Vol. 63

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 63, NUMBER 3

Level structure of doubly ionized erbium (Er iII)

Nissan SpectorObservatoire de Paris, 92-Meudon, France*

(Received 2 June 1972)

The low levels of the four basic configurations of doubly ionized erbium 4f'2 (

3H6, 5,3F4), 4f 1 7(417j)5d,

4f'l(417 1, 6j)6 s, and 4f' (

4I7I,6J)6p are reported. More than a hundred Er in lines are classified by 24 odd and

18 even levels. Values for the spin-orbit parameters obtained directly from the observed levels arer6,= 3743 cm-', D5d= 1326 cml.Index Headings: Erbium; Spectra.

Unlike the spectra of neutral and singly ionized rareearths, which have attracted the attention of spectro-scopists in the last five years, only a single doublyionized spectrum has been analyzed, that of thulium,by Sugar.1 Recent theoretical investigations, however,in particular those by Martin2 and Brewer,3 have indi-cated the special significance of the three elements Dy,Ho, and Er, which lie around an inflexion point of thesystem difference (SD) curve. Therefore, configurationintervals in these atoms and ions cannot be inferred bysimple linear interpolation. Particularly, in doubly

ionized erbium, a local energy minimum appears toexist, characteristic of the middle of a half-shell. Theexperimental manifestation of this theoretical relationhas recently been reported.4 We consider it worthwhile,therefore, to present the results of our recent investiga-tions in the spectrum of doubly ionized erbium, whichillustrate this point.

I. EXPERIMENTAL OBSERVATIONS

Most of our relevant experimental observations onEr II were made in 1971, when we used the 10-m Eagle

MARCH 1973

358

March 1973 LEVEL STRUCTURE OF DOUBLY IONIZED ERBIUM

spectrograph at the National Bureau of Standards inWashington, D.C., to cover the wavelength region2000-3000 A, with a reciprocal dispersion of about0.72 A/mm. To this, we added outstanding Er in linesin the visible region observed on spectrograms that weprepared at the National Bureau of Standards in 1963,with a 6.3-m Wadsworth spectrograph. In both cases,the light source for the Er III lines was the sliding sparkat 20 torr of helium described by Sugar.5' 6 The ionseparation was made by varying the peak electriccurrent in the spark. At 6 A, the predominant spectrumwas Er II. At 50, it was Er iII and at 500 A it was Er Iv.A comparison of the relative intensities of the samespectral line under these three conditions led, in almost

TABLE I. Observed 4f 1" (4I)6p levels ofdoubly ionized erbium (Er III).

PositionDesignation 1 (cm-')

4f" (4I77I)6PJ 7 55 547.26

8 56 025.354f (4 I7i)6pli 9 61 032.47

6 61493.778 61 539.167 61 699.32

4f1 (4I6i)6pi 6 62 598.127 62 607.86

4f ll( 4 I5)6pj 5 65 934.666 66 077.65

4f 1(K61) 6pli 5 67 986.437 68 084.756 68 186.17

4f1 (4I5T,)6p,1 5 71779.466 71 785.85

TABLE II. Observed 4f "1 (41)5d, 6s levels ofdoubly ionized erbium (Er III).

PositionDesignation 1 (cm-')

4f (417) 5dli 6 16 976.097 17 647.76

4f" (4171)6s1 8 19 315.904f "( 4 I71 )5d,1 9 18 976.74

8 19 918.174f" e170 6sj 7 20 226.204f1"(4 17)5d2j 10 20 470.13

9 21688.175 22 016.776 22 606.078 22 951.427 23 302.78

4f" (4 16 1)5di 8 24 961.074f"( 4I6O)6si 7 26 102.804f u(4161)5d,1 5 26 192.664f"( 4 I6o)6sj 6 26 411.804f"(4I6j)5djj 7 26 579.91

6 26 654.93Miscellaneous 6 27 472.42

5 27 870.826 28 777.677 28 818.346 29 610.925 29 806.49

30

25

20

15

- 1000 c.-

odd levels

('160)5dal -J:::

(0171)5d21

<

((7

1)5dli

0 4 5 6 7 8 9 10

0 o000 .- '

f., ('H.)

3 4 5 6 7 8 9

70

(4151

)6pl e levels

e0016)6p

1 1

('151)6p0 l

('161)6poi

('717)6pll -

,(.17)6po- _/

f 2( H.) -

FIG. 1. Observed levels of doubly ionized erbium.

all cases, to its unequivocal assignment to a particulardegree of ionization. The spectrograms were measuredat the spectroscopy laboratory at Soreq, Israel, on aGrant comparator. We used as standard wavelengthsiron lines above 2300 A and silicon and copper linesbelow this wavelength. The estimated inaccuracy in ourmeasurements is 40.002 A.

