Spectrum and energy levels of thirteen-times ionizedmolybdenum (Mo xiv)

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

(Received 27 June 1978)

The spectrum of Mo xiv was observed with a low-inductance spark and a laser-produced plasmain the region from 70 to 630 A on thelO.7-m grazing-incidence spectrograph at NBS. From theidentification of 35 lines, a system of 22 energy levels was determined. The level system (Cu I isoelec-tronic sequence, 3d '0 nl ) includes the series ns (n = 4-6), np (n = 4-6), nd (n = 4,5), nf (n = 4-6),and ng (n = 5-7). The observed energy levels are compared with Hartree-Fock calculations. Theionization energy is determined from the ng series (n = 5-7) to be 2 440 600 - 300 cm- 3

(302.60 : 0.04 eV).

The spectra of highly ionized molybdenum atoms havebeen of considerable interest lately because of their appear-ance in controlled thermonuclear research plasmas. The MoxIv ion is especially useful for plasma diagnosis because it hasa simple spectrum, with the total emitted intensity concen-trated in just a few lines.

Mo XIV is a member of the Cu I isoelectronic sequence; theground configuration is 3d' 0 4s, and the excited configurationsare all of the type 3d10 ni. In 1971, Alexander, Even-Zohar,Fraenkel, and Goldsmith1 observed the spectrum of Mo XIVin the region from 45 to 350 A with a low-inductance spark andidentified the strong 4s-5p, 4s-6p, 4p-5s, 4p-5d, and 4d-5ftransitions. In 1972, Hinnov, Johnson, Meservey, and Di-mock2 observed the 4s-4p resonance doublet (373 and 424 A)in the Princeton ST tokamak and measured the wavelengthsto an accuracy of + 1 A. In 1976, Hinnov3 measured theselines to an accuracy of + 0.5 A.

Recently two of us" observed the 4s-4p resonance lines ofthe six copper-like atoms Rb Ix - Mo XIV in a low-inductancespark. These observations confirmed the identification ofthe Mo XIV lines in tokamak plasmas.2' 3 In the present paperwe report our complete observations and energy levels for MoXIV.

As the present work was nearing completion, a paper on MoXIV by Curtis, Lindgard, Edl6n, Martinson, and Nielsen5

appeared. This paper reports the observation of the Mo XIVspectrum with a high-voltage spark in the region from 35 to184 A. Identifications are given for the 4s-7p, 4p-6s, 4p-7s,4 p-8 s, 4f-5g, 4f-6g, and 4d-5p transitions, with wavelengthsranging in accuracy from +0.05 to 10.2 A. By combiningthese measurements with those in Refs. 1 and 3, a set oftwenty-nine energy levels was obtained. Nineteen of the levelvalues in this set were derived directly from observed lines;ten were deduced from semiempirical considerations. Incomparing the present results with those in this paper we findthat our 4p-6s line identifications are the same. However,our 4d-5p, 4f-5g, and 4f-6g identifications are different. Theenergy level systems thus differ considerably.

EXPERIMENT

The spectra were excited in two different light sources. Thefirst was a low-inductance open spark, essentially the sameas described by Feldman, Schwartz, and Cohen.6 In thissource the spark takes place between metallic electrodes in

144 J. Opt. Soc. Am., Vol. 69, No. 1, January 1979

vacuum after being triggered by a high-frequency dischargefrom a third electrode. In the present work we used capaci-tors of either 4.7 or 14.2 ,uF at voltages varying between 1 and15 kV.

The second source was a laser-produced plasma. This wasobtained by focussing the light from a Nd /glass laser (wave-length 1.06 rtm) onto a flat metallic target. The focussing lenswas a two-component system having an effective focal lengthof about 70 mm. The geometrical arrangement is shownschematially in Fig. 1. The diameter of the focal spot at thetarget was about 200 ,um. Typical laser pulses had an energyof 15 J and a duration of 10 ns.

