4 s 4p 4~4s4p5 transitions in ZrvII, Nbviii, and Moix*Joseph Reader and Nicolo Acquista

National Bureau of Standards, Washington, D.C. 20234(Received 25 April 1976)

Spectra of ionized Zr, Nb, and Mo have been observed in sliding spark discharges at peak currents up to 4000A on the 10.7 m normal and grazing incidence spectrographs at NBS. From these observations the group of4s 24p 4-4s4p 5 transitions in Zrvii, Nbvin, and Moix have been identified and measured. The energyparameters obtained from least-squares fits to the resultant energy levels are compared with Hartree-Fockcalculations.

The ions Zr vii, Nb viii, and Moix are isoelectronic withneutral selenium. Their ground configurations are allof the type 4s2 4p4 and their low excited configurationsare of the type 4s4p5 , 4s2 4p3 4d, and 4s2 4p3 5s. In 1970,Chaghtail published identifications for a number of4s 2 4p4 -4s 2 4p3 4d, 5s transitions in these ions. The re-gion of observation was 164-388 A. No other spectraldata for these ions have been reported.

In the present work we have observed the spectra ofZrvii, Nbviii, and Moix in the region 338-689 A andfrom these observations have identified a group oftwelve 4s2 4p 4-4s 4p5 transitions in each of these ions.We give here the results of our measurements for thesetransitions as well as the values of the derived energylevels and Slater parameters. Our results for the lev-els of the 4s 2 4p4 configurations differ significantly fromthose of Chaghtai.

EXPERIMENT

The spectra were recorded on the 10.7 m normal andgrazing incidence spectrographs at NBS. In the firstorder the plate factor of the normal incidence spectro-graph is 0 78 A/mm. The plate factor of the grazingincidence spectrograph is 0. 25 A/mm at 340 A and0. 32 A/mm at 625 A.

The light source was a low voltage sliding spark be-tween metallic electrodes with a quartz spacer, oper-ated in general as described by Reader, Epstein, andEkberg. 2 For the present exposures the capacitanceranged from 24 to 80 gF. No external inductance wasused. Peak currents in the spark varied from 1000 to4000 A, the duration of full pulse width at half-maxi-mum being typically 30 gs.

Considerable difficulty was encountered in trying togenerate high peak current sparks with the present met-

896 J. Opt. Soc. Am., Vol. 66, No. 9, September 1976

als, due to the presence of hydrogen dissolved in theelectrodes. The liberation of this gas during the earlyphases of high peak current discharges resulted in apremature, irregular breakdown in the spark gap. Al-though this situation could be alleviated by prolongedoperation of the discharge and rapid pumping at thesource, exposures at peak currents above 3000 A werealways troublesome.

Spectral lines belonging to different stages of ioniza-tion were distinguished by comparing their relative in-tensities at different peak currrents. The lines ofMo ix could also be recognized by their large widthsin the 4000 A sparks. These lines are evidently pro-duced in a very hot region of the discharge.

General wavelength calibration of our spectrogramswas provided by lines of Cu Ir3 excited in a hollow cath-ode discharge and lines of yttrium excited in a slidingspark. (The spectrum of yttrium from a sliding sparkis currently being developed as a source of referencelines in our laboratory. 4 Values accurate to a fewthousandths of an angstrom have been given for Y iN, 5Y IV, 2 y v, 6 and Y v,7 but most of the wavelengths areas yet unpublished.) Impurity lines' 1 1 of oxygen, ni-trogen, carbon, and silicon were used to correct forshifts between the reference and unknown spectra.

The wavelengths of the lines identified as 4s2 4p4A4s 4pS transitions in Zr vii, Nb viii, and Mo Ix are givenin Tables I, II, and Ill. These wavelengths were derivedfrom measurements made in the first and second ordersof the normal incidence spectrograph. They have anestimated uncertainty of ±0.005 A. The intensities arevisual estimates of photographic blackening as observedin the first order, with some effort made to take intoaccount the rapidly changing response of both spectro-graphs around 500 A.

Copyright © 1976 by the Optical Society of America 896

TABLE I.of Zr vII.

