JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Relative Transition Probabilities for KryptonMYRON H. MILLER* AND RANDY A. RoIGt

Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland 20742

AND

ROGER D. BENGTSONDepartment of Physics, University of Texas at A ustin, A ustin, Texas 78712

(Received 27 April 1972)

Relative transition probabilities of the more prominent Kr i and Kr 11 lines have been measured usinga gas-driven shock tube as a spectroscopic source. Results for 22 Kr I lines (4200 <cX < 8500 A) and 33 Kr IIlines (4t100<X<5300 A) have estimated reliabilities of 8-50%. The data are compared with other measure-ments and with theoretical calculations.INDEX HEADINGS: Spectra; Krypton; Source; Plasma.

Oscillator strengths of the visible and near-infraredkrypton lines are difficult to determine, &ither experi-mentally or theoretically. Inherent weakness andsusceptibility to Stark broadening tend to make theselines troublesome spectroscopic subjects, whereasquantum-mechanical predictions must contend withpronounced intermediate coupling and configurationmixing in both the atom and first ion. This paperpresents first experimental line strength data for thevisible Kr ii lines as well as for several of the moreprominent Kr i lines.

EXPERIMENTAL METHOD

The spectroscopic light source used for this investiga-tion is the thermal plasma behind the reflected shockwave in a gas-driven shock tube. Instrumentation andtechniques are similar to those described in earlierinvestigations of transition probabilities.'- 3 Plasmaconditions were measured by a variety of methods.4

Temperatures, determined three or four independentways4 in each experiment, should be accurate to ±t3%.Pressures and electron densities are usually reliable to7 and 20%, respectively. A neon carrier was the majorconstituent of the test gas with small percentages ofspectroscopic additives. Table I summarizes theexperimental conditions.

A 4-m spectrograph (2-A resolution) and a 1-mspectrograph (4-A resolution) were employed simul-taneously to provide redundant photometry. Time-resolved spectrograms recorded on Kodak type IN,103-0, and 2475 plates were transformed to relativeintensity-vs-wavelength profiles by a digital-computercode.5 Characteristic curves were obtained (i) by placinga seven-step neutral density filter over the spectrographslit, (ii) by using a continuously variable filter, and(iii) by photoelectrically monitoring the light incidenton the plates from continuum sources. A xenon flashlamp was used to check for reciprocity failure. Spectralresponses of all emulsions were calibrated against theanode emission of a well-regulated carbon arc.6 A fastmechanical shutter,7 located at an intermediate focal

plane common to both spectrographs, was adjusted togive exposure times of 40-150 /s. Precautions weretaken to ensure that film-development conditions wereheld constant.

Accuracy of photographic data is limited by (i)grain noise, which is particularly troublesome whendealing with the profiles of faint, diffuse, and partiallyblended Kr I lines, and (ii) the fact that useful portionsof the characteristic curves generally span 14 decadesin intensity. Thus a single exposure tends to yield dataon either stronger or weaker lines. In a given experiment,the integrated intensity within a typical profile canbe determined with a precision of 15-20%.

By virtue of their comparatively small transitionprobabilities and fairly large Stark widths at electrondensities of (4-14) X 1016 cm-3 , the krypton lines requireslight, if any, corrections for radiative trapping, evenin the infrared. Re-absorption within shock-tubeboundary layers is negligible because lower-stateenergies exceed thermal energies by factors of 6 or more.

RESULTS AND DISCUSSION

Neutral-krypton transition probabilities measuredrelative to Kr I 4502.35 A are presented in Table II.Tolerances (67% confidence limits) were computedfrom observed scatter and estimated limits of possible

TABLE I. Experimental conditions used in determiningkrypton relative-transition probabilities.

