Experimental absolute-rate coefficients for electron-impact excitation of C3+ (2s2S1/2→2p2P1/2,3/2) near threshold [D. W. Savin, L. D. Gardner, D. B. Reisenfeld, A. R. Young, and J. L. Kohl, Phys. Rev. A 51, 2162 (1995)] have been reanalyzed to include a more accurate determination of optical efficiency and revised radiometric uncertainties which reduce the total systematic uncertainty of the results. Also, new R matrix with pseudostates (RMPS) calculations for this transition near threshold are presented. Comparison of the RMPS results to those of simpler close-coupling calculations indicates the importance of accounting for target continuum effects. The reanalyzed results of Savin et al. are in excellent agreement with the RMPS calculations; comparisons are also made to other measurements of this excitation. Agreement with the RMPS results is better for fluorescence technique measurements than for electron-energy-loss measurements

Bartschat, K.

Gardner, L. D.

Janzen, P. H.

Kohl, J. L.

Reisenfeld, D. B.

Savin, Daniel Wolf

Columbia University Academic Commons

PHYSICAL REVIEW A JUNE 1999VOLUME 59, NUMBER 6Reevaluation of experiments and new theoretical calculationsfor electron-impact excitation of C31P. H. Janzen, L. D. Gardner, D. B. Reisenfeld,* D. W. Savin,† and J. L. KohlHarvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138K. BartschatDepartment of Physics and Astronomy, Drake University, Des Moines, Iowa 50311~Received 7 January 1999!Experimental absolute-rate coefficients for electron-impact excitation of C31 (2s 2S1/2!2p 2P1/2,3/2) nearthreshold @D. W. Savin, L. D. Gardner, D. B. Reisenfeld, A. R. Young, and J. L. Kohl, Phys. Rev. A 51, 2162~1995!# have been reanalyzed to include a more accurate determination of optical efficiency and revisedradiometric uncertainties which reduce the total systematic uncertainty of the results. Also, new R matrix withpseudostates ~RMPS! calculations for this transition near threshold are presented. Comparison of the RMPSresults to those of simpler close-coupling calculations indicates the importance of accounting for target con-tinuum effects. The reanalyzed results of Savin et al. are in excellent agreement with the RMPS calculations;comparisons are also made to other measurements of this excitation. Agreement with the RMPS results isbetter for fluorescence technique measurements than for electron-energy-loss measurements.@S1050-2947~99!07506-X#PACS number~s!: 34.80.Kw, 34.80.LxI. INTRODUCTIONOver the last quarter century, electron-impact excitation~EIE! of ions has been the subject of intense study, bothexperimental and theoretical, as it is the dominant mecha-nism for the formation of emission lines in many laboratoryand astrophysical plasmas. Accurate knowledge of cross sec-tions, and thus rate coefficients, is necessary for interpreta-tion and modeling of the spectra of such plasmas. C31 hasparticular importance as its EIE generated 2p!2s doublet at155 nm is one of the most widely observed UV lines inastrophysics.Several measurements of the electron-impact excitationcross section of C31 (2s 2S1/2!2p 2P1/2,3/2) have beenperformed. In 1977 a crossed-beams fluorescence measure-ment was performed by Taylor et al. @1#. This measurementagrees very well with two-state close-coupling ~2CC! theory@2#, with later nine-state close-coupling ~9CC! calculations@3,4#, which agree with each other to better than 1% nearthreshold, and with a simpler Coulomb-Born with exchange~CBX! calculation @5#, which gives values slightly largerthan 2CC near threshold. Savin et al. @6# also used a crossed-beams fluorescence technique in 1995, reporting results thatwere lower: only the 9CC calculations fell within the experi-mental 90% confidence limits. In 1998 Bannister et al. @7#used a merged electron-ion-beams energy-loss technique tomeasure the same cross section, with the intent of resolvingany discrepancy between the first two measurements. Theirvalues are higher than CBX, although their 90% confidence*Present address: Los Alamos National Laboratory, M/S-D466,Los Alamos, NM 87545.†Present address: Columbia Astrophysics Laboratory, ColumbiaUniversity, New York, NY 10027.PRA 591050-2947/99/59~6!/4821~4!