The line list used in the present work comprised800 Er iII lines. They were selected on the basis of theirappearance, also, in the 6-A spark. Since the latter is alow-excitation spark, we believed that the Er linesemitted were transitions involving low-energy levels ofdoubly ionized erbium. However, many strong Er inlines that appear on our spectrograms do not satisfythis criterion. We are now preparing a complete Er iIIline list, with which to extend our analysis.

II. THE ANALYSIS

The problem of analyzing third spectra of lanthanonscan be divided into three parts: (a) identifying thefN-1s levels (by transitions from fNlp levels, involving

TABLE III. Observed 4fl2 levels of Er III compared with thecorresponding 4f 1"6s' levels of Er I.

ErIII ErIDesignation i (cm',) (cm-')

4f 12 3R 6 0.00 0.003F 4 5081.79 5035.193H 5 6969.78 6958.34

O0

359

-

0

360

ClassificationLow level High level

x (A) a (cm-') Intensity (cm-') J (cm-') J

5903.300 16 934.985 80 000 5 081 4 22 016 54876.066 20 502.610 80 6 969 5 27 472 64783.122 20 901.004 20 000 6 969 5 27 870 54735.563 21 110.908 150 000 5 081 4 26 192 44612.930 21 672.125 300 33 875 6 55 547 74386.855 22 788.971 200 000 5 081 4 27 870 54338.236 23 044.365 3 000 6 969 5 30 014 54290.056 23 303.163 400 000 0 6 23 302 74288.180 23 313.357 10 000 6 969 5 30 282 64088.575 24 451.497 20 31095 6 55 547 74009.700 24 932.473 400 5 081 4 30 014 53962.873 25 227.080 6 000 6 969 5 32 196 43816.780 26 192.662 40 000 0 6 26 192 53739.432 26 734.428 2 000 6 969 5 33 704 63715.667 26 905.414 6 000 6 969 5 33 875 63592.962 27 824.250 80 33 875 6 61 699 73480.539 28 722.960 2 000 33 875 6 62 598 63341.003 29 922.528 80 26 102 7 56 025 83301.228 30 283.039 20 000 0 6 30 283 63214.950 31 095.701 4 000 24 451 7 55 547 73175.743 31 479.587 500 30 014 5 61493 63173.454 31.502.292 10 31095 6 62 598 63172.470 31 512.063 30 31 095 6 62 607 73166.254 31 573.925 15 000 24 451 7 56 025 83100.405 32 244.493 5 000 23 302 7 55 547 73093.625 32 315.158 1 30 282 6 62 598 63092.695 32 324.875 2 30 282 6 62 607 73070.396 32 559.627 10 000 28 934 5 61 493 63055.102 32 722.616 10 000 23 302 7 56 025 83040.383 32 881.025 1 28 818 7 61 699 73036.623 32 921.737 5 28 777 6 61 699 72958.633 33 789.522 10 28 818 7 62 667 72955.928 33 820.442 10 28 777 6 62 598 62955.074 33 830.215 2 28 777 6 62 607 72920.825 34 226.883 2 27 472 6 61 699 72916.112 34 311.000 8 33 875 6 68 186 62878.235 34 727.292 80 27 870 5 62 598 62869.517 34 838.844 10 26 654 6 61 493 62863.352 34 913.851 1 26 579 7 61 493 62859.634 34 959.242 5 26 579 7 61 539 82849.631 35 081.953 60 26 411 6 61493 62846.590 35 119.429 1 26 579 7 61 699 72846.083 35 125.685 600 27 472 6 62 598 62845.294 35 135.425 80 27 472 6 62 607 72833.033 35 287.429 80 26411 6 61699 72831.948 35 300.998 10 26 192 5 61493 62830.345 35 320.990 1 500 20 226 7 55 547 72824.749 35 390.960 500 26 102 7 61 493 62808.436 35 596.521 60 26 102 7 61 699 72805.869 35 629.885 1 000 19 918 8 55 547 72804.096 35 651.612 100 30 283 6 65 934 52792.539 35 799.150 5 000 20 226 7 56 025 82783.107 35 920.467 800 30 014 5 65 934 52780.595 35 952.916 20 26 654 6 62 607 72775.553 36 018.224 200 26 579 7 62 598 62774.804 36 027.945 600 26 579 7 62 607 72772.072 36 063.451 600 30 014 5 66 077 62768.717 36 107.149 1 000 19 918 8 56 025 82767.106 36 128.169 150 29 806 5 65 934 52762.660 36 186.308 600 26 411 6 62 598 62761.916 36 196.055 1 500 26 411 6 62 607 72759.227 36 231.328 4 000 19 315 8 55 547 72756.196 36 271.17 800 28 806 5 66 077 62752.204 36 323.778 60 29 610 6 65 934 52746.030 36 405.441 800 26 192 5 62 598 62741.414 36 466.738 80 29 610 6 66 077 62739.270 36 495.278 5 000 26 102 7 62 598 6