Plasma Number ofGases added to Temperatures pressures experi-

neon carrier [10'K] (106 dyn/cmr) ments

0.2% SiH4 } 10.8-12.9 6.1-25.2 9+0.57% Kr J

0.68% B2Hs\ 10.7-12.2 5.7-19.0 7+7.95% Kr

0.66% B32H} 10.1-11.4 8.0-22.0 6±12.42% Kr2

1.92% Ar+1.057 Kr 10.2-12.4 6.3-22.0 4+0.63% Xe

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VOLUME 62, NUMBER 9 SEPTEMBER 1972

18MILLER, ROIG, AND BENGTSON

TABLE II. Relative-transition probabilities for Kr i.All values relative to 4502.35 A.

MurphyThis Experi- Calcu- Fried-

Xiir (A) Classification Jt-Jk work, ment lation ricks

4273.97 Ss[14]° 6p[11] 2-2 2.0 A 3.30 1.194282.97 Ss[14] 0 -6p[14] 2-1 0.54B 0.31 0.174318.55 5sE131]0-6p[2-k] 2-2 1.37A 0.79 0.424319.58 5s[I-I]0 -6p[24k] 2-37 3 2.34 2.444•362.64 5sE1-21]'-6p[41] 2-1 0.90A 1.03 1.534376.12 5s[1-2]0 -6pfj] 1-0 4.70A 7.00 1.654399.97 5s'C[l]-6p'[1A] 1-2 1.93A 2.25 1.61 1.054410.37 5s'[-4]7-6p{E-2] 1-1 0.48C4425.19 Ss'L-2]`-6p'[141] 1-1 0.95A 1.21 0.994453.92 5s[1l] 0 -6pE[-1] 1-2 0.72A 0.89 0.51 0.734463.69 SsEl[-.20 -6p[14J - 1-1 2.14A 2.48 1.36 1.464502.35 5s[1-415 -6p[2-41] 1-2 1.0 1.0 1.0 1.05562.23 Ss[1-4J

0 -Sp'[142L] 2-2 1.90C5570.29 Ss[l-] 0 -p'[-41] 2-1 11.3 D5870.91 5s[1X]0 -5p'[-1-] 1-2 9.40A7587.41 Ss[1!] 0 -5p[-4] 1-0 12.8 C7601.54 Ss[14J 0 -5p[14] 2-2 4.6 B 26.2 14.47685.25 5s'[4110-5p'[4] 1-0 13.1 D 2.57694.54 5s[1430 -5p[14] 2-1 0.56D7854.82 Ss'[4] 0 -5p'[4] 0-1 6.29C 15.4 9.27928.60 5p[2-&Sd[3]- 0 2-3 1.71C8059.50 5ss'C1-0-Sp'[1-] 0-1 4.9 D 20.6 8.68508.87 5s'[7-1]-Sp'[1-4] 1-1 12.2 C 34.0 7.4

Uncertainty 7%< A< 12%; 12% <B< 20%; 20% <C< 30%; D >30%.

systematic errors; for most lines, scatter accounts forless than half the tabulated uncertainty.

Data for comparison include Friedrichs8 measuredA values for four Kr i lines. His results from twoseparate arc studies have been averaged in Table II.There is a factor-of-2 discrepancy between presentresults and those of Friedrichs.' Differences betweenexcitation potentials are not large compared to meanthermal energies in either experiment so that thereshould be only slight sensitivity to a possible bias inmeasured source conditions.

Murphy9 employed the same shock tube used for thepresent work, but with distinctly different spectroscopicinstrumentation. For visible lines, agreement betweenthese data and the present work is generally within thecombined tolerance of the two sets of experiments.Despite the generally satisfactory agreement in thevisible, there is pronounced disagreement between thetwo sets of infrared results. In this regard, it may bepertinent that Murphy chose independent absolutescales for his visible and infrared data results.

The intermediate-coupling calculations of Murphy," 0

have in most cases predicted the observed relativeline strengths within the overlap of jointly estimateduncertainties. However, there are some conspicuousdisagreements. Transitions involving the 6p levels areprone to cancellation in the radial matrix elements aswell as to large perturbation from configurationinteraction.

Osherovich and Verolianen" have measured thelifetimes of several levels of Kr i, but the complexity ofthe branching ratios prohibits direct comparisons withthe present results.