/$15.00limits overlap the 9CC theory. Greenwood et al. @8# alsohave measured this cross section using a merged-beamsenergy-loss technique; again, results are higher than CBX.Recently, a subtle effect in a calibration technique used bySavin et al. was discovered that caused a small shift in theresults. In addition, information about the uncertainties ofcalibrated photodiodes came to light allowing the total speci-fied systematic uncertainty of this measurement to be re-duced. In light of the perceived discrepancy between experi-mental results and the marginal agreement between therecent energy-loss experiments and 9CC theory, this paperpresents reanalyzed results of Savin et al., along with a 26-state R matrix with pseudostates ~RMPS! calculation ofgreater sophistication than earlier calculations.II. EXPERIMENTThe experimental apparatus and data collection tech-niques used by Savin et al. were discussed in detail in theiroriginal paper @6#; only the calibration of the optical systemis relevant to this reanalysis. Briefly, an electron beam wassent across a carefully prepared C31 beam at an angle ofnominally 55°. The currents and shapes of both beams weremeasured. Photons were counted using beam chopping andsynchronous detection to subtract background. A large mir-ror below the collision volume, which subtended slightlyover p sr, concentrated photons onto a photomultiplier tube~PMT!, which itself subtended '0.17 sr ~see Fig. 1!. Theelements of the optical system were calibrated individually,and a ray-tracing code was used to determine the overallabsolute photon detection efficiency of the system. The ab-solute quantum efficiency of the PMT was determined byreferencing the PMT to a CsTe photodiode calibrated by theNational Institute of Standards and Technology ~NIST!. Inthis manner an absolute rate coefficient was derived.During the analysis of a recent Si21(3s2 1S!3s3p 1P)measurement @9#, which used calibration techniques similar4821 ©1999 The American Physical Society4822 PRA 59BRIEF REPORTSto those of the C31 measurement, it was discovered that theanalysis of the mirror calibration of Savin et al. had not fullyaccounted for multiple reflections particular to the calibrationapparatus. Accounting for these reflections yields a mirrorreflectivity 6% lower than that used by Savin et al. in theirdata reduction. All measured rate coefficients and statisticaluncertainties then increase correspondingly. This correctionis three times larger than the 90% confidence level assignedby Savin et al. to mirror reflectance uncertainty, and, there-fore, it is not taken into account by their systematic errorbars.A separate matter in this reanalysis stems from the lead-ing contribution to the total experimental uncertainty: theuncertainty in the absolute efficiency of the NIST-calibratedphotodiode. The photodiode efficiency calibration immedi-ately preceding the C31 EIE measurement had a quoted un-certainty around 155 nm of 6% ‘‘probable error,’’ which wastaken to be 15% at a confidence level considered to beequivalent to a statistical 90% confidence level. However, bythe time of the follow-up photodiode calibration, NISTquoted an uncertainty of 9% at 2s at the same wavelength.The reduction in uncertainty came largely from a reevalua-tion of the methodology used at NIST for assigning calibra-tion uncertainties, rather than from changes in the calibrationtechnique itself @10#. Therefore, it seems appropriate to usethe more recent uncertainty value, along with an additional0.5% to cover the 1% drop in the photodiode efficiency be-tween calibrations. This reduces the total systematic uncer-tainty of the experiment from 26% to 22% ~see Table I!.The reanalyzed C31 (2s!2p) data are listed in Table IIand plotted in Fig. 2. Although the results were originallyreported as rate coefficients ^vs& convolved over the experi-mental energy spread @a Gaussian with a full width at halfmaximum ~FWHM! of 1.7460.37 eV#, they are reportedhere as cross sections ^vs&/^v& as well, in keeping withcurrent convention. The error bars on the circles in Fig. 2 andthe uncertainties quoted in Table II represent the statisticaluncertainty at the 90% confidence level (1.65s). The totalexperimental uncertainty (623%) is shown by the large er-ror bar on the 10.10-eV data point in Fig. 2.III. THEORYThe numerical calculations performed for this paper arebased on the nonrelativistic R-matrix ~close-coupling! ap-FIG. 1. Diagram of the experimental apparatus.proach. In addition to standard 2-state and 9-state calcula-tions that were carried out for comparison with earlier work@2–4#, the RMPS method was employed in order to accountfor coupling between both discrete and continuum parts ofTABLE I. Summary of systematic uncertainties. All uncertain-ties are quoted at a