Observed 4s24p4-4s4p5 transitions in the spectrum

)(A) Int. u(cm-t) Classification

410. 332 5 243 705. 1 4s24P

4 3P 2-4s4p

5 1P,

461.833 40 216528.5 tD2 - 'P1495.100 50 201979.4

3P2- 3P,

512.586 35 195 089.2 3

P1 - 3PO518.638 100 192 812.7 3P2 -

3P 2

527.918 40 189423.4 3P0- 3P1

530. 700 35 188 430. 4 3P, - 3Pt

535.445 3 186 760.5 ISO- 'Pt

557. 835 70 179 264. 5 3P 1 -

3P2

572. 064 1 174 805. 6 kD2 -3Pn

603.736 30 165 635. 3 tD2- 3P2

689.476 5 145 037. 7 ISO - 3P,

LINE IDENTIFICATIONS AND ENERGY LEVELS

Our line identifications for the present ions wereguided by theoretical calculations of the structure of the4s 24p4 and 4s 4p5 configurations carried out by diagonal-izing the energy matrices with scaled Hartree-Fock(HF) parameters. The HF parameters were calculatedwith the computer program of Froese-Fischer. 12 Scal-ing factors were obtained by extrapolating the ratios be-tween fitted and HF energy parameters through the iso-electronic sequence.1317

In most cases our identifications are confirmed byrepetition of the energy level intervals to within the un-certainty of the measurements. This is not true forlines that connect either the 4S2 4p4 3p 0 or 4s 4P5 3pO lev-els, inasmuch as these levels make only single combina-tions within the array. (Although it is possible for the4s2 4p4 3PO level to combine with 4s 4p5 1P1 as well as with4s 4p5 3Pi, the 4s2 4p4 3P0 -4s 4p5 1P1 combination is notobserved anywhere in the isoelectronic sequence pastKr rrr.) However, because the positions of the 3po lev-els can be calculated to within a few cm-' once the re-maining levels are known, and because the transitionsthat the levels do make are prominent, there is no doubtabout any of these identifications.

The spectrograms made on the grazing incidencespectrograph reveal the presence of unresolved hyper-fine structure in the three downward transitions from

TABLE II. Observed 4s 24p4-4s4p5 transitions in the spectrumof NbvIII. Symbol: c, complex.

M 6A) Int. a(cmnt ) Classification

371.226 5 269 377.7 4s 2 4p4 2 P2 -4s4p5 'Pi419.846 50 238182.6 tD2- '.'446. 944 50 223 741. 7 3P2- 3p1464.455 20 215 306. 1 3P,_ 3P0

470.055 100c 212 741.1 3 P2.3P2

478.055 20 209181.0 3P'- 3P,

483.276 18 206 921.1 3P1. 3pt488.023 3 204908.4 iSo - 'Pt510.413 75c 195 919.8 3P,- 3P2519.358 1 192 545.4 'D2 3Pt

550.832 30c 181543.6 ID2- 3P2627. 846 5 159 274.7 ISO - 3Pt

897 J. Opt. Soc. Am., Vol. 66, No. 9, September 1976

TABLE III. Observed 4s24p

4-4s4p

5 transitions in the spectrum

of MO ix.

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

338. 264 15 295 627.1 4s24p4a3P2-4s4pslP-

384.691 75 259948.9 1D2- tP406.319 50 246 112.0 3P 2 -

3p

423.800 25 235960.4 3P ½0 3P,

428.959 100 233122.5 3P 2-

3P2

435. 684 20 229524.2 3P 0-

3P1

443.388 18 225 536.1 3

P1 -3P1

448. 956 3 222 739. 0 Is0- IP1470. 484 40 212547.1

3P1 -

3P2

475.197 1 210 439.0 °D 2-3P1

506.462 30 197 448.2 iD2- 3P 2

577.272 8 173 228. 6 S0 -3

P,

the 4s4p 5 3P2 level of Nbviii. These lines are noted ascomplex in Table HI. Because of the unpaired, some-what inner s electron in the 4s 4p5 configuration and thelarge nuclear magnetic moment of the stable isotope ofniobium, this hyperfine structure is not unexpected.The grazing incidence spectrograms also show that theNbviii line at 550.832 A is blended with a close line dueto Nb vi. However, the Nbvi line practically disappearsat the higher peak currents, so the Nbvnii line can stillbe well measured on the normal incidence spectrograph.The Mo ix line at 448.956 A cannot be observed on thegrazing incidence spectrograph as it is masked there bya strong second order line due to Mo vi. The Mo vi lineis not present on our normal incidence spectrograms.

