Kallne, E.

Kallne, J.

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PFC/JA-83-41PRECISION MEASUREMENT OF THE H-LIKE X-RAYSPECTRUM OF C1 AND THE is LAMB-SHIFTE. Kaline and J. KallneSmithsonian Astrophysical ObservatoryandPlasma Fusion CenterMassachusetts Institute of TechnologyCambridge, MA 02139 U.S.A.Patrick Richard and M. StockliKansas State UniversityManhattan, KN 66506 U.S.A.November 1983This work was supported by the U.S. Department of Energy ContractNo. DE-AC02-78ET51013. Reproduction, translation, publication, useand disposal, in whole or in part by or for the United States govern-ment is permitted.By acceptance of this article, the publisher and/or recipient ac-knowledges the U.S. Government's right to retain a non-exclusive,royalty-free license in and to any copyright covering this paper.PRECISION MEASUREMENT OF THE H-LIKE X-RAY SPECTRUM OFC1 AND THE is LAMB-SHIFTE. Kllne and 1. K;lneSmithsonian Astrophysical Observatory'Cambridge, MA 02138, U. S. A.andPlasma Fusion CenterMassachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.Patrick Richard and M. St~ckliKansas State University, Manhattan, KN 66506, U. S. A.ABSTRACTThe H-like spectrum of chlorine emitted from the Alcator C tokamak has beenmeasured using a Bragg crystal x-ray spectrometer and in situ wavelengthcalibration. The 1s-2p transition energies were determined to an accuracy of34 ppm allowing for a test of the theoretically calculated Lamb shift of the islevel in C 16+ at the 10% level. This new technique of spectroscopy of highlyionized atoms could be further refined to approach the 5 ppm accuracy level inthe absolute transition energy determination.*Present address: JET Joint European Undertaking, Abingdon, 0X14 3EA, ENGLANDPage 2In this letter we present the results of a precision measurement of thewavelengths of x-ray transitions in highly ionized atoms. Such experiments havebeen done with the aim of determining the radiative QED corrections to the Diracenergy which cause a significant Lamb shift of strongly bound 92= 0 atomicorbitals. The information can be obtained by accurately measuring the energy ofthe ls-2p transitions in H-like atoms, for which the Dirac energies are wellknown, and comparing the data with theoretically calculated energies includingthe Lamb shift. Only two such experiments',s have been reported whichdetermined the Lamb shift of the is ground state through direct measurement ofthe ls-2p resonance transition. Accuracies of 18% and 13% were achieved for theLamb shift in iron' and chlorines, respectively. These two experiments usedenergetic ion beams and the greatest source of error was the experimentalDoppler shift correction due to the high ion velocities involved. Our approachto circumvent this problem is to observe the x-ray emission from highly ionizedatoms in tokamak plasmas. These plasmas provide the high thermal velocitiesneeded, i.e., electron temperatures of T > 1 keV, for the formation andexcitation of the ion species of interest while the velocities connected withany net ion motion are favorably much smaller. High resolution atomic plasmaspectroscopy studies have been reported',4 . Here, however, we present the firstexperiment of this kind designed for precise absolute determination of thewavelengths of x-ray transitions of particular interest to the fundamentals ofphysics.The experiment was carried out at the Alcator C tokamak at MIT. The plasmaconditions for our measurements were: electron temperature of T. = 1.2-1.8 keVand densities of N = 1-3 10 14cm for toroidal magnetic fields of BT = 8 or10 T with plasma currents of I = 400-500 kA. A discharge lasts typically some500 ms of which the middle 200 ms represent constant conditions. In the plasmasPage 3of hydrogen or deuterium, there are small amounts of impurities among whichchlorine is usually present at a concentration of 10 to 1075 relative to N .This ambient Cl concentration could be boosted by gas puff injection (HC1+Hemixtures) between discharges; injection during discharges was inhibited bycondensation on the walls of the entrance port due to the liquid nitrogencooling of the