confidence level considered to be equivalent toa statistical 90% confidence level. Sources of uncertainty not dis-cussed in this paper are discussed in the original paper by Savinet al. @6#.Sources of Uncertainty UncertaintyUncertainty in beam densitiesaperture area of the ion probe 7%ion-beam probe biasing procedure 2%correction factor for O41 contamination 1%aperture area of the electron probe 4%electron-beam probe biasing procedure 8%Uncertainties in beams’ geometric-overlap/detection-efficiency factorspatial coordinates of the collision volume 5%ion source fluctuations 4%electron spiraling 8%C31(2p 2P) lifetime 2%computational error in overlap determination 1%radiometric calibrationNIST standard photodiode accuracy 7%photodiode calibration variation 1%PMT photocathode response map 9%mirror reflectance 3%crystalline quartz filter transmittance 2%MgF2 window transmittance 1%computational error in ray tracing 1%Uncertainty from normalizing the nonabsolute 10%EIE dataTotal quadrature sum a 22%aTotal experimental uncertainty ~in %)5@2221(90% statisticaluncertainty!2#1/2.TABLE II. Absolute C31 (2s 2S!2p 2P) electron-impactexcitation results. Statistical uncertainty is given in parentheses at1.65s and does not include systematic uncertainty.Rate coefficient Cross sectionEnergy ~eV! (1028 cm3 s21) (10216 cm2)5.79 -0.12 ~0.23! -0.08 ~0.16!7.09 1.04 ~0.21! 0.66 ~0.13!7.46 2.27 ~0.37! 1.40 ~0.23!7.71 3.32 ~0.64! 2.02 ~0.39!8.16 5.51 ~0.40! 3.25 ~0.24!8.84 8.07 ~0.84! 4.58 ~0.48!9.07 7.80 ~0.35! 4.37 ~0.20!10.00 8.59 ~0.50! 4.58 ~0.27!10.10 8.29 ~0.63! 4.40 ~0.33!11.22 7.52 ~0.53! 3.79 ~0.27!12.04 8.19 ~0.51! 3.98 ~0.25!PRA 59 4823BRIEF REPORTSFIG. 2. Absolute C31 (2s 2S!2p 2P) electron-impact excitation cross sections. The circles in ~a! are the reevaluated results of Savinet al. Error bars represent statistical uncertainty at the 90% confidence level, except for the large error bar on the 10.10-eV data point, whichrepresents the total experimental uncertainty at a confidence level that is considered to be equivalent to a statistical 90% confidence level.The diamonds in ~a! are from Taylor et al. @1,20#; the triangles and squares in ~b! are the results of Bannister et al. @7# and Greenwood etal. @8#, respectively. Error bars shown for these experiments represent the typical total uncertainties at a 90% confidence level. Fourtheoretical calculations are also presented, convolved with the experimental energy spreads @a 1.74-eV FWHM Gaussian in ~a! and a 0.17-eVFWHM Gaussian in ~b!#. Also in ~a!, the RMPS theory has been convolved with the 2.3-eV FWHM spread of Taylor et al. for a bettercomparison near threshold; this is shown by the dotted line.the target spectrum. The RMPS calculation was very similarto the corresponding work on the Be1 @11# and B21 @12#targets described before, and hence, we give only a very briefsummary here.To begin with, the Hartree-Fock orbitals 1s-4s , 2p-4p ,3d-4d , and 4 f were used to construct the lowest nine physi-cal (1s2nl )2L states of the C31 target. In addition, pseu-doorbitals n¯ l ~up to 9¯ s , 8¯ p , 8¯d , and 7¯ f ) were constructedby taking the minimum linear combination of Sturmian-typeorbitals rie2ar orthogonal to the above-mentioned orbitals.The pseudostates were then obtained through diagonalizationof the target Hamiltonian. Since we were interested in resultsfor electron-impact excitation of the resonance (2s!2p)transition, which are relatively insensitive to minor changesin the choice of a , we set a51.5 in order to produce onepseudostate with negative energy per total target angular mo-mentum, with the remaining pseudostates lying in the targetcontinuum. All states could be fit into an R-matrix box ofradius 20 a0, and 25 basis functions per angular momentumof the projectile electron were sufficient to produce con-verged results for total collision energies up to 20 eV.One indication about the quality of the target descriptioncan be obtained by investigating the theoretical results forthe oscillator strength in both the length and the velocityforms of the dipole operator. In the present calculations, weobtained values of 0.292 and 0.322, respectively, essentiallyindependent of the number of states included. This is notsurprising, since the 2p orbital was optimized on the energyof the 2Po state while the core orbitals were kept fixed.Despite the remaining difference between the length and ve-locity results, we judge the target description to be suffi-ciently accurate, since the length