2738.5322723.2882683.0952651.4862637.7722637.5202626.372.2625.1942618.9422618.3952617.6422616.5532614.5322604.9092603.6232599.1752598.3942591.8322591.5602590.7212589.5482580.0152570.7372557.2212549.6882545.9472543.3082540.9062536.7612532.3592531.0302508.5882492.0422464.5962431.5072422.4742419.8112410.4692404.5802402.7532398.9072396.4002393.6022393.0802391.9652386.3512381.7522381.3962381.2472377.0722375.5052367.6382359.3312358.7872358.6932348.7672309.1912277.6512269.3642255.9542245.6012235.2822232.3462223.9802198.1462190.7712165.257

ClassificationLow level High level

a (cm-') Intensity (cm-,) J (cm-,) J-

36 505.11336 709.44137 259.32437 703.47637 899.48837 903.10938 063.98438 081.06438 171.96638 179.94038 190.92238 206.81638 236.34838 377.59138 396.54638 462.25038 473.81038 571.21238 575.26038 587.75238 605.23038 747.86538 887.70039 093.27639 208.71839 266.32739 307.06839 344.22439 408.50739 477.60739 497.73439 851.05940 115.63440 562.33441 114.28341 267.58041 312.98441 473.09141 574.65441 606.26441 672.96441 716.55641 765.31741 774.42741 793.89441 892.21241 973.09741 979.37141 981.99842 055.72742 083.46742 223.28742 371.94042 381.71142 383.40042 562.44743 291.89343 891.32844 051.59044 313.42044 517.70144 723.19344 782.00844 950.44945 478.68145 631.76446 169.402

Vol. 63

-

1 000 26 102 7 62 607 74 000 19 315 8 56 025 8

250 28 818 6 66 077 650 30 282 6 67 986 5

2 000 17 647 7 55 547 740 30 282 6 68 186 6

200 27 870 5 65 934 580 22 951 8 61032 920 30 014 5 68 186 620 29 886 5 67 986 5

300 23 302 7 61 493 65 27 870 5 65 934 6

250 23 302 7 61 559 8400 17647 7 56025 8

1 000 23 302 7 61699 730 27 472 6 65 934 5

200 29 610 6 68 084 72 000 16 976 6 55 547 7

200 29 610 6 68 186 6800 22 951 8 61 539 825 27 472 6 66 077 6

400 22 951 8 61 699 7800 22 606 6 61493 6500 22 606 6 61 699 7

6 28 777 6 67 986 5100 28 818 7 68 084 730 28.777 6 68 084 7

800 21 688 9 61 032 980 28777 6 68 186 6

1 000 22 016 5 61493 620 26 579 7 66 077 6

1000 21 688 9 61 539 820 27 870 5 67 986 5

600 20 470 10 61 032 9400 19 918 8 61 032 9

2 000 20 226 7 61493 62 000 20 226 7 61539 81 000 20 226 7 61699 7

800 26 411 6 67 986 515 26 579 7 68 186 6

100 26411 6 68084 62 500 19 315 8 61032 9

50 30 014 5 71 779 5600 26411 6 68 186 660 26 192 5 67 986 53 26 192 5 68 084 6

400 29 806 5 71 779 5200 29 806 5 71 785 6800 26 102 7 68 084 7100 18 976 9 61032 9200 26 102 7 68 186 6

2 000 19 315 8 61 539 8500 20 226 7 62 598 6100 20 226 7 62 607 7400 19 315 8 61699 7

6 18 976 9 61539 81 000 19 315 8 62 607 76 000 17 647 7 61 539 8

800 17 647 7 61699 720 .27 472 6 71 785 680 16 976 6 61403 6

600 16 976 6 61699 740 23 302 7 68 084 710 17 647 7 62 598 6

100 22 606 6 68 084 730 16 976 6 62 607 720 22 016 5 68 186 6

NISSAN SPECTOR

TABLE IV. Classified Er In lines,

March 1973 LEVEL STRUCTURE OF

usually the strongest lines); (b) obtaining the low fNld

levels (which are lower than the fN-ls levels, but in-volve somewhat weaker transitions to fNip); and (c)establishing the SD value, that is, the connection to theground configuration fN. This can be done only withfiNId levels, since the fN-ls- fN transition is forbidden.

