June 1970

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 60, NUMBER 6

Extension of the Analysis of Singly Ionized Gadolinium (Gd II)*

NIssAN SPECTOR

Israel Atomic Energy Commission, Soreq Nuclear Research Centre, Yavne, Israel(Received 21 November 1969)

Energy levels belonging to a system of three newly identified configurations of singly ionized gadoliniumare established. This system is obtained by adding to the 7 F term of the 4f8 core the 6s, 6p, and 5d electrons.The lowest level of this system, designated at 'F6 of 4f 8 (7F)6s, lies 7992.31 cm-' above the 4f7('S)5d6s"D2 j'ground level. Transitions connecting the new system to the ground configuration strictly obey the selectionrule AS,= 0, where Si is the parent spin. Coupling calculations furnish the theoretical basis for this selectionrule and explain the unusual intensity relations found experimentally in the infrared. Energy levels for the4f8(7 F)5d and 4f'(7F)6p are designated in L-S and J-J coupling, respectively. Best values for the radialparameters of 4f8( 7F)6p are obtained by least-squares calculation, with an rms error of 197 cm-'. About300 lines are classified.INDEX HEADING: Gadolinium; Infrared; Spectra; Wavelengths.

In the spectra of singly ionized lanthanons, the con-figuration 4fN6s, as a rule, is the lowest for the Nthlanthanon, where N=1 for lanthanum. Gadolinium,with N=8, furnishes a glaring exception to this rule,since the lowest configuration of Gd ii was establishedby Albertson et al.' thirty years ago to be 4fl5d6s. Tenyears later, Russell2 extended the analysis, but did notfind levels of 4f8 6s. Such levels were expected to involvesome of the strongest unclassified Gd ii lines, nine ofwhich appear in the solar spectrum. The structure of thelow levels of singly ionized gadolinium could not, thus,be considered fully known until levels belonging to thefundamental configuration 4f'6s had been identified.

For 20 years the problem remained open, untilrecently we reported (March 1969 Meeting of theOptical Society of America) our success in locating thisconfiguration. About the same time, Blaise and VanKleefI published a report containing similar results.In the present paper we identify the experimental datathat we used in establishing our levels and set forth theirtheoretical basis.

I. ANALYSIS OF THE OBSERVED SPECTRUM

A. Review of the Situation in Gd ii

Two 4 fN core configurations in singly ionized gado-linium, 4f7 and 4f', manifest the unusual characteristicof having a single term of highest multiplicity. Accord-ing to Hund's rule, this term is the lowest in each ofthem. It is well isolated from the remaining levels of theconfiguration. In the case of 4f, it is the IS level, whichis more than 30 000 cm-l below the next level. For 4f'the 7F is separated by about 20 000 cm-' from its near-est neighbor. This large isolation of the lowest core termis the dominant feature of the level structure of singlyionized gadolinium. The addition of the remaining outerelectrons to these core terms gives rise to small sub-configurations and results in a characteristic strongspectrum, comprising identifiable groups of prominentlines.

By analogy with singly ionized cerium, two systemsof energy levels are to be expected:

JUNE 1970

763

764 ~~NISSAN SPECTORVo.6

TABLE I. Observed lines connected wvith system 13.

Line Level(cm-,) (cm-,)

27119.5327280.3429577.2424685.2530018.3327612.9630474.6733505.1534582.3024603.0427370.4126615.8733447.33

26448.70426512.81329463.38734186.75129374.5062763 1.24230994.38126019.37535797.85528477.07133482.09325515.60328918.13832691.92732347.00523502.81532292.68432404.92323585.04229137.83828550.39326270.16033533.66425015.947

34946.58226621.89027699. 14724664.32532682.41630143.06726779.91731495.71328612.04331441.40225168.06125661.45728286.55722733.75524164.68231553.62628066.82532630.76534043.72527625.72225418.836

26105.92223815.96732299.92526273. 12933411.59830963.84528584.6543 1491.89326339.44125698.80022302.77 128263.287

