Spectrum and energy levels of twelve-times ionized niobium (Nb xii,)Joseph Reader and Nicolo Acquista

National Bureau of Standards, Washington, D. C. 20234(Received 27 September 1979)

The spectrum of Nb xiii was observed with a low-inductance spark and a laser-produced plasma inthe region from 70-630 A on the 10.7-mi grazing incidence spectrograph at NBS. From the identifica-tion of 38 lines, a system of 29 energy levels was determined. The level system (Cu I isoelectronicsequence, 3d 10nl) includes the series ns(n = 4-6), np(n = 4-7), nd(n = 4-6), nfln = 4-7), andng(n = 5-8). The observed energy levels are compared with Hartree-Fock calculations. The ionizationenergy is determined from the nf and ng series to be 2 166 300 + 300 cm - 1 (268.59 + 0.04 eV).

The twelve-times ionized niobium atom, Nbxiii, is amember of the Cu I isoelectronic sequence. Ions in this se-quence have become important recently because of their rolein the diagnosis of controlled fusion plasmas. Since niobium

has a very high melting point, it is being considered as a ma-terial for use in the interior of tokamaks. The spectra andatomic structure of the ions of Nb are thus of special in-terest.

317 J. Opt. Soc. Am., Vol. 70, No. 3, March 1980 317

TABLE 1. Observed lines of Nbxiii. Symbols: c, complex; h, hazy.

( lx(A) Int. (cm'1) Classification

68.224a68.491a75.39476.88284.01085.44885.76685.93892.42993.38593.52293.62197.43897.84998.449

100.910101.111108.687115.938116.529116.713120.346127.026127.722132.346137.198144.130208.914210.843213.867214.284261.353277.576280.979284.437287.974404.295453.260

50301015c30101260

1000600

24

6080

2006004015h10803080h

300400

20003000

500h50

500300

1 200h400700300350350

200004000

14657601460050132637013006901190330117030011659601 1636301081910107084010692701068140102629010219801015750

990982989012920073862530858155856803830937787240782950755595728874693818478666474287467580466670382624360262355898351572347254247 344.1220623.9

4s 2 S1/2 -6p 2P3 /24s 2 S1/2 -6p 2 Pl/24p 2Pl/2-6d 2D3/24p

2 P3/2 -6d 2D5 /24p 2 Pl/2-6s 2 S 1/24d

2 D3/2 -7f 2F5/24d

2 D5/2 -7f 2F7 /24p 2P3/2-6S 2 S1/24s 2S1/2-5p 2 P3 /24s 2 S1/2 -5p 2 P1/24d 2 D3/2 -7p 2 P1/24d

2 D5/2 -7p 2 P3 /24d 2 D3 /2 -6f 2F5 /24d 2 D5/2 -6f 2 F7 /24p 2 Pl/2 -5d 2D3 /24p 2p3/2-5d 2D5 /24p 2P3/2-5d 2D3 /2

4/ 2F-8g 2G4d 2 D3/2 -6p 2 P3/24d 2 D5/2-6p 2 P3 /24d 2 D3/2-6p 2 Pl/2

4f 2 F-7g 2 G4d

2 D3/2 -5f 2F5 /24d 2 D5 /2-5f 2F7/24p 2pl/ 2 -5s 2S1 /24p 2P3 /2 -5s 2S1/2

4/ 2F-6g 2G4d 2 D3 /2 -5p 2P3 /24d 2 D5 /2 -5p 2P3 /24d 2 D3 /2 -5p 2 Pl/2

4/ 2F-5g 2G4p 2 P,/ 2 -4d 2D3 /24p

2 P3 /2 -4d 2 D5 /24p 2 P3 /2 -4d 2 D3 /24d

2 D3 /2 -4f 2 F5 /24d

2 D5 /2 -4f 2 F7 /24s 2S 1/2-4 P 2 P3/24s 2 S 1/2-4p 2 P1 /2

a Observed by Alexander et al., Ref. 1, but not in present work; wavelength ascalculated from present level values, intensity roughly estimated so as to beon present scale.