The values of the energy levels of the 4s2 4p' and4s 4p' configurations are given in Table IV. These lev-el values were determined by an optimization procedurethat uses all of the measured wavenumbers. 14 From ouroriginal estimate of the uncertainty of the wavelengthsand from the repetition of the energy level intervals, weestimate that within each configuration the level valueshave relative uncertainties of ± 1. 0 cm-'. The values ofthe 4s 4p5 levels have absolute uncertainties of ± 2 cm-'.

In Table V we give the results of fitting the energyparameters to the observed levels by the usual least-squares method along with the Hartree-Fock values.The percentage compositions found by diagonalizing the4s 2 4p4 energy matrix with the fitted values of the param-eters are given in Table VI. (Matrix calculations were

TABLE IV. Energy levels in cm-1 of the 4s24p4 and 4s4p5 con-figurations of Zr vii, Nb viii, and MO ix.

Config. Term J Zrvii Nbviii MOIX

4s24p4 3p 2 0.0 0.0 0.00 12 557. 1 14 561. 4 16 588. 81 13 548. 8 16 821.0 20 576.3

1D 2 27175. 9 31196. 7 35 674.5Is 0 56 943. 0 64468. 0 72 884. 6

4s4p5 3

P 2 192 812. 2 212 740.6 233 122.9

1 201 980. 5 223 742.4 246 113.0

0 208638.0 232 127.1 256 536.7p 1 243 704. 0 269 377. 5 295 624.1

J. Reader and N. Acquista 897

TABLE V. Energy parameters in cm1

l and mean errors A of least-squares fits for the 4s24p4 and 4s4p5

configurations of Zrvii,Nb vii, and MO ix. Value of Eav for the 4s'4p' configuration listedmatrix with the HF parameters, 3P2 level set at zero.

in the HF column is that obtained by diagonalizing the energy

Zr vii Nb viii MoIx

Config. Parameter HF Fitted Fitted/HF HF Fitted Fitted/HF HF Fitted Fitted/HF

4s2

4p4

Eav 16 934 16 397 ± 22 19 340 19 025 ± 25 22 014 21 963 ± 26F

2 (4p4p) 83 722 70 565 ± 160 0. 843 89 093 75 514 ± 188 0. 848 94 331 80 369 ± 204 0. 852

tp 10 039 11 076 ± 44 1. 103 12 278 13 554 ± 46 1. 104 14 809 16 355 ± 44 1. 104a (4p4p) -59±12 -62±13 -65±14A 45 49 51

4s4p5

Eav 222691 209146±1 241044 231266±5 261622 253947±10G'(4p4s) 111379 66357±4 0.59578 118196 72402±18 0.6126 124847 78157±33 0.6260

10 018 10 551 ± 2 1. 0532 12 253 12 925 ± 9 1. 0548 14 780 15 610 16 1.056A 2 10 18

TABLEcentageNb viii,

VI. Calculated energy level values in cm l and per-compositions for the 4s 24p 4 configurations of Zrvii,and Moix. Negative eigenvector components are pre-

ceded by a minus sign.

PercentageAtom J E(obs) E(calc) O-C composition

Zrvii 0 12557 12596 -39 85% 3 P-15% 'S56 943 56 937 6 85% iS + 15% 3P

1 13 549 13 538 11 100% 3P

2 0 -19 19 91%'3P+ 9%'D27176 27181 -5 91%' D-9% 3P

Nb vii 0 14561 14601 -40 82% 3P-18% IS64468 64460 8 82% IS+18% 3p

1 16 821 16 814 7 100% 3 P

2 0 -27 27 89% 3 P+ 11% ID31 197 31 200 -3 89% 1 D-11% 3P

MOIX 0 16 589 16 627 - 38 78% 3P-22%0 S72 885 72 873 12 78% IS + 22% 3 P

1 20 576 20 574 2 100% 3P

2 0 -32 32 88% 3 P+12% t D35 674 35 677 -3 88% ID-12% 3P

TABLE VII. Comparison of present level values with previousresults.