27119.5327280.3429577.2324685.2330018.3127612.9330474.6433505.1134582.2624602.9927370.3626615.7733447.18

27548.80027612.93030563.51035286.88030474.64028731.38032094.53027 119.53036898.01029577.23034582.26026615.77030018.31033792. 10033447.18024602.9933392.87033505.11024685.23030238.03029650.59027370.36034633.87026116. 160

36898.01028573.33029650.59026615.77034633.87032094.53028731.38033447.18030563.51033392.87027 119.53027612.93030238.03024685.23026116.16033505. 11030018.31034582.26035995.22029577.23027370.360

28406.11026116.16034600.12028573.33035711.80033264.05030884.86033792. 10028639.65027999.01024602.9930563.5 10

Newlevel

Ja (cm-,)

Wave-length(A) Int. Desig

0.000.000.010.020.020.030.030.040.040.050.050.100.15

1100.0961100.1171100. 1231100. 1291100. 1341100. 1381100.1491100. 1551100. 1551100. 1591100. 1671100. 1671100. 1721100. 1731100. 1751100. 1751100.1861100. 1871100.1881100.1921100. 1971100.2001100.2061100.213

1951.4281951.4401951.4431951.4451951.4541951.4631951.4631951.4671951.4671951.4681951.4691951.4731951.4731951.4751951.4781951.4841951.4851951.4951951.4951951.5081951.524

2300.1882300.1932300.1952300.2012300.2022300.2052300.2062300.2072300.2092300.2102300.2192300.223

NewLevel level(cm-') J (cm-,)

a Only the integral part of J is given.

Int. Desig.

Wave-length(A)

3686.3303664.6003380.0074049.8583330.3403620.4563280.4692983.7452890.8054063.3903652.5403756.0902988.903

3779.8303770.6903393.0692924.2543403.3363618.0603225.4603842.2002792.6403510.5932985.8003918.0613457.0473057.9703090.5794253.6123095.7783085.0554238.7823430.9803501.5773805.5202981.2083996.320

2860.6703755.2403609. 1904053.2943058.8603316.5583733.0803174.1173494.0323179.6003972. 1663895.7913534.2384397.5104137. 1043168.2913561.9083063.7022936.5403618.7833932.977

3829.4624197.6813095.0843805.0902992.1003228.6413497.3803174.5023795.5103890.1304482.493537. 148

1002000200

200080015010

20020

15002001060

2030030

2004015

60040015108

1503008060

80015

12550020030

200125800

503010

10008

200300308053040040

3005006081040650

4800880415

100151565

30

8F6 1

8F51

GF51

Line(cm-')

27937.80326431.15231146.94933451.48625312.68924315.52928174.39733079.89627350.34232282.00732986.59732333.57329794.232

30300.918343 10.69428551.34725734.98524320.4743 1510.54432903.24230700. 12 131541.88930172.06932288. 158253 14. 12525481.34328696.41227146.04024907.01827302.21832 191.25233806.00934130.25224456.79131508.11032619.78834031.90527471.49228630.84829002.44026558.488

30096.00827533.68332028.95429912.85827043.01831935.68624197.60530041.67428743.33226299.39224647.81023264.56827123.43030440.88025380.15624261.70125054.88032400.48025222.07127212.246

33446.47327252.67433544.78126716.72435109.19332034.31133725. 15527873.79024728.609

30238.03028731.38033447.18035751.72027612.93026615.77030474.64035380. 14029650.59034582.26035286.88034633.87032094.530

33392.87037402.65031643.31028826.96027412.45034602.52035995.22033792.10034633.87033264.05035380.14028406. 11028573.33031788.40030238.03027999.01030394.21035283.25036898.01037222.26027548.80034600.120357 11.80037123.92030563.51031722.90032094.53029650.590

33447.18030884.86035380.14033264.05030394.21035286.88027548.80033392.87032094.53029650.59027999.01026615.77030474.64033792. 10028731.38027612.93028406.11035751.72028573.33030563.510

