Spectrum and energy levels of eleven-times ionized zirconium(Zr xii)

Joseph Reader and Nicolo AcquistaNational Bureau of Standards, Washington, D. C. 20234

(Received 21 May 1979)

The spectrum of Zr xii was observed with a low-inductance spark and a laser-produced plasma inthe region from 70 to 630 A on the 10.7-m grazing incidence spectrograph at NBS. From the identifi-cation of 36 lines, a system of 28 energy levels was determined. The level system (Cu i isoelectronicsequence, 3d "'nl) includes the series np (n = 4-6), nd (n = 4-6), nf (n = 4-8), and ng (n = 5-7). The4f 2-F term has an anomalously small fine-structure interval (1 ± 3 cm '). The ionization energy isdetermined from the ng series (n = 5-7) to be 1 905 500 + 200 cm 1 (236.25 + 0.03 eV).

The eleven-times ionized zirconium atom Zr XII is a memberof the Cu i isoelectronic sequence. Ions in this sequence havebecome important recently because of their role in the diag-nosis of controlled fusion plasmas. Zirconium has a relativelyhigh melting point and, as it acts as a getter for oxygen, it isbeing considered as a material for use in the interior of toka-maks. The spectra and atomic structure of the ions of Zr arethus of special interest.

The first line identifications for Zr XII were given by Alex-ander et al. 1 They used a vacuum spark to observe eight linesof the type 4s-5p, 4p-5d, 4d-5f, and 4p-5s lying in the region103-156 A. In 1977 the present authors 2 used a vacuum sparkto identify the 4s-4p resonance lines. In the present work weused a vacuum spark and a laser-produced plasma to carry outa relatively complete spectral analysis of this ion. Some 36lines, representing transitions between 28 energy levels, wereidentified.

EXPERIMENT

Our experimental procedure has been described in detailin recent papers 3,4 on the copperlike ions YxI and Mo xiv.The spark was a low-inductance, three-electrode type, as de-scribed by Feldman et al. 5 We used capacitors of either 4.7or 14.2 AF at voltages varying between 1 and 15 kV. Thespectrum of Zr XII was generally well developed at a voltageof 3 kV.

The laser-produced plasma was obtained by focusing thelight from a Nd/glass laser (wavelength 1.06 4m) onto flatmetallic targets. Typical laser pulses had an energy of 15 Jand a duration 10 ns. The spectrum of ZrxiI could be en-hanced relative to higher stages of ionization by using laserpulses of greater energy and longer duration, typically 30 J in20 ns. Ions below Zr IX were not generated to a significantextent in the laser-produced plasma.

The spectra were photographed on our 10.7-m grazing-incidence spectrograph. The angle of incidence was 800. Thegrating had 1200 lines/mm, providing a plate factor of 0.25A/mm at 300 A. The region covered was 70-630 A. Wave-length calibration in the region around 100A was obtainedfrom a vacuum spark of Ti.6 At longer wavelengths calibra-tion was obtained from vacuum spark spectra of Y (see Ref.3), spectra of Zrv-vII measured previously with slidingsparks,7-10 and impurity lines of oxygen and fluorine.

1659 J. Opt. Soc. Am., Vol. 69, No. 12, December 1979

Most of the wavelength measurements were taken fromobservations with the vacuum spark, the laser-producedplasma being used primarily to distinguish stages of ionization.However, several lines of Zr XII were seriously blended with

TABLE I. Observed lines of Zrxii.

x(A) Int. U(cm- 1) Classification

76.923 10 1300000 4s 2S31/2 - 6p 2P3/2

77.206 3 1295240 4s 2S1/ 2 - 6p 2P1 /2

85.536 10 1169100 4p 2P1 /2 - 6d 2D 3/2

87.147 200a 1147490 4p 2P 3/2 - 6d 2D 5/ 2?

91.412 2 1093950 4d 2D3/2-8f2F 5/2

91.710 3 1090390 4d 2D5/2 -8f 2 F 7/2

95.669 25 1045270 4p 2P1 /2 - 6s 2S 1/ 297.766 70 1022850 4p 2P 3/2 -6s 2S1/2

98.542 6 1014800 4d 2D 3/ 2 -7f

2F 5/2

98.885 8 1011280 4d 2D 5 /2-7f

2F 7/2103.707 1000 964255 4s

2S1/2 - 5p 2P 3/2

104.707 700 955046 4s 2S1/2 - 5p 2P1/2

111.014- 150 900787 4p2Pl1/2- 5d

2D 3/2

112.058 30 892395 4d 2D 3/2 - 6f2F5/2112.500 50 888889 4d 2D 5/2-6f

2F7/2

113.640 450 879972 4p 2P 3/2- 5d 2D 5/2

113.848 25 878364 4p 2P 3/2- 5d

2D 3/2

135.224 50 739514 4d 2D 5/2- 6p 2P3/2

135.435 25 738362 4d 2D 3/2 - 6p 2Pi/ 2141.660 50 705916 4f 2F - 7g 2G145.087 300 689242 4d 2D 3/2 - 5f2F5/2145.834 400 685711 4d 2D 5/2 - 5f 2F7/2150.841 2000 662950 4p 2P 1/2-5s