The spectra were recorded on our 10.7-m grazing-incidencespectrograph. The grating had 1200 lines/mm, providing aplate factor of 0.25 A/mm at 300 A. The angle of incidencewas 800. At this angle the lowest wavelength that could beobserved was about 70 A; the highest was 630 A.

Wavelength calibration in the region around 100 A wasobtained from a low-inductance spark of Ti.7 In higher re-gions calibration was obtained from internal lines of Mo VII-ix8-' 0 and impurity lines of oxygen and fluorine.11 -15 Mostof the Mo lines around 100 A were also measured in the 2ndand 3rd orders. No shifts of wavelength with order were de-tected.

The ionization stages of the observed lines were distin-guished in several ways. First, the spectra were comparedwith spectra taken with a low-voltage sliding spark. Ourprevious work10 showed that the sliding spark would notproduce atoms of Mo ionized more than about eight times.Second, the variation of line intensity with spark voltage wasobserved. We found that the spectrum of Mo XIV was notsignificantly excited at voltages below 3 kV and showedpractically no enhancement at voltages above 3 kV. Third,the spectrum of the low-inductance spark was compared withthe spectrum of the laser-produced plasma. The laser-pro-duced spectrum was much simpler than the spark spectrumbecause it did not contain spectra of ions below Mo x. Wealso found that with the laser-produced plasma the spectrumof Mo xIv could be enhanced relative to spectra of higherstages of ionization by using laser pulses of greater energy andlonger duration, typically 30 J in 20 ns. Finally, in the longwavelength region of the spark spectra, lines belonging tohigher ionization stages could be recognized by their relativelylarge widths. In general the observed line widths varied di-

144

FIG. 1. Experimental arrangement for laser-produced plasma. The laserbeam is about 2 cm in diameter. The target is inclined toward the spec-trograph at an angle of about 5°.

2000

1600

TE

C=cr

LU

1200

800I

4 001

0

6

5.

- 4.

ns

rectly with the stage of ionization. Theses line width obser-vations are more fully described in Ref. 4.

ANALYSIS OF THE SPECTRUM

In the first stage of the analysis, we combined our mea-surements of the 4s -4p resonance lines with the identificationsof Alexander et al. 1 to construct a system of levels containingthe 4s, 4p, 5s, 5p, 5d, 5f, and 6p configurations. A plot of theenergy levels and observed lines of Mo XIV is shown in Fig.2.

We then considered the 4d configuration. The 4p-4dtransitions were predicted by Weiss16 to lie in the regionaround 250 A, which is extremely dense in the spark spectrumand also fairly complicated in the laser-produced spectrum.We therefore turned to the 4d-5p transitions, expected atabout 180 A. This is a much simpler region in the sparkspectrum and extremely simple in the laser-produced spec-trum. A portion of the spectrum in this region is reproducedin Fig. 3. As shown, all three of the 4d-5p transitions of MoxIv can be identified readily. The 5p 2 p interval of 13 227cm-1 implied by these identifications agrees well with theinterval of 13 203 cm-1 given by the 4s-5p transitions at 83A.

I / 7

9/27/2

6 . 7s/2

/5 ,72

1,

7125/2

Mo xIV

- I

np nd nf ng

FIG. 2. Grotrian diagram for Mo xiv. Wavelengths are in A. Intensities are indicated in parentheses following the wavelengths.4s-6p, and 4p-5d transitions are those calculated from the optimized level values.

Wavelengths for the 4 s-5p,

145 J. Opt. Soc. Am., Vol. 69, No. 1, January 1979 Reader et al. 145

I .

7

6 ; I/12I

4a.

01cL

-.01

OOCo CoJo CO. CO

CoC- cCco - C-

I1 11CI C. al I I

I ICo Co

-a -4, -

FIG. 3. Spectrum of Mo at 180 A. (a) Laser-produced plasma; indicatedlines are due to Mo xiv. The 4p-5d lines of Mo xiv are in the 2nd order. (b)Low-inductance spark; indicated lines are due to Mo viii.

With the 4d levels established, the 4p-4d transitions couldthen be located. The observed 4p-4d wavelengths, 241.609,257.993, and 261.544 A are very close to Weiss's16 predictedvalues of 243, 258, and 261 A.

