(F−like)2s2 2p5  2P3/2 − 2P1/2553.3265±0.0002553.34±0.02[19]554.751,554.202553.803553.339             [16]Ar +10(O−like)2s2 2p4  3P2 − 3P1691.6878±0.0012691.686±0.006[15]693.241687.3               [17]691.7           [20] 692.862691.8               [18]691.72         [21] 692.283691.6               [14]Ar +13(B−like)2s2 2p  2P1/2 − 2P3/2441.2559±0.0001441.250±0.003[15]441.26±0.02[22]441.2563±0.0004*441.132±0.2[23]441.32±0.2[24]438.7[17]441.1    [6]442.1[4]441.65[24]441.2[5]441.32[14]Ar +14(Be−like)2s 2p  3P1 − 3P2594.3880±0.0005594.373±0.004[15]596.461594.5[8]594.0   [9]594.4           [7] 594.792594.37[10]597.9[17]1 Calculation using zero order approximation. 2 Calculation including valence−shell correlation.3 Calculation including core−valence and core−core correlation. * A recent independentmeasurement.Table 311Ion CIDF (cm−1) QED(cm−1)Total QED(nm)Theory,(nm, air)Experiment, (nm, air)Ar+13 22612.8(12.0)49.5(7.0) 22662(14) −0.96 441.14(27)441.2559(1)Ar+14 16770.9(3.0) 53.4(8.0) 16824.3(8.5)−1.89 594.22(30)594.3880(3)12Captions:Fig.1: An example of a typical line shape (single exposure) for a forbidden transitionmeasured in this work. The insert shows a Gaussian fit in logarithmic scale.Fig.2: Residuals from the dispersion function fitting, using a linear (solid square)dependence, a second (solid circle), and third degree polynomial (cross). a) all thecases. b) shows only second degree and third degree polynomial fitting residuals in anenlarged scale. Each single exposure includes two such calibration fits. Table 1: Error budget: main error sources and contributions to the final uncertaintiesof the wavelengths.Table 2: Experimental and theoretical results of this work in comparison with otherexisting data.Table 3: Results of the configuration interaction Dirac−Fock and QED calculationsfrom this work.13

High Precision Wavelength Measurements of Magnetic Dipole Transitions in Highly Charged Ar and Kr Ions

http://hdl.handle.net/11858/00-001M-0000-0011-82C0-D

High Precision Wavelength Measurements of Magnetic Dipole Transitions in Highly Charged Ar and Kr Ions

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