2S31/ 2

156.120 4000 640533 4p 2P 3/2-5s2S31/2

169.761 200 589063 4f 2F - 6g 2G245.477 50 407 370 4d 2D 3/2 - 5p 2P 3/2247.642 500 403 809 4d 2D 5/2 - 5p 2P 3/2251.152 300 398165 4d 2D 3/2 - 5p 2P1/2252.826 1000 395529 4f 2F -5g 2G284.338 250 351694 4p 2P1 /2 - 4d 2D 3/2

300.446 200 332 838.5 4p 2P 3/ 2 - 4d 2D 5/2

303.702 100 329270.1 4p 2P 3/ 2 - 4d 2D 3/2

313.376 125 319105.5 4d 2D 3/2 -4/ 2F 5/2

316.917 125 315540.0 4d 2D 5/2-4f2F 7/2

439.315 16000 227627.1 4s 2S31/2- 4p 2P3/2

487.325 5000 205201.9 4s 2S31/2- 4p 2P1/2

a Blended with strong 3p63d8-3p 53d9 transition of Zr xv. Present identificationas being partially due to ZrxII is tentative.

1659

6 5/2,/'/-1 '-3/12

8 1/2t - 5/2

7 /72 7 9/2r - 5/12 7/2

76 7f2 6 9/25 1 27/2

5 9/25 7/2 -7 712

ns np nd nf ng

FIG. 1. Grotrian diagram forZrxii. Wavelengths are in A.Intensities are indicated in pa-rentheses following the wave-lengths. Wavelengths of the4s-5p and 4s-6p transitions arethose calculated from the opti-mized level values.

lines of lower ionization stage in the spark spectra and had tobe measured in the laser-produced plasma.

LINE IDENTIFICATIONS, WAVELENGTHS, ANDENERGY LEVELS

The wavelengths, intensities, and classifications of theobserved lines of Zr XII are given in Table I. The uncertaintyof the wavelengths is ±0.005 A. The intensities are visualestimates of photographic blackening.

The classification of the line at 87.147 A is tentative. Thisline is due primarily to Zrxv. However, its behavior at dif-ferent excitation conditions indicates that it is probably ablend of two ionization stages. As the 4p 2P 3/2 - 6d 2D5/2transition of Zr xii is expected at this wavelength and shouldbe observable, we have classified X87.147 accordingly. Itsobserved intensity of 200 is due mostly to Zr xv; the intensityof the 4p 2P3/2 - 6d 2D5/2 transition of Zr xii should be about20 on the present scale.

The energy levels are given in Table II. They are plottedwith the observed transitions in Fig. 1. The level values andtheir uncertainties were determined by a least-squares opti-mization procedure11 that minimizes the differences betweenthe observed and calculated wave numbers. The fine struc-ture intervals of the observed terms are also given in Table II.

1660 J. Opt. Soc. Am., Vol. 69, No. 12, December 1979

The uncertainties of these intervals are estimates based ona relative uncertainty of +±0.003 A in the values of the longestwavelength transitions that define each interval.

For the np and nd terms the fine structure intervals are veryregular. The values of=n *( = 1 + 1/2) - n*( = 1- 1/2)for the 4p, 5p, and 6p 2p terms are 0.0203, 0.0199, and 0.0198,respectively. For the 4d, 5d, and 6d 2D terms the values ofhn* are 0.0045, 0.0044, and 0.0042, respectively.

As shown in Table II, the 4/ 2F term has practically nosplitting, although the nonrelativistic Hartree-Fock (HF)value of the interval is 252 cm-1. This anomaly is charac-teristic of nf configurations of copperlike ions; it has beendiscussed in some detail in Refs. 3 and 4. As noted in Ref. 3,the fully relativistic calculations of Cheng and Kim12 accountrather well for the observed 2F intervals. A comparison of theobserved intervals, the nonrelativistic HF values, and therelativistic values of Cheng and Kim12 is given in Table III.

The 4/ 2F interval has not been observed for most of the ionspreceding Y xI in the Cu I isoelectronic sequence. In a recentbeam-foil spectroscopy experiment13 the 4/ 2F splitting inKrVIII was measured as -60 ± 35 cm-1. This value agreeswith the splitting of -40 cm-1 predicted by Cheng and Kim12for this ion. It also follows the trend of the values observedfor the higher sequence members: -18 cm-1 for YxI, +1

Joseph Reader and Nicolo Acquista 1660

160MH

1200

800-

400 F-

0I I I [ 1

I

TABLE II. Energy levels of Zrxii.