Of further interest in Fig. 3 is the broad line at 183.949 A.We first thought this to be the strong 0 VI line at 183.937 A.However, we finally concluded that spectra of oxygen were notpresent in the laser-produced plasma. By comparing thespectrum of Mo XIV with spectra of the isoelectronic ions YXI, Zr xIi, and Nb XIII and by calculating the structure ofthese copper-like ions with the Hartree-Fock (HF) computerprogram of Froese-Fischer,17 we identified this line as theunresolved 4f-5g multiplet. The 4f-5g transitions in severalsodium-like ions from Fe XVI to Br xxv have recently beenfound to be similarly strong by Kononov, Kovalev, Ryabtsev,and Churilov.18 As this multiplet is essentially collapsed inMo XIV, it follows that the 4f 2F and 5g 2G fine-structure in-tervals must be nearly equal. This is clearly anomalous be-cause according to the HF results the 4f 2F interval should beabout five times larger than the 5g 2G interval. (The HFvalues of the intervals are 488 cm-' for 4f 2F and 90 cm-' for5g 2G).

We next considered the 4f configuration. The location ofthis configuration was greatly aided by a calculation of Weiss' 9

that predicted the 4d-4f transitions to be at 260.9 A (2D3/2 -2F5/2), 264.3 A (2D5/2 - 2F7/2) and 264.7 A (2D5/2 - 2F5/2).Again, this was a very complicated region of the spectrum, andalthough several lines in the laser-produced spectrum weresuggestive of these transitions, no positive identificationscould be made. Efforts to. find the 4f-5d transitions, expectedat about 290 A, were similarly unsuccessful. We finally ac-complished the 4d-4f identifications by comparing the posi-tions of the lines thought to be the 4d 2D3/2 -4f 2F,/2 and 4d2Ds/2 - 4f 2F7/2 transitions with the positions of the 4p 2P3/2- 4d 2Ds/2 and 4p 2P3/2 - 4d 2D3/2 transitions in the isoelec-tronic ions from Y XI to Ag xix. As the 4f 2F interval wasthought to be small, these four lines should occur as two pairs,each pair having the 4d 2D splitting, that vary smoothly rel-ative to each other through the sequence. This comparisonshowed that the main 4d-4f transitions in Mo XIV were thelines at 260.501 and 264.043 A. With these identifications,the weak line at 264.126 A could be identified as the 4d 2D5/2- 4f 2F,/2 transition and the weak lines at 293.374 and 295.366

146 J. Opt. Soc. Am., Vol. 69, No. 1, January 1979

FIG. 4. Spectrum of Mo at 260 A. (a) Laser-produced plasma; indicatedlines are due to Mo xiv. The weak line on the long wavelength side of264.043 A is the 4d2D5 /2-4f2F5/2 transition. (b) Low-inductance spark;lines due to Mo xiv as well as low stages of ionization are indicated. Theline at 257.597 A is due to Mo viii.

TABLE I. Observed lines of Mo xiv. Symbols: h: hazy; p: perturbedby close line; u: unresolved from close line.

A(A) Int. a (cm-') Classification

60.957a 60 1 640 510 4s 2S1 /2 - 6p 2P 3 /261.201a 40 1 633 960 4s 2S1 2 - 6p 2P1/274.425 20 1 343 635 4p 2P1/2 - 6s 2S1/276.216 50 1 312 060 4p 2P3/2 - 6s 2S1/282.971 600 1 205 240 4s 2S1/2 - 5p 2 P3/2

83.890 400 1 192 037 4s 2S1/2 - 5p 2 P1/285.597 70 1 168 268 4d 2D3/2 - 6f 2F5/285.979 100 p 1 163 075 4d 2D.5/2 - 6f 2F7/288.000 150 1 136 359 4p 2P 1/2 - 5d 2D3/2