Pery-Thorne and Chamberlain'2 determined relativef values for infrared Kr i lines by the hook method.Their results for the only two lines in common withthe present work, 7601 and 7695 A, yield the ratioA(7601)/A(7695)>3 as opposed to our ratio of 9.Malakhov'3 measured the same lines using a reabsorp-tion method and found the ratio to be 1.2. Since thispair of lines originates from states having nearly thesame excitation energy, and considering their proximityin wavelength, it is puzzling that there should be solarge a spread between the various experiments.Unrecognized radiative trapping, which would notaffect a hook-method measurement, would cause the

TABLE III. Relative-transition probabilities for Kr iI.All values relative to 4355.47 A.

Kooze-kanani

This et al.Xair (A) Classification Ji-Jk works (Ref. 15)

4057.014065.114088.334098.724145.124236.644250.584268.814292.924300.494322.984355.474369.694381.524386.544422.704431.674475.004523.144577.204615.284619.154633.884658.874680.414739.004762.434765.744811.764825.184832.004846.605208.32

5s' 'D-5p' 2p° a- 0.78ESs' 2D-5p 2D0

2 a 0.63D5s' 2D-5p' 2DI 2-5 0.84CSs 4 P-5p 2 DI 2-2 1.83CSs 4P-5p 4S0 4-2 0.38C2 aSp 4P°-6s 4p 2-2 1.58DSs 2 P-5p 2D° 2-4 0.51E

Sp 4 S5 -5d 2P 2-2 2.7bE5s 4P-5p D'D0

2-2 0.67A5s 2p-5p 4S0 2-2 0.35B

5s" 2

D-5p" 2p5

2-3 9.5 E5s 4 P-5p 4DI A 7 1.0

5p' 2 F0 -4d" 2D L-2 18.4 DSS"

2S-5f 2D' I-_ 24.4 E

Sp 4P°-6s 4P 2-2 1.83fE5s' 2D-5p' 2P° 3-2 1.17C

554

P-5p 4D' 4-4 1.14B

6s' 2D-5pt 2p0

25-2 1.12C5p

4 P°-6s 4P 4-4 5.8E

5s' 4D-5p' 2F0 2-2 1.54A

5s 'P-5p 2P0 A-23 0.87C

5s 2P-5p 2D H 1.47A5s' 2D-5p' 2F 1.24C5s 4P-5p 4P° 2-2 1.12A5sPS~p'5fi5 4-4 1.66DSs 4P-Sp 4D0

2-2 1.5OB5s 'P-Sp 'B0 4-3 0.78B5s 4P-5p4D0

2-- 1.21B53

4 P-5p 4D0 2-2 0.46D

Ss 2P-5p 4S° 4-4 0.50f55 4 P-5P 4P0

2-2 1.46B5s 2p-5p 2P° 2-2 1.75C5s 4P-5p 4PO ' -- 3.21C

0.110.42

0.290.02

1.0

0.59

0.480.56

0.700.030.640.420.250.050.65

0.09

- Uncertainty 9%< A< 14%, 14% 0cB< 25%, 25% <C< 37%, 37% <D< 50%, E >50%.

b Blending with weaker 4268.81 A approximately compensated for usingrelative intensity of Ref. 14.

1028 Vol. 62

RELATIVE TRANSITION PROBABILITIES FOR Kr

TABLE IV. Comparison with lifetime measurements for Kr ii.

Lifetime (ns)Fink et al. Lifetime (ns)a

Level Energy (Ref. 16) Present results

5p 4P5/2 16.60 8.5 5.25p 'P3/2' 16.65 10.6 7.85p 4D7/2' 16.83 8.7 8.7Sp 4 D5/2, 16.87 7.6 7.25p 4DI/2° 17.16 7.7 7.75p 2D5/2' 17.37 8.9 5.9Sp 4S,/2° 17.57 8.3 7.15p 2D,/2, 17.60 7.8 4.8Sp' 2F5/20 18.49 11.3 7.05p' 2F7 /20 18.56 8.5 6.55p' 2P3/20 18.62 7.6 7.75p

1 2p, 1 2 o 18.87 5.2 11.0

5p' 2D,/25 18.88 7.5 10.0Sp" 2P3 / 2

5 20.94 6.2 0.9

a All results normalized to measured lifetime of Kr ii 4355 A.

present ratio to err towards a lower rather than ahigher value.