Finestructure

Unc. intervalTerm J E(cm-1) (cm-1) n* (cm-1)

4s 2S 1/2 0 3 2.8797

4p 2p 1/2 205202 3 3.0486 22 425 ±- 23/2 227627 3 3.0689

4d 2D 3/2 556897 4 3.4231 3567±25/2 560464 5 3.4276

5s2S 1/2 868156 15 3.9030

4/2F 5/2 876003 6 3.9178 1 ± 37/2 876004 7 3.9178

5p 2p 1/2 955062 9 4.0775 9208 43/2 964270 7 4.0974

5d 2D 3/2 1105990 28 4.4458 1609 ±L 145/2 1107 599 39 4.4502

5f 2F 5/2 1246139 24 4.8955 36 ± 147/2 1246175 24 4.8956

6sWS 1/2 1250475 38 4.9117

5g 2G 7/2, 9/2 1271532 10 4.9926

6p 2p 1/2 1295257 26 5.0887 4723 ± 163/2 1299980 27 5.1085

6d 2D 3/2 1374300 68 5.4542 813 ± 405/2 1375113? 66 5.4583

6f 2F 5/2 1449292 40 5.8854 60 ± 247/2 1449352 40 5.8858

6g 2G 7/2, 9/2 1465066 19 5.9899

7/ 2F 5/2 1571693 52 6.880 47 ±L 317/2 1571740 51 6.881

7g 2G 7/2, 9/2 1581919 26 6.988

8f 2F 5/2 1650845 60 7.877 13 ± 357/2 1650858 60 7.878

LIMIT 1905500

cm- 1 for ZrXII, and +118 cm- 1 for MoxIv. The calculatedvalues of Cheng and Kim,12 which are negative from Geivthrough Zr xII, also follow this trend very well.

In Table IV we list the wavelengths calculated from theoptimized energy levels for the 4s-5p and 4s-6p transitions.

TABLE Ill. Observed and calculated nf2F fine-structure intervals in Zrxii.Values are in cm- 1 .

Nonrelati- RelativisticTerm Observed vistic HFa HFb

4/ 2F 1 ± 3 252 -205f2F 36 ± 14 150 146f 2F 60 ± 24 94 207f/2F 47 ± 31 608f2F 13 ± 35

a Calculated with the program of Froese-Fischer, Ref. 14.b Cheng and Kim, Ref. 12.

1661 J. Opt. Soc. Am., Vol. 69, No. 12, December 1979

TABLE IV. Wavelengths of selected Zrxii lines as calculated from opti-mized level values.

X(A) Uncertainty(A)

76.9243 0.001677.2048 0.0016

103.7054 0.0008104.7052 0.0009

The small uncertainties in the calculated values make themsuitable as Ritz-type wavelength standards.

In Table V we give the nonrelativistic Hartree-Fock valuesof the average energies and spin-orbit constants of all observedconfigurations from n = 4 to n = 7, as calculated with thecomputer program of Froese-Fischer.14 The observed valuesare also given. The HF energies have been normalized to zerofoi the 4s configuration. As in Y xi and Mo xiv, the HF cal-culations yield good relative energies, except for configurationsthat are greatly affected by relativity. Since the ng electronsare not significantly affected by relativity, we conclude thatthe binding energy of the 4s electron is increased by about42000 cm- 1 due to relativistic effects. The 4p, 5s, 5p, and 6sconfigurations are also significantly affected.

TABLE V. Energy parameters in cm- 1 for Zrxii.

Para-Config. meter HF Obs. Obs./HF Obs.-HF

4s Eav 0 05s Eav 843188 868156 249686s Eav 1216467 1250475 340084p Eav 196494 220152 23658

ý4p 13250 14950 1.1285p Eav 927393 961201 33808

ý5p 5450 6139 1.1266p Eav 1260201 1298406 38205

ý6p 2805 3149 1.123

4d Eav 522490 559037 36547

ý4d 1360 1427 1.0495d Eav 1067036 1106955 39919

ý5d 615 644 1.0476d Eav 1333970 1374788 40818

ý6d 333 325 0.976

4f Eav 838305 876004 37699ý4f 72

5f Eav 1206290 1246160 39870•'5f 43

6f Eav 1407914 1449326 41412•'6f 27

7/ Eav 1529379 1571720 42341ý7f 17

5g Eav 1229551 1271532 41981

•'5g 116g Eav 1422656 1465066 42410

ý6g 77g Eav 1539459 1581919 42460

•*7g 4

Joseph Reader and Nicolo Acquista 1661

TABLE VI. Values for the ionization energy of Zrxii determined fromvarious series. The adopted value of the ionization energy is 1905500

S200 cm-1.