The first line identifications for Nb XIII were given byAlexander et al. l They used a vacuum spark to observe tenlines of the type 4s-5p, 4p-5d, 4d-5f, 4p-5s, and 4s-6p lyingin the region 68-137 A. In 1977 the present authors 2 used avacuum spark to identify the 4s-4p resonance lines. In thepresent work we used a vacuum spark and a laser-producedplasma to carry out a relatively complete spectral analysis ofthis ion. Some 38 lines, representing transitions between 29energy levels, were identified.

EXPERIMENT

Our experimental procedure has been described in detailin recent papers3 -5 on the copperlike ions Y XI, ZrXII, and

MoXIV. The gpark was a low-inductance, three Qlectrodetype, as described by Feldman et al.6 We used capacitors ofeither 4.7 or 14.2 AF at voltages varying between 1 and 15 kV.

The spectrum of Nbxiii was generally well developed at avoltage of 4 kV.

The laser-produced plasma was obtained by focusing thelight from a Nd-glass laser (wavelength 1.06 ,tm) onto flatmetallic targets. Typical laser pulses had an energy of 15 Jand a duration of 10 ns. The spectrum of Nb xIII could beenhanced relative to higher stages of ionization by using laserpulses of greater energy and longer duration, typically 30 J in20 ns. Ions below Nb 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 80°. 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 100 A was obtainedfrom a vacuum spark of Ti.7 At longer wavelengths calibra-tion was obtained from vacuum spark spectra of Nb measured

TABLE I1. Energy levels of Nbxiii.

Fine-structureE Unc. interval

Term J (cm-l) (cm-') n* (cm-l)

4s 2S 1/2

4p 2P 1/23/2

4d 2D 3/25/2

4f 2F 5/27/2

5s 2 S 1/2

5p 2P 1/23/2

5d 2D 3/25/2

5f 2F 5/27/2

0

220624247344

603241607609

954813954863

976219

10708211081901

12363671238327

4

44

76

149

20

1310

3649

2.9259

3.08733.1088

3.44453.4494

3.91253.9126

3.9476

4.11454.1355

4.46574.4705

1390481 32 4.88921390559 31 4.8895

26720 + 4

4368 + 6

50I 6

11080 + 8

1960 + 20

78 + 20

6s 2S 1/2 1410966 49 4.9551

5g 2 G 7/2,9/2

6p 2P 1/23/2

6d 2D 3/25/2

6f 2F 5/27/2

6g 2G 7/2,9/2

1421512

14600441465767

15469891548040

16295351629592

1648660

18

3727

8885

5353

42

4.9900

5.12435.1452

5.47225.4769

5.87805.8783

5.9856

7p 2p 1/2 1672508 58 6.12843/2 1675745 57 6.1486

7f 2F 5/27/2

7g 2G 7/2,9/2

8g 2G 7/2,9/2

Limit

17735431773571

1785779

1874915

2166300

6966

51

59

6.8726.872

6.981

7.978

5723 + 20

1051 + 50

57 + 30

3237 + 34

28 : 40

318 J. Opt. Soc. Am., Vol. 70, No. 3, March 1980J Joseph Reader and Nicolo Acquista 318

2000

16001

12001

800

400k

0

ns np nd nf

previously with sliding sparks8' 0 and impurity lines of oxygenand fluorine.

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 Nb XIII were seriously blended withlines of lower ionization in the spark spectra and had to bemeasured in spectra of the laser-produced plasma.

LINE IDENTIFICATIONS, WAVELENGTHS, ENERGYLEVELS

The wavelengths, intensities, and classifications of theobserved lines of Nb XIII are given in Table I. The uncer-tainty of most of the wavelengths is +0.005 A. For the linesat 261.353, 280.979, and 284.437 A, which were measured ina region of the laser-produced plasma where only a few ref-erence lines were available, the uncertainty is +0.010 A. Theintensities are visual estimates of photographic blackening.