90.319 400 1 107 187 4p 2P 3 /2 - 5d 2D5/2

90.519 70 1 104 740 4p 2P 3/2 - 5d 2D3/2101.004 5 990 063 4d 2D3/2 - 6p 2P3/2

101.543 70 984 809 4d 2D5/2 - 6p 2P 3 /2

101.663 30 983 638 4d 2D3/2 - 6p 2P1 /2103.500 40 h 966 184 4f 2F-7g 2G

112.300 150 890 472 4d 2D3/2 - 5f 2F5/2112.952 300 885 332 4d 2D5/2 - 5f 2F7/2112.973 30 u 885 167 4d 2D5/2 - 5f 2F5/2

117.149 1000 853 614 4p 2P1 ,/2 - 5s 2S1/2121.647 1500 822 051 4p 2P 3/2 - 5s 2S 1/2

123.902 150 h 807 089 4f 2F-6g 2G180.087 85 555 287 4d 2D3/2 - 5p 2P 3 /2

181.817 600 550 004 4d 2Ds/2 - 5p 2P3/2

183.949 1200h 543 629 4f 2F - 5g 2G184.481 300 542 060 4d 2D3/2 - 5p 'P1/2241.609 800 413 892 4p 2P1/2 - 4d 2D3/2257.993 800 387 607 4p 2P3 /2 - 4d 2D,5/2260.501 300 383 875 4d 2D3/2 - 4f 2F5/2261.544 200 382 345 4p 2P 3 /2 - 4d 2D3/2264.043 400 378 726 4d 2D5/2 - 4f 2F7/2264.126 40 378 607 4d 2D5/2 - 4f 'F5/2293.374 15 340 862 4f 2F7 /2 - 5d 2D5/2295.366 10 338 563 4f 2F5/2 - 5d 2D3/2373.647 10 000 267 632 4s 2S1/2 - 4p 2P3/2423.576 2 000 236 085 4s 2S1/2 - 4p 2 P1 /2

a Wavelength from Alexander et al., Ref. 1; intensity roughly estimated so asto be on same scale as for lines observed in present work.

Reader et al. 146

la)

(b)

_-t

4/\

. -

CL

-a2 a

ffe flt:;f :Tt-0;00 f(a)

(b)U1,

I iI II1Co a.!D =

CJ -P1

'I I-a.- .014: "

w

-I

I

C.

Z

Ix

A as 4f 2F 7/2 - 5d 2D 5/2 and 4f 2F5 /2 - 5d 2D3/2. The 4f 2Finterval is indeed only 118 cm'. The two pairs of 4p-4d and4d-4f transitions for Mo XIV are shown in Fig. 4.

The level system was completed with the addition of the 6s,6f,6g, and 7g configurations. Although the 4s-6p transitionswere beyond our region of observation, the 6p levels of Alex-ander et al. 1 were confirmed by observation of the three 4d-6ptransitions at iO1 A.

WAVELENGTHS AND ENERGY LEVELS

The wavelengths, intensities, and classifications of theobserved lines of Mo XIV are given in Table I. Almost all ofthe wavelengths are derived from spectra taken with the lowinductance spark. This was necessitated by the absence ofcalibration lines of impurities and low ionization stages of Moin the laser-produced plasma. The line at 183.949 A, whichis slightly perturbed by an 0 VI line in the spark spectrum, wasmeasured relative to other lines of Mo XIV in the laser-pro-duced spectrum. The uncertainty of the wavelengths is ±0.005 A, except for the unresolved line at 112.973 A, for whichthe uncertainty is ±0.010 A. The intensities are visual esti-mates of photographic blackening.

The energy levels are given in Table II. The level valuesand their uncertainties were determined by a least-squares

TABLE Mll. Wavelengths of selected Mo xiv lines as calculated from op-timized level values.

A(A) Uncertainty (A)

60.974 0.00261.214 0.00282.9701 0.001083.8901 0.001088.0028 0.000790.3181 0.000890.5157 0.0007

optimization procedure that minimizes the differences be-tween the observed and calculated wave numbers.2 0

In Table III we list the wavelengths calculated from theoptimized energy levels for the 4s-5p, 4s-6p, and 4p-5dtransitions. The small uncertainties in these calculated valuesmake them suitable as Ritz-type wavelength standards in the60-90 A region.