form ~which is generallypreferred in such optimization procedures! predicts an Avalue of 2.753108/s, in very good agreement with the ex-perimental result of (2.7160.07)3108/s obtained by Knys-tautas et al. @13# and also in other measurements. ~A list ofadditional references can be found in Savin et al. @6#.!IV. DISCUSSIONExperimental data and theoretical calculations are shownin Fig. 2. Care must be taken to convolve the theory with theenergy spread of each experiment for a valid comparison.The new RMPS values fall slightly below the 9CC resultswhich, in turn, lie below the 2CC predictions. This trend oflowering the 9CC predictions by approximately 2–5% is notunexpected, since it was also seen in the corresponding workon Be1 @11# and B21 @12#. Note that our 2CC and 9CCresults agree very well with those of Refs. @2–4#. We believethat the RMPS results represent the most reliable theoreticalpredictions for the collision part of the problem; the structureresults for this and simpler models such as CBX, 2CC, and9CC are apparently very similar. If results from simplermodels should indeed lie closer to experiment, this would besomewhat fortuitous. The reanalyzed results of Savin et al.and the measurement of Taylor et al. are in excellent agree-ment with the RMPS calculations. Although the RMPStheory agrees with the measurement of Bannister et al.within their 90% absolute error bars, the agreement is not asgood as with either of the fluorescence technique measure-ments. Agreement with the energy-loss measurement ofGreenwood et al. is, for the most part, outside their 90%absolute error bars.The reanalysis of the Savin et al. EIE measurement alsoapplies to the dielectronic recombination ~DR! measurementusing the same apparatus @14#. This measured absolute DRrate in an external electric field of 11.460.9(1s) V cm214824 PRA 59BRIEF REPORTSgoes from (2.7660.75)310210 cm3 s21 to (2.9460.76)310210 cm3 s21, where the total experimental uncertaintyis quoted at 1 s . Thus the measurement no longer agrees aswell with theory. The source of the discrepancy betweenthese measurements and field-enhanced DR calculations@15–17# may be due to the presence of crossed electric andmagnetic fields in the interaction region of the experiment@18,19#.ACKNOWLEDGMENTSThis work was supported by NASA Supporting Researchand Technology Program in Solar Physics Grant Nos.NAGW-1687 and NAG5-5059, and by the Smithsonian As-trophysical Observatory. This paper was also supported bythe National Science Foundation under Grant No. PHY-9605124 ~KB!.@1# P. O. Taylor, D. Gregory, G. H. Dunn, R. A. Phaneuf, and D.H. Crandall, Phys. Rev. Lett. 39, 1256 ~1977!.@2# J. N. Gau and R. J. W. Henry, Phys. Rev. A 16, 986 ~1977!.@3# V. M. Burke, J. Phys. B 25, 4917 ~1992!.@4# A. K. Pradhan ~private communication!.@5# N. H. Magee, Jr., J. B. Mann, A. L. Merts, W. D. Robb, LosAlamos Scientific Laboratory Report No. LA-6691-MS, 1977~unpublished!.@6# D. W. Savin, L. D. Gardner, D. B. Reisenfeld, A. R. Young,and J. L. Kohl, Phys. Rev. A 51, 2162 ~1995!.@7# M. E. Bannister, Y.-S. Chung, N. Djuric, B. Wallbank, O.Woitke, S. Zhou, G. H. Dunn, and A. C. H. Smith, Phys. Rev.A 57, 278 ~1998!.@8# J. B. Greenwood, S. J. Smith, A. Chutjian, and E. Pollack,Phys. Rev. A 59, 1348 ~1999!.@9# D. B. Reisenfeld, L. D. Gardner, P. H. Janzen, D. W. Savin,and J. L. Kohl ~unpublished!.@10# L. R. Canfield ~private communication!.@11# K. Bartschat and I. Bray, J. Phys. B 30, L109 ~1997!.@12# P. J. Marchalant, K. Bartschat, and I. Bray, J. Phys. B 30, L435~1997!.@13# E. J. Knystautas, L. Barette, B. Neveu, and R. Drouin, J.Quant. Spectrosc. Radiat. Transf. 11, 75 ~1971!.@14# D. W. Savin, L. D. Gardner, D. B. Reisenfeld, A. R. Young,and J. L. Kohl, Phys. Rev. A 53, 280 ~1996!.@15# D. J. McLaughlin and Y. Hahn, Phys. Rev. A 27, 1389 ~1983!.@16# K. J. LaGattuta, J. Phys. B 18, L467 ~1985!.@17# D. C. Griffin, M. S. Pindzola, and C. Bottcher, Phys. Rev. A33, 3124 ~1986!.@18# F. Robicheaux and M. S. Pindzola, Phys. Rev. Lett. 79, 2237~1997!.@19# D. C. Griffin, F. Robicheaux, and M. S. Pindzola, Phys. Rev.A 57, 2708 ~1998!.@20# D. Gregory, G. H. Dunn, R. A. Phaneuf, and D. H. Crandall,Phys. Rev. A 20, 410 ~1979!.

Reevaluation of experiments and new theoretical calculations for electron-impact excitation of C3+

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Reevaluation of experiments and new theoretical calculations for electron-impact excitation of C3+

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