Alcator C vacuum vessel. The plasma temperature values mentionedfavor the formation of the ionization states C11 5+ and C 16+. The H-likespectrum of n = 2 to n = 1 transitions studied here emanate from electron impactexcitation of the C1 6+ ground state leading to the principal 1S1/2 - 2P2/3,1/2transitions (which are also known as Lyman a1 and a2 denoted here by W and W2and from dielectronic recombinations leading to satellite lines such as thestrong transitions 1s2s1 S -2s2p Pi, is2s3 S -2s2p3P2, ls2s S -2s2p311s2p3p2-2p2 3P2 and 1s2p1P -2p2 1D2 denoted by T, Q, R, A, and Is. The plasmawas viewed through a 130 gm thick Be-window with the line of sight beingperpendicular to the toroidal axis and the vertical field of view intersectingabout 10 cm of the central part of the plasma whose minor radius is 16.5 cm.Furthermore, the C11 6+ ions are found predominately in the hot core of theplasma where they are confined for time periods of the order 10 ms and reachtemperatures generally 200-400 eV below Te, i.e., the thermal velocities for ourconditions are Vi = 6-9 106 cm/s and hence the C1 x-ray lines have a Dopplerbroadening amounting to r D = 1.0 to 1.7 eV (FWHM). In comparison, ionvelocities due to net mass motions in our ohmically heated plasma are small(<106 cm/s)' and mainly in the toroidal direction so that along our line ofsight we estimate the Doppler line shifts to be at the most 0.01 eV.The x-ray line emission was measured with a Bragg crystal spectrometer.The instrumentation and methods used were basically the same as describedearlier 7 except for the facilities for obtaining the absolute wavelengthPage 4determination. For the photon detection, we alternatively used two positionsensitive proportional counters of different types for consistency checks.Furthermore, the spectrometer was placed 25 cm from the torus window making thetotal distance between plasma center and spectrometer entrance slit about110 cm. The 25 cm gap made it possible to use calibration sources withoutchanging the conditions used for the Cl measurement apart for the simple removalof the He-bag connecting the torus and the spectrometer. For the principalwavelength calibration we used a 5-keV electron beam shining on Ar gas kept at afew millitorr pressure; the Ka line at hv = 2957.813*0.008 eV was ourreference line and this together with Ka2 at 2955.684*0.013 eV and Ka4  at2977.51±0.06 eV gave the wavelength scales. The Ar source produced count ratesup to 50 c/s in the spectrometer compared to those of the C1 emission from theplasma reaching 50 kc/s. Count rates of up to 10 kc/s were obtained with theAg La emission, hv(La1 ) = 2984.3 eV with a line width of 2.6 eV FWHM6, from anx-ray tube. By measuring the Ag spectrum during the discharge compared withrecordings during the quiescent interval between discharges, we could verifythat the transient electromagnetic conditions of the discharge did not interferewith the measurement.An example of a measured Cl spectrum from a single plasma discharge isshown in Figure 1. Such a spectrum was obtained every 6 min and we generallyaccumulated some 5 C1 spectra before moving the Ar-source into position torecord calibration spectra (see Figure 2). A full measuring cycle thus tookabout an hour's time and was repeated some five to ten times during a day's run.Data were obtained from three production runs (I, II, and III in Table 1), eachconsisting of several measuring cycles and altogether Cl spectra were recordedfrom more than 100 plasma discharges. The data were divided into four subsets,according to detector type used (the 10 cm detector7,' for data sets I and IIPage 5and the 35 mm detector1 0 for III) and depending on the Cl emission rate (whereIa is low rate and all others are high). This provided a check on systematictrends in the data. The results are given in Table 1. The first column givesthe experimental difference in position (x) between the Ar Ka 1  reference lineand the W line in Cl including two corrections. The position of the Clspectrum was found to vary with count rate which was later identified with arate dependent off-set