In Table IV we compare the average energies and spin-orbitconstants of the observed configurations with the values cal-culated with the (nonrelativistic) Froese-Fischer HF pro-gram.17 The HF energies have been normalized to zero forthe 4s configuration. It can be seen that, except for config-

TABLE II. Energy levels of Mo xiv.

Fine-structureTerm J E(cm-1) Unc (cm-') n* interval (cm-')

4s 2S 1/2 0 4 2.9686

4p 2P 1/2 236 085 4 3.1235 31 5473/2 267 632 4 3.1461

4d 2D 3/2 649 976 5 3.4658 5 2665/2 655 242 5 3.4709

4f 2F 5/2 1 033 850 6 3.9102 1187/2 1 033 968 8 3.9103

5s 2S 1/2 1 089 691 26 3.9902

5p 2p 1/2 1 192 036 15 4.1505 13 2183/2 1 205 254 13 4.1726

5d 2D 3/2 1 372 413 8 4.4873 2 4175/2 1 374 830 9 4.4923

5f 2F 5/2 1 540440 37 4.8881 1347/2 1 540 574 40 4.8885

5g 2G 7/2, 9/2 1 577 546 16 4.9921

6s 2S 1/2 1 579 705 63 4.9984

6p 2p 1/2 1 633 615 49 5.1626 6 4313/2 1 640 046 35 5.1833

6f 2F 5/2 1 818244 68 5.8787 737/2 1 818 317 68 5.8791

6g 2G 7/2, 9/2 1 841 006 33 5.9893

7g 2G 7/2, 9/2 2 000 101 47 6.9877

Limit 2 440 600

147 J. Opt. Soc. Am., Vol. 69, No. 1, January 1979 Reader et al. 147

TABLE IV. Energy parameters in cm' for Mo xiv.

Configuration Parameter HF Observed Observed/HF Observed-HF

4s Eav 0 05s Eav 1 056420 1 089 691 33 2716s Eav 1 535 956 1 579 705 43 7494 p Eav 226 540 257 116 30 576

P4p 18 697 21031 1.1255 p Eav 1 156431 1 200848 44417

psp 7 855 8 812 1.1226p Eav 1 587 429 1 637 902 50473

P6p 4 058 4 287 1.05

4d Eav 604 056 653 136 49080P4d 2 048 2 106 1.028

5d Eav 1 321 914 1 373 863 51 949Prd 931 967 1.039

6d Eav 1 675519t6d 506

4f E/v 983 387 1 033 917 50 530P4f 139

5f Env 1 487 176 1 540 517 53 341P5f 82

6f Eav 1 763 856 1 818 286 54 430P6p 50

5g ERv 1 521 985 1 577 546 55 561Pig 21

6g Env 1 785 336 1 841 006 55 670

P6g 127g Eav 1 944 148 2 000 101 55 953

7g 8-8

urations that are greatly affected by relativity, the HF cal-culation yields good relative energies. Since the ng electronsare not significantly affected by relativity, we conclude thatthe binding energy of the 4s electron is increased by some56 000 cm-' due to relativistic effects. To a first approxi-mation, the binding energies of the other valence electrons areincreased due to relativity to the extent that their obser-ved-HF values differ from 56 000 cm-'. Clearly the 4p, 5s,5p, and 6s configurations are also significantly affected.

In his theoretical treatment of the copper isoelectronic se-quence, Weiss16 calculates relativistic shifts for the 4s, 4p, and4d configurations of 67.459, 67.327, and 67.247 au, respec-tively. However, Younger2 ' notes that these shifts are mostlydue to the core electrons, the shift for the core being nearlyconstant at 67.223 au. The shifts2 2 in cm-1 relative to con-figurations in which the valence electron is not affected byrelativity are thus 52 000 cm-' for 4s, 23 000 cm-' for 4p, and5300 cm-' for 4d. These shifts are in good agreement withthe values in Table IV.