Atom Level Present value Previousa

Zrvii 4s24p4 3P2 0.0 0

3P, 12 557.1 12 5323pt 13 548. 8 13 5261D2 27175.9 27142ISO 56 943.0 56 861

Nb viII 4s24p4 3

P2 0.0 03P0 14 561.4 14 5453P, 16 821.0 16 8221D2 31196. 7 31228'SO 64 468. 0 64 555

Mo Ix 4s24P4 3

P2 0.0 03P0 16 588.8 16 3353P1 20 576.3 20 0521D2 35 674.5 35 856.,so 72 884. 6 71903?

aM. S. Z. Chaghtai, Ref. 1.

898 J. Opt. Soc. Am., Vol. 66, No. 9, September 1976

TABLE VIII. Predicted wavelengths in A of transitions withinthe 4s 24p4 configurations of Zr vii, Nb viii, and MO ix. Wave-lengths below 2000 A are in vacuum, those above 2000 A are inair. The uncertainties correspond to an estimated uncertaintyof ± 1.4 cm-t in the calculated wavenumbers.

Transition Zrvii Nb viii Mo Ix3P2- SO 1756.14 ± 0. 04 1551. 16 0. 03 1372. 03 ± 0. 033 P,-_S 0 2303. 75 ± 0. 07 2098. 10 0. 06 1911. 74 ± 0. 051D2-IS, 3358.44 ± 0. 16 3004. 71 ± 0.13 2686. 64 ± 0.103 P2-1 D 2 3678. 68 ± 0.19 3204. 54 ± 0.14 2802. 29 ± 0.113P2- 3 P1 7378.7 ± 0. 8 5943. 3 ± 0. 5 4858. 6 ± 0.3

3 PC-ID2 6838.6 ± 0.7 6009.6±0.5 5238.1 ±0.43 p2 - p0 7961. 4 ± 0. 9 6865. 6 ± 0.7 6026. 5 ± 0. 53 P1-

1D2 7336. 3 ± 0. 8 6954. 3 ± 0. 7 6621. 5 ± 0. 6

carried out in an SL scheme with the Condon and Short-ley phase convention.) The very smooth progression ofparameter values and differences between observed andcalculated level values through the sequence providesfurther confirmation of our line identifications.

As has already been noted"3 ,7 the 4s 4p5 configurationis expected to interact strongly with the 4s2 4p3 4d con-figuration, and since we have not included this interac-tion in the calculations, we omit the percentage com-positions for 4s 4p5 . The fitted values of the parame-ters for 4s 4p5 may be considered as effective valuesthat absorb the effects of this configuration interaction.As described by Hansen and Persson, 13 the 4s 4p5-452 4p3 4d interaction displaces the entire 4s 4p5 config-uration to lower energies and also depresses the 'P lev-el of 4s 4p5 relative to the 4s4p5 3P levels. This ac-counts for the low fitted value of GI(4s 4p) as comparedwith the HF value. Our preliminary calculations forthe 4s4p5 configuration of Moix that include interactionwith 4S2 4p3 4d indicate downward displacements for the3P and 1P terms of about 26 000 and 45 000 cm-', respec-tively. The levels of the 4s 4p5 3P and 'P terms contain4s3 4p 3 4d admixtures of about 15% and 35%, respective-ly. These admixtures are only slightly less than thecorresponding values of 16% and 38% calculated forY VI. 7

In Table VII we compare the present values for thelevels of the 4S 2 4p4 configuration with previous results.For Mo ix the results differ so greatly that it is apparentthat the previous analysis' of this spectrum must be

J. Reader and N. Acquista 898

completely revised. The need for such revision has infact already been recognized. 15 For the 1Sb levels ofZrvii and Nbviii the differences are again so large thatthese levels must be considered as newly located. Forthe other levels of these two ions the situation is notcompletely clear, because the discrepancies are notoutside the realm of possible uncertainties in plate cali-bration in the lower wavelength region. We are pres-ently investigating the 452 4p4-4s 2 4p3 4d, 5s transitionarrays in Zrvii and Nbviii as well as in Moix in orderto clarify this matter and possibly contribute to theanalyses.