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 procedure that minimizes the differences betweenthe observed and calculated wave numbers." The fine-structure intervals of the observed terms are also given inTable II. ThevaluesofAn* = n*(j = 1+ 1/2) - n*(= 1- 1/2)for the 4p, 5p, 6p, and 7p 2

P terms are 0.0215, 0.0210, 0.0209,

ng

B 9/27/2

7 7/2 r7 9/2

5 /2 7/2

7 3/2 9/in2 7/292

6, 5/2 = 7/26 5/2

3//22 ,2 I

6 5/21/

1/ / 77 7/2

5/2- 4 3/2

4 3/21/2

- 4 1/2

and 0.0202, respectively. For the 4d, 5d, and 6d 2D terms thevalues of 5n* are 0.0049, 0.0048, and 0.0047, respectively.

As shown in Table II, the 4f 2F term has a fine-structureinterval of only 50 cm-'. This may be compared to a nonre-lativistic Hartree-Fock (HF) value of 357 cm-'. Thisanomaly, which is characteristic of nf configurations of cop-perlike ions, has been discussed in some detail in Refs. 3-5.As noted there the fully relativistic calculations of Cheng andKim1 2 account rather well for the observed 2F intervals. Acomparison of the observed intervals, the nonrelativistic HFvalues, and the relativistic values of Cheng and Kim12 is givenin Table III.

In Table IV we list the wavelengths calculated from the

TABLE 11. Observed and calculated nf 2Ffine-structure intervals in Nbxiii.Values are in cm-1 .

Non-relativistic Relativistic

Term Observed HFa HFb

4f 2 F 50 4 6 357 185f2F 78 ± 20 210 516f 2 F 57 + 30 130 467f 2F 28 + 40 84

a Calculated with the program of Froese-Fischer, Ref. 13.b Cheng and Kim, Ref. 12.

319 J. Opt. Soc. Am., Vol. 70, No. 3, March 1980

FIG. 1. Grotrian diagram forNbxiii. 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.

I I I I I

Joseph Reader and Nicolo Acquista 319

TABLE IV. Wavelengths of selected Nb xill lines as calculated from opti-mized level values. The 4s-7p transitions have not been observed.

X UncertaintyTransition (A) (A)

4s 2S1/2-7p 2P3/2 59.675 0.0024s 2S 1/2-7p 2 P1/ 2 59.790 0.0024s 2S1/2 -6p 2P3 /2 68.2237 0.00134s 2 S1/2 -6p 2 P1/2 68.4911 0.00184s 2 S1/2 -5p 2P3 /2 92.4299 0.00094s 2S1/2-5p 2Pl/ 2 93.3863 0.0011

optimized energy levels for the 4s-5p, 4s-6p, and 4s-7ptransitions. The small uncertainties in the calculated valuesmake them suitable 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.13 The observed valuesare also given. The HF energies have been normalized to zerofor the 4s configuration. As in Y xi, Zr XII, and Mo xiv, theHF calculations yield good relative energies, except for con-figurations that are greatly affected by relativity. Since theng electrons are not significantly affected we conclude thatthe binding energy of the 4s electron is increased by about

TABLE V. Energy parameters in cm1 for Nbxiii.

Config. Parameter HF Obs. Obs./HF Obs.-HF

4s Eav 0 05s E,,v 948531 976219 27 6886s Eav 1374271 1410966 36695

4 p Eav 213004 238437 25433t4p 15818 17813 1.126

6p Eav 1040700 1078208 37508A5p 6579 7 387 1.123

6p Eav 1421390 1463859 42469

t6p 3406 3815 1.1207 p Eav 1630690 1674666 43976

{7p 1994 2158 1.082

4d Eav 565363 605862 40499

¢4d 1681 1747 1.0395d Eav 1193490 1237543 44053

t5d 761 784 1.0306d Eav 1502601 1547620 45019

t6d 413 420 1.017

4f Eav 913 615 954842 41227

t4f 1025f Eav 1346375 1390526 44151

¢5f 606f Eav 1583886 1629568 45 682

t6f 377f Eav 1727407 1773560 46153

¢7f 24

5g Eav 1375550 1421512 45962

t5g 156g Eav 1601950 1648660 46710

D6g 97g Eav 1738572 1785779 47 207

{7g 6

TABLE VI. Values for the ionization energy of Nbxiii determined fromvarious series. The adopted value of the ionization energy is 2166300t 300 cm-'.