Quantumdefect

Series formula Limit (cm-1)

4s-6s linear 1904370

4p-6p linear 1904180

4d-6d linear 1903750

4f-6f lirrear 1906810

5f-7[ linear 1905950

6f-8f linear 1905540

4f-8f quadratic 1905550

5g-7g linear 1905490

IONIZATION ENERGY

In Table VI we list the values for the ionization energy ofZr XII obtained from the various observed series. As in Y xIand Mo xiv the value of the limit derived from the nf seriesis slightly higher than the limit from the ng series. That is,the value from the n/ series (n = 4-6) is 0.07% higher than thevalue from the ng series (n = 5-7), the analogous differencesfor YxI and Mo xIv being 0.05% and 0.08%, respectively. Thevalues of the limits of the ns series (n = 4-6), np series (n =4-6), and nd series (n = 4-6) are again slightly low relative tothe ng-series (n = 5-7) value. As seen in Table VI, the in-clusion of higher n/-series members reduces the apparentdifferences in the limits significantly. For the ionizationenergy we adopt the value 1905 500 cm-1, which is very nearlythe limit of the nf and ng series. From the uncertainty of thelevel values, we estimate the uncertainty in the limit to be4200 cm-1. The ionization energy of ZrxII is thus 1905500± 200 cm-1 (236.25 + 0.03 eV).

ACKNOWLEDGMENTS

The spectrograms of the laser-produced plasma were madein cooperation with G. Luther, for whose assistance we aregrateful. This work was supported in part by the Office ofMagnetic Fusion Energy of the United States Department ofEnergy.

1E. Alexander, M. Even-Zohar, B. S. Fraenkel, and S. Goldsmith,"Classification of transitions in the euv spectra of Y IX-XIII,Zr x-xiv, Nb xI-xv, and Mo xii-xvi," J. Opt. Soc. Am. 61, 508-514(1971).2j. Reader and N. Acquista, "4s-4p resonance transitions in highlycharged Cu- and Zn-like ions," Phys. Rev. Lett. 39, 184-187(1977).

3J. Reader and N. Acquista, "Spectrum and energy levels of ten-timesionized yttrium (Yxi)," J. Opt. Soc. Am. 69, 1285-1288 (1979)."4J. Reader, G. Luther, and N. Acquista, "Spectrum and energy levelsof thirteen-times ionized molybdenum (Mo xiv)," J. Opt. Soc. Am.69, 144-149 (1979).5U. Feldman, M. Swartz, and L. Cohen, "Vacuum ultraviolet source,"Rev. Sci. Instrum. 38, 1372-1373 (1967).6L. A. Svensson and J. 0. Ekberg, "The titanium vacuum-sparkspectrum from 50 to 425 A," Ark. Fys. 40, 145-164 (1969).7J. Reader, G. L. Epstein, and J. 0. Ekberg, "Spectra of Rb II, Sr III,Y Iv, Zr v, Nb VI, and Mo vii in the vacuum ultraviolet," J. Opt. Soc.Am. 62, 273-284 (1972).

8J. Reader and N. Acquista, "Spectrum and energy levels of four-timesionized zirconium (Zrv)," J. Opt. Soc. Am. 69, 239-253 (1979).

9J. 0. Ekberg, J. E. Hansen, and J. Reader, "Analysis of the Spectrumof Five-times Ionized Zirconium (ZrvI)," J. Opt. Soc. Am. 62,1134-1139 (1972).

]0J. Reader and N. Acquista, "4s 24p 4 - 4s4p 5 transitions in ZrVII,Nb viII, and Mo Ix," J. Opt. Soc. Am. 66, 896-899 (1976).

"Optimization of the level values was done with the computer pro-gram ELCALC, due to L. Radziemski, Jr.

12K. T. Cheng and Y.-K. Kim, "Energy Levels, Wavelengths, andTransition Probabilities for Cu-like Ions," At. Data Nucl. DataTables 22, 547-563 (1978)."13A. E. Livingston, H. G. Berry, L. J. Curtis, and R. M. Schectman,"Energies and lifetimes of excited states in Copper-like Kr VIII,"Phys. Rev. A (to be published).

14 C. Froese, "Numerical Solution of the Hartree-Fock Equations,"Can. J. Phys. 41, 1895-1910 (1963), and C. Froese-Fischer and M.Wilson, "Programs for Atomic Structure Calculations," ArgonneNational Laboratory Report No. 7404 (National Technical In-formation Service, Springfield, Virginia 22161).

1662 J. Opt. Soc. Am., Vol. 69, No. 12, December 1979 Joseph Reader and Nicolo Acquista 1662