FORBIDDEN LINES

In Table VIII we have tabulated the predicted wave-lengths of parity-forbidden transitions within the 4S2 4p4

configurations. These lines might be observed in diluteplasmas such as tokamak discharges.

*This work was partially supported by the U. S. Energy Re-search and Development Administration.

'M. S. Z. Chaghtai, "Term Analysis of Zrvvi, Nb viri andMoix", Phys. Scr. 1, 104-108 (1970).

2 J. Reader, G. L. Epstein, and J. 0. Ekberg, "Spectra ofRb II, SriiI, Yiv, Zr v, Nb vi, and Mo viI in the Vacuum Ultra-violet," J. Opt. Soc. Am. 62, 273-284 (1972).

3 C. B. Ross, "Wavelengths and Energy Levels of Singly'Ionized Copper, Cu ii," Los Alamos Scientific LaboratoryReport No. 4498 (available from Clearinghouse for FederalScientific and Technical Information, National Bureau of Stan-dards, U. S. Department of Commerce, Springfield, Va.22151).

4 J. Reader, C. H. Corliss, and R. Zalubas, "Reference Wave-lengths of Y v in the 200-460 A Region, " program and ab-stracts of Atomic Spectroscopy Symposium, National Bureauof Standards, Washington, D. C., 1975.

5G. L. Epstein and J. Reader, "Spectrum of doubly ionized

yttrium (Y iII)," J. Opt. Soc. Am. 65, 310-314 (1975).6J. Reader and G. L. Epstein, "Analysis of the Spectrum of

Quadruply Ionized Yttrium (Yv)," J. Opt. Soc. Am. 62, 619-622 (1972).

7R. Zalubas, J. Reader, and C. H. Corliss, "4s 24p 4-4s4p 5

transitions in five-times ionized yttrium (Y vi), " J. Opt. Soc.Am. 66, 35-36 (1976).

8B. Edl6n, "Wellenllingen und Termsysteme zu den Atom-spektrenderElemente Lithium, Beryllium, Bor, Kohlenstoff,Stickstoff und Sauerstoff, " Nova Acta Regiae Soc. Sci. Ups.(IV) 9, No. 6 (1934).

9B. Edl6n, "Wavelength Measurements in the Vacuum Ultra-violet," Rep. Prog. Phys. 26, 181-212 (1963).

'OR. L. Kelly and L. J. Palumbo, Atomic and Ionic EmissionLines Below 2000 Angstroms-Hydrogen Through Krypton,Naval Research Laboratory Report 7599 (U. S. GPO, Washing-ton, D.C., 1973).

"1V. Kaufman and B. Edlhn, "Reference Wavelengths fromAtomic Spectra in the Range 15 A to 25000 A, "J. Phys. Chem.Ref. Data 3, 825-895 (1974).

t2C. Froese, "Numerical Solution of the Hartree-Fock Equa-tions," Can. J. Phys. 41, 1895-1910 (1963); and C. Froese-Fischer and M. Wilson, "Programs for Atomic StructureCalculations, " Argonne National Laboratory Report No. 7404(available from Clearinghouse for Federal Scientific andTechnical Information, National Bureau of Standards, U. S.Department of Commerce, Springfield, Va, 22151).

' 3J. E. Hansen and W. Persson, "4S24p4 and 4s4P5 configura-tions in Rb iv and Sr v, " J. Opt. Soc. Am. 64, 696-698(1974). The values of Eav for the 4s24p 4 configuration in thispaper do not take into account the contribution of the effec-tive interaction parameter cI4p4p) to the average energy ofthe configuration. To account for this contribution, the val-ues of Eav for KrIii, Rbiv, and Sr v in this reference shouldbe increased by 3.2ca.

'4Optimization of the level values was done with the computerprogram ELCALC communicated to us privately by L. J. Rad-ziemski, Jr.

15M. S. Z. Chaghtai and K. Rahimullah, "Coupling Conditionsand Level Structure of the np 4 -Configurations," Nuovo Ci-mento A 17, 162-170 (1973).

Copyright © 1976 by the Optical Society of America 899899 J. Opt. Soc. Am., Vol. 66, No. 9, September 1976