The very small value of the observed 4f 2F fine-structureinterval indicates a large core-polarization effect (correlation)for this configuration. Although core-polarization anomaliesare not uncommon in one-electron spectra, such effects do notusually persist for such highly ionized atoms. As the observednf

2F intervals in Mo xIv probably do not reflect the truespin-orbit interaction, we have omitted comparison with theHF values in Table IV.

IONIZATION ENERGY

The results of calculating the ionization energy of Mo XIVfrom the various observed series are given in Table V. Exceptfor the nd series, these limits were obtained from an exactsolution of the Rydberg-Ritz formula, T - RZ' (n*)-2, witha quadratic dependence for the quantum defect,

n - n* = a + b (n*)-2.

Z, is the net charge of the atomic core. For the nd series thelimit was calculated by assuming a change in the effectivequantum number An*(5d-4d) = 1.0215, as estimated fromlower members of the sequence.

The limits in Table IV follow the trend of limits found inlower members of the isoelectronic sequence. For example,

TABLE V. Series limits in Mo xiv.energy is 2 440 600 ± 300 cm-'.

The adopted value for the ionization

Series Limit (cm-')

4s-66" 2 439 2004p-6p 2 439 6004d-5d 2 440 6004f-6f 2 442 6005g-7g 2 440 600

148 J. Opt. Soc. Am., Vol. 69, No. 1, January 1979 Reader et al. 148

in Zn II (Ref. 23) the limit of the nf series (n = 4-6) is 0.09 %above the limit of the ng series (n = 5-7). In Mo Xiv theanalogous difference is 0.08%. In Zn II the limit of the ns se-ries (n = 4-6) is below the limit of the ng series (n = 5-7) by0.05 %. The analogous difference in Mo XIV is 0.06%. Thelimits of the full ns series and nf series in Zn II agree well withthe limit of the ng series.

For the ionization energy of Mo xIv we adopt the limit ofthe ng series (n = 5-7). From the uncertainties of the wave-lengths we estimate an uncertainty in the limit of A:300 cm-1.The ionization energy is thus 2 440 600 i 300 cm-1 (302.60+ 0.04 eV).

Our present value of the ionization energy may be comparedwith the value 2 450 000 +: 5000 cm-' obtained by Alexanderet al. l from the np series (n = 5,6) and the value 2 441 000 A:2000 cm'1 obtained by Curtis et al. 5 from the 4s-8s and 4p-7pseries.

ACKNOWLEDGMENTS

This work was supported in part by the Division of Mag-netic Fusion Energy of the U.S. Department of Energy. Wewould like to thank A. Weiss for predicting the wavelengthsof the 4d-4f transitions for us.

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5B. Edl6n, "The Oxygen Spectrum below 200 A and the High-limitTerms of 0 IV," Phys. Scr. 11, 366-370 (1975).

1A. Weiss, "Hartree-Fock Line Strengths for the Lithium, Sodium,and Copper Isoelectronic Sequences," J. Quant. Spectrosc. Radiat.Transfer 18, 481-490 (1977).

'7C. 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, Va., 22161).

i8:, Ya. Kononov, V. I. Kovalev, A. N. Ryabtsev, and S. S. Churilov,"Laser-plasma spectra of ions of elements from Fe to Br with 15-24lost electrons, recorded in the 50-150 A range," Sov. J. QuantumElectron. 7, 111-112 (1977).

19A. Weiss, private communication (1977).20Optimization of the level values was done with the computer pro-

gram ELCALC, communicated to us privately by L. J. Radziemski,Jr.

21S. Younger, private communication (1978).221 a.u. = 219 474 cm-1 .23W. C. Martin and V. Kaufman, "New Vacuum Ultraviolet Wave-

lengths and Revised Energy Levels in the Second Spectrum of Zinc(Zn II)," J. Res. Natl. Bur. Std. (U.S.) 74A, 11-22 (1970).

149 J. Opt. Soc. Am., Vol. 69, No. 1, January 1979 Reader et al. 149