in the electronic modules used for the time-to-analogconversion (TAC). A correction was applied on the basis of the known averagecount rates for each discharge and the TAC rate dependence determined after theexperiment. An additional correction was applied to the data taken with the10 cm detector because a rate dependent space charge build-up causing aninterference between the adjacent 2P3/2 and 2P,/2 "Res. An empiricalcorrection was established on the basis of the observed rate dependence of theline separation and the assumption that the 2P3/2  line was shiftedproportionally to the distance from the center of charge gravity. The x valuesgiven are the mean of all the data points of each set and the assigned errorrepresents the standard deviation. The next column gives the energy scalefactor (k) with the energy E = k - X given in column four. The weighted meanvalue is E = 4.65±0.06 eV. The scatter in the data can largely be ascribed tothe uncertainty in the mentioned count rate corrections which are estimated tobe about ±15% for an average value of about 0.5 eV. Allowing for someadditional systematic uncertainty in the line fitting analysis, the total erroris estimated to be ±0.10 eV. Our results for the 1S 1/2-2P3/2 transition energyin Cl16+ is thus hv = 2962.46±0.10 eV. The result for the V -W fine structure12splitting is Ahv = 3.84±0.03 eV. Moreover, the two satellite lines (T and .)are determined to lie 20.2±0.2 eV and 33.6±0.2 eV to the low energy side of theW1 line.Page 6The theoretical transition energies are based on the Dirac energy gvinghv = 2963.310 eV for W1 with a small correction of -0.006 eV for the finitenuclear size. The radiative corrections due to self-energy (-1.009 eV of which+0.003 eV comes from the 2P3/2 level) and vacuum polarization (+0.068 eV) givesa Lamb shift of -0.941 eV. The total energy is predicted by Erikson'% to behv = 2962.266 eV for W with the -W 2 fine structure splitting beingAhv = 3.827 eV (see Table 2). In another calculation Mohrll obtainshv = 2962.3765 eV and AhV = 3.82718(3) eV. Both these theoretical results onhv(W1 ) are lower than our data but still within the experimental uncertainty of0.1 eV or 34 ppm in the energy of the W1,2 lines and about 0.03 eV in the finestructure splitting. The experimental Lamb shift is hvL = 2962.46-2963.31 =-0.85 eV and hence smaller than the theoretical one. For the fine structuresplitting we find agreement with theory within the error of 0.03 eV. In theexperiment of Briand et al.1 on Fe2 4+, the Lamb shift was found to be smallerthan predicted but not to exceed the error. They, however, reported a rathersurprising disagreement between experiment and theory on the fine structuresplitting. As an aside we note that the calculated energies of satellites lines(relative to 1 ) are 20.2 and 33.8 eV and hence consistent with our results towithin the experimental errors.The present study is important with regard to the implied potential ofatomic-plasma spectroscopy as a new technique among high precision measurements.We first point out the possibility for further improvement in the accuracy. Weenvisage to reach an accuracy of 8 pm in the detector (being one-tenth of theFWH.M spatial resolution) which, together with new high-count-rate electronics,should give a line position determination at an accuracy of a few ppm foraccumulation times as short as 50 ms. Second, by having designated tokamakruns, plasma conditions could be optimized to give minimum line broadening byPage 7choosing the lowest temperature compatible with the emission rate requirements.Finally, the ion net velocities, which can give line shifts at the 0.01 eV levelcan be dealt with by using instruments capable of radial plasma scans andultimately by usinga.dual spectrometer system for simultaneous viewing of theplasma from opposing directions. The atomic-plasma spectroscopy technique couldthus approach the accuracy of the calibration line used which, for instance, is8 meV or 3 ppm for the Ar Kai. Therefore, these tokamak measurements areparticularly suited for high precision work on few-electron systems of highlyionized