Quantum defect LimitSeries formula (cm-,)

4s-6s linear 2 164480

4p- 6 p linear 2 1642805p-7p linear 2165 2204p-7p quadratic 2 165470

4d-6d linear 2 163480

4f-6f linear 2 167 3405f-7f linear 21664804f-7f quadratic 2166160

5g-7g linear 21654306g-8g linear 21660805g-8g quadratic 2166410

47000 cm- due to relativistic effects. The 4p,5s,5p, and 6sconfigurations are also significantly affected.

IONIZATION ENERGY

In Table VI we list the values for the ionization energy ofNb XIII obtained from the various observed series. As in Y XI,Zr XII, and Mo XIV the value of the limit derived from the nfseries is slightly higher than the limit from the ng series. Thatis, the value from the nf series (n = 4-6) is 0.09% higher thanthe value from the ng series (n = 5-7), the analogous differ-ences for YXI, Zr XII, and Mo XIV being 0.05%, 0.07%, and0.08%, respectively. The values of the limits of the ns series(n = 4-6), np series (n = 4-6), and nd series (n = 4-6) areagain slightly low relative to the ng series (n = 5-7) value. Asseen in Table VI, the inclusion of higher nf series membersreduces the apparent differences in the limits significantly.For the ionization energy we adopt the value 2 166 300 cm- 1 ,which is approximately the limit of the nf and ng series.From the uncertainty of the level values, we estimate theuncertainty in the limit to be 1300 cm-'. The ionizationenergy of Nb XIII is thus 2 166 300 ±300 cm- 1 (268.59 a 0.04eV).

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.

'E. Alexander, M. Even-Zohar, B. S. Fraenkel, and S. Goldsmith,"Classification of Transitions in the euv Spectra of YIX-XIII,Zrx-xiv, Nbxi-xv, and MoXiI-XVI," J. Opt. Soc. Am. 61, 508-514(1971).

2 J. 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 and N. Acquista, "Spectrum and energy levels of eleven-times ionized zirconium (Zr XII)," J. Opt. Soc. Am. 69, 1659-1662(1979).

5J. Reader, G. Luther, and N. Acquista, "Spectrum and energy levels

320 J. Opt. Soc. Am., Vol. 70, No. 3, March 1980 Joseph Reader and Nicolo Acquista 320

of thirteen-times ionized molybdenum (Mo xiv)," J. Opt. Soc. Am.69, 144-149 (1979).

6U. Feldman, M. Swartz, and L. Cohen, "Vacuum ultraviolet source,"Rev. Sci. Instrum. 38, 1372-1373 (1967).

7L. A. Svensson and J. 0. Ekberg, "The titanium vacuum-sparkspectrum from 50 to 425 A," Ark. Fys. 40, 145-164 (1969).

8J. Reader, G. L. Epstein, and J. 0. Ekberg, "Spectra of Rbii, Sr III,YIV, Zrv, Nb vI, and Mo VII in the Vacuum Ultraviolet," J. Opt.Soc. Am. 62, 273-284 (1972).

9 J. 0. Ekberg, J. E. Hansen, and J. Reader, "Analysis of the Spectrumof Six-Times Ionized Niobium (NbvnI)," J. Opt. Soc. Am. 62,1139-1142 (1972).

10J. Reader and N. Acquista, "4s24p4-4s4p5 transitions in ZrVII,NbvIIi, and MoIX," 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.

12 K. T. Cheng and Y.-K. Kim, "Energy Levels, Wavelengths, andTransition Probabilities for Cu-like Ions," At. Data Nucl. DataTables 22, 547-563 (1978).

13C. 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 Infor-mation Service, Springfield, Virginia, 22161).

321 J. Opt. Soc. Am., Vol. 70, No. 3, March 1980 0030-3941/80/030321-08$00.50 � 1980 Optical Society of America 321