For the purpose of breaking into the spectrum, weselected a limited group of about a 100 lines that werestrongest in the 6-A spark. Differences between theselines and the most intense 30 in the group revealed twosignificant intervals, 910.30 and 478.10 cm-l. Theycould be recognized at once as the 4f" (4 71)6s J = 8-J = 7,and fl"(4 I7-)6po1 J= 7-J=8 intervals, respectively. Thefj 1 N-lp, (JQ=Jd) interval is usually difficult to pre-dict without accurate theoretical calculations, but thefjN11si (J==J1 +2, J1 -2) is easily predicted fromneighboring spectra. In fact, in order to obtain thisinterval for the doubly ionized Nth lanthanon, it issufficient to multiply the corresponding interval in theisoelectronic singly ionized (N- 1)th lanthanon by 1.4,which is the ratio of the G3(4f6s) electrostatic param-eters for singly and doubly ionized lanthanons. Theseparameters are known to be practically constant alongthe 4f shell, their values being 210 and 295 cm-l, re-spectively. (The value of G3 for the third spectra seemsto decrease slightly along the shell.) This ratio can beverified from both Ho iII/Dy ii, and Tm iii/Er ii. Thus,a prediction for Er in can be obtained from Er iII/Ho nby using the already known Ho ii value of 637 cm-l.The calculated value, 893 cm-l, agrees well with theexperimental interval, 910 cm-l.

We carried out the analysis on this basis and wereable to establish the full 6-level group of 4f"1(4I7-)6pand some levels belonging to 4f"1(4I6-)6p. With theseupper levels, we were able to locate the 4f"1(4171 )5dlevels, whose lowest level was established at 2339.80cm-' below the lowest 4f"1(4I7-)6s level. This intervalis clearly off the interpolation curve B given in Fig. 2 ofRef. 1, and demonstrates a marked deviation fromlinearity for the fN-1s - fNld distance. We have alreadypointed out such a deviation and depicted it in Fig. 1 ofRef. 4. It was later substantiated by observations inother spectra. When we established more levels of4f"( 41)5d, in particular, some with J=5 and 6, weattempted to locate the 4f'2 levels. We found 3HI6 of4f12 at 16 976.79 cm-l below the 4f"1(4I 7 ,)5d1, levelswith J= 6. This separation agrees well with bothMartin's and Brewer's predictions of 17.1:h 1 and17.24t 1 kK, respectively. We were also able to locate the3F4 and 3IH5 levels of 4f 12. Thus, all members of the

ground configuration of Er iII up to 10 000 cm-' abovezero have been found.

Table I contains the even levels of Er iII and Table IIthe odd levels. The 4f"1(4 71 )5d21 (J=10) level can beestablished on the basis of one line only: its combinationwith the 4 f"1(4I71)6 pqIJ=9. The position we suggestfor this level cannot be further confirmed. It is sub-stantiated, however, by the fact that the one classifiedline was the only strong one in the region, and by theregularity of the J1-j umbrella formed by it. In Fig. 1,we depict the J-j coupling grouping of the Er iII levels.

In Table III, the positions of the observed 4f12 6s2

and 4f12 levels in Er i and Er iII, respectively, arecompared. The very close agreement is an indication ofthe uninvolvement of the closed 6s2 shell in the inter-action within the open 4f shell. The classified lines ofEr iII are given in Table IV. The wavelength of thestrongest line, at 4290.056 A, a transition from theground level to the 4f"'(4 I7 -)5d21 (J=7) level, agreeswell with the unidentified wavelength 4290.18 A ob-served by Przybylski7 in the spectrum of the starHD 101 065, which exhibits great enhancement ofionized lanthanon spectra.

III. PARAMETERS

From the well-separated group, in good Jj coupling,of the 4f1"(4I70)6p levels, a value of 3743 cm-' can bededuced for the spin-orbit parameter ¢6p. This is in goodagreement with the values of ¢6, obtained from Fig. 1 ofRef. 1. The coupling in the 4f"1(4 I)5d6s2 configurationin Er i is known8 to exhibit hi features rather thanJr-j ones. Therefore, the value for Cod of 1326 cm-lobtained from the ten 4f"( 417 )5d levels of Er in is tobe considered as preliminary. The same applies for thevalue of 298 cm-l for G3(4f,6s). These values shouldserve as good starting values for the radial parameterswhen the number of observed Er iII levels justifies anoptimization calculation.

REFERENCES

* Permanent address: Israel Atomic Energy Commission, Soreq,Yavne, Israel.

'J. Sugar, J. Opt. Soc. Am. 60, 454 (1970).2W. C. Martin, J. Opt. Soc. Am. 61, 1682 (1971).3 L. Brewer, J. Opt. Soc. Am. 61, 1666 (1971).4 N. Spector, J. Opt. Soc. Am. 61, 1350 (1971).5 We wish to express our indebtedness to Dr. J. Sugar for kindly

extending to us his active help in obtaining these spectrograms.6 J. Sugar (private communication).7 A. Przybylski, Acta Astron. 13, 217 (1963)."N. Spector, J. Opt. Soc. Am. 56, 341 (1966).

361DOUBLY IONIZED ERBIUM