atoms with Z in the range 10 to 30 which are amenable to accuratetheoretical calculations of fundamental interest to atomic physics.In conclusion, we have demonstrated the use of tokamak plasmas to performhigh precision measurements of soft x-ray resonance line spectra. Results arepresented on the H-like ls-2p spectrum of Cl of which the Lya lines are used toextract the is Lamb shift. We find that the predicted Lamb shift is larger thanour results but within the experimental uncertainty of 0.1 eV, so thatcorroborative data are needed to determine at which level present theories ceaseto be valid. On the other hand, augmented accuracy can be expected. Theexperience from this study suggests that with certain refinements in theinstrumentation and with control over the tokamak to optimize plasma conditions,the plasma-atomic spectroscopy is a viable technique for high precisionmeasurements of energies of highly ionized few-electron atoms at the ppm levelof accuracy.Page 8ACKNOWLEDGMENTSWe are grateful to Dr. R. Parker for his interest and support for this workand to Drs. E. Marmar and .. Rice for help on the experiment. We also thank thewhole Alcator staff for diligent machine operation and for help in mounting theexperiment.This work was supported by the United States Department of Energy (ContractDE-ASO2-76ET53052), and the United States Department of Energy, Division ofChemical Sciences.Page 9REFERENCES1. J.P. Briand, M. Tavernier, P. Indelicato, R. Marrus, and H. Gould,Phys. Rev. Lett., 50, 832 (1983).2. M.P. Stockli, P. Richard, R. Mann, R.D. Deslattes, P. Cowan, R.E. Lavilla,B. Johnson, K. Jones, M. Meron, and K. Schartnes, Bull. Am. Phys., 28, 781(1983), to be published.3. M. Bitter, S. von Goeler, R. Horton, M. Goldman, K.W. Hill, N.R. Sauthoff,and W. Stodiek, Phys. Rev. Lett., -422, 304 (1979), and Phys. Rev. A (to bepublished).4. E. Kellne, J. Kallne and J. Rice, Phys, Rev. Lett., 49, 330 (1982), andAmerican Institute of Physics Conference Proceedings No, , 463 (1982).5. L.A. Vainshtein and U.I. Safronova, Nucl, Data Tables 21. 4.9 (1978), andpreprint (unpublished).6. S. Suckewer, H.P. Eubank, R.J. Goldston, J. McEnery, N.R. Sauthoff, andH.H. Tower, Nucl. Fusion, 21, 1301 (1981); and K. Brau, M. Bitter,R.J. Goldston, D. Manos, K. McGuire, and S. Suckewer, Princeton PlasmaPhysics Laboratory Report PPPL-2013 (1982), unpublished.7. E. Kallne and J. Kallne, Physica Scripta T3, 185 (1983).8. J.A. Bearden in "X-ray Wavelengths", US Atomic Energy. Commission,NYO 10586, Oak Ridge, TN, USA (1964), unpublished.Page 109. C.J. Borkowski and M.K. Kopp, Rev. Sci. Inst., 46, 951 (1975).10. 1. K;lne, E. K;lne, L.G. Atencio, C.L. Morris,Nucl. Inst. Meth., 203, 415 (1983).and A.C. Thompson,11. G.W. Erikson, L. Phys. Chem. Ref. Data, k, 831 (1977).12. P.J. Mohr, Ann. of Phys., 88, 51 (1974) and Nuclear Data Tables, submittedfor publication.Page 11TABLE 1Comparison of results on the position (x) and energy (E) separation betweenthe Cl W line and the Ar Ka1 line and scale factors (k) for the four subsets ofthe data.x k ESet [Chs] [meV/ch] [eV]17.9810.3818.30*0.4617.68±0.2519.16±0.32257.5*1.5257.5±1.5258.3±1.2245.0±2.04.62*0.104.71±0.124.60±0.084.69±0.08IaIbIIIIIPage 12TABLE 2Summary of Results on Energieshv(eV) Experiment Theory 2w2w -W2Lamb Shif t2962.46±0.102958.62*0.103.84±0.03-0.85±0.102962.2662958.4393.827-0.941Page 13FIGURE CAPTIONSFigure 1: The Ka spectrum from the argon source obtained with the 10 cmdetector. The result of the line fit is also shown.Figure 2: The H-like spectrum of Cl from the Alcator C plasma obtained with the35 mm detector. The result of the line fit to the main lines (W and1W2 ) and the n = 2 satellites (T, Q, R, A, and J) is also shown withthe latter marked at the positions predicted in Reference 5.0 0V(IN00(N 0 000N'J eOHO SI~noI IWI)I00110-01.CN00z l00%0000%0 0 00H 0 0no

Precision measurements of the H-like x-ray spectrum of c1 and the 1s lamb-shift

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Precision measurements of the H-like x-ray spectrum of c1 and the 1s lamb-shift

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