Measured relative Kr ii transition probabilities arecompared in Table III with the predictions of Kooze-kanani and Trusty.' 5 There is striking disagreementbetween these intermediate-coupling calculations andour findings. The most probable reason for the differenceis strong mixing between the 5s and 4d levels. Anotherpossible source of error is the assumption made byKoozekanani and Trusty" that the lower states arenot mixed in the intermediate-coupling calculations.

Table IV compares relative lifetimes deduced fromour measured transition probabilities with lifetimesmeasured by a beam-foil technique'6 (with photographicdata recording). To correct our relative transitionprobabilities to lifetimes, all modes of decay other thanthe dominant transitions were ignored and all datawere normalized to the lifetime of Kr Ii 4355.47 Ameasured by Fink et al."6 with an estimated uncertaintyof 30%. On the basis of relative-intensity data,' 4 weestimate that less than 50% error is introduced into therelative lifetimes by this procedure. The agreementbetween the two sets of lifetimes is generally withinestimated tolerances. There is a trend for the agreementto deteriorate, however, as the level energy increases.

Whereas the relative A values measured with the shocktube are only weakly dependent on energy differencesof 2 eV, the results of the beam-foil investigation maybecome sensitive to cascading from higher levels.

The data in Tables II and III can be interrelated bythe measured A value ratio

A (4355 A Kr ii)

-- _=5.04 30%,A (4502 A Kr i)

where the error assigned to this ratio includes observedscatter and best estimates of possible bias of tempera-ture data.

ACKNOWLEDGMENTS

The authors would like to thank Dr. T. D. Wilkersonfor the encouragement of this work and Nick Parr andJoe Clawson for assistance in data reduction.

REFERENCES

* Research supported in part by NSF Grant No. GP-29255and NASA Grant No. NGR-21-002-007/8.

t Present address: Physics Department, Harvard University,Cambridge, Mass. 02138.

1 R. D. Bengtson and M. H. Miller, J. Opt. Soc. Am. 60, 1093(1970).

2R. D. Bengtson, M. H. Miller, D. W. Koopman, and T. D.Wilkerson, Phys. Rev. A 3, 16 (1971).

' M. H. Miller, R. A. Roig, and R. D. Bengtson, Phys. Rev.A 4, 1709 (1971).

4R. D. Bengtson, M. H. Miller, D. W. Koopman, and T. D.Wilkerson, Phys. Fluids 13, 372 (1970).

5 R. A. Bell, R. D. Bengtson, D. R. Branch, D. M. Gottlieb,and R. Roig, University of Maryland Report No. BN 572 (1968).

6 A. T. Hattenburg, Appl. Opt. 6, 95 (1967).7S. M. Wood and M. H. Miller, Rev. Sci. Instr. 41, 1196

(1970).H. Friedrichs, Z. Astrophys. 60, 176 (1964).P. W. Murphy, Ph. D. Dissertation, University of Maryland

(1968).P. W. Murphy, J. Opt. Soc. Am. 58, 1200 (1968).

"A. L. Osherovich and Ya. F. Verolianen, Vestnik LeningradUniversity, Fiz. i Khim. 1, 140 (1967).

12 A. Pery-Thorne and J. E. Chamberlain, Proc. Phys. Soc.(London) A82, 133 (1963).

1" V. P. Malakhov, Izv. Vysshikh Uchebnykh Zavedenii Fiz.8,180 (1965).

14 A. R. Striganov and N. S. Sventitskii, Tables of SpectralLines of Neutral and Ionized Atoms (Plenum, New York, 1968).

16 S. H. Koozekanani and G. L. Trusty, J. Opt. Soc. Am. 59,1281 (1969).

16 U. Fink, S. Bashkin, and W. S. Bickel, J. Quant. Spectrosc.Radiative Transfer 10, 1241 (1971).

September 1972 1029