37123.92030930.1537222.26030394.21038786.68035711.80037402.6503 155 1.29028406.110

2300.2272300.2282300.2312300.2342300.2412300.2412300.2432300.2442300.2482300.2532300.2832300.2972300.298

3091.9523091.9563091.9633091.9753091.9763091.9763091.9783091.9793091.9813091.9813091.9823091.9853091.9873091.9883091.9903091.9923091.9923091.9983092.0013092.0083092.0093092.0103092.0123092.0153092.0183092.0523092.0903092.102

335 1. 1723351. 1773351.1863351. 192335 1. 1923351. 1943351. 1953351.1963351. 1983351.1983351.2003351.2023351.2 103351.2203351.2243351.2293351.2303351.2403351.2593351.264

3677.4473677.4763677.4793677.4863677.4873677.4893677.4953677.5003677.501

3578.3583782.3403209.6602988.5323949.4704111.4383548.3083022. 1043655.2203096.8023030.6523091.8633355.390

3299.2802913.6903501.4603884.66041 10.6023172.6233038.3303256.3773169.4703313.3703096.2123949.2463923.3293483.7593682.7304013.7983661.6633105.5332957. 1902929.0954087.6903172.8683064.7332937.5603639.1003491.7373446.9983764.205

3321.7443630.8803 12 1.2703342.0833696.7603130.3864131.4753327.7523478.0723801.2904056.0104297.1733685.8003284. 1103938.9714120.5603990.1103085.4783963.6603673.770

2988.9803668.3202980.2203741.9102847.4203120.7482964.2803586.5764042.757

15300

60100

250030

150250

150403

83

1515

1505158080805025802520

25030803

200200401565

1508

50

1530104

10050

200815

40030

40054502220

1508

4251030

585

1020

8rF2j

8F41

8F3i

764 Vol. 60

June 1970EXTENSION OF ANALYSIS OF Gd ix 6

TABLE I (continued)

NewLine Level level

(cm-,) (CM-') J (CM'J)29586.54927697.45927207.35831885.80832119.48724703.62925149.44730925.00624962. 13130922.59527567.62124321.47431605.69728045.346

30523. 13024301.74527563.89727643.48127471.86927295.53233142.83131483.88024747.530,31717.55924935.44-023333.00026850.691

27462.51226068.29226919.23027225.36233076.722243 13.71427396.96231669.28230957.30621790.21632896.31330274. 17130307.91824080.15823086.495

Wave-length

Int. Desig.

33264.05031374.96030884.86035563.31035796.99028381. 14028826.96034602.52028639.65034600.12031245. 15027999.01035283.25031722.900

34602.52028381. 14031643.3 1031722.90031551.29031374.96037222.26035563.31028826.96035796.99029014.88027412.45030930. 150

31788.40030394.21031245.1503 155 1.2903 7402.65028639.6503 1722.90035995.22035283.25026116.16037222.26034600. 12034633.87028406. 11027412.450

3677 .5013677.5013677.5023677.5023677.5033677.5i113677.5133677.5143677.5193677 .5253677.5293677.5363677.5533677.554

4079.3904,079.3954079.4134079.4194079.4214079.4284079.4294079.4304079.4304079.4314079.4404079.4504079.459

4325.8884325.9184325.9204325.9284325.9284325.9364325.9384325.9384325.9444325.9444325.9474325.9494325.9524325.9524325.955

NewLevel level(cmn-') J (cm'-)

(A) 4fT(S)E(5d+6s)2 -. (5d+6s)6p]

(B) 4f8%7F)[(5d+6s) -6p].

System A is lower and richer in levels. By establishingpractically all of its levels, Russell 2 classified 1177 outof the 2627 Gd ii lines listed by King,4 accounting for75% of the recorded intensity of this spectrum. Still,more than half the lines (1450 of them) remained un-classified, notably 146 whose intensities exceed 100. Weconcluded that transitions belonging to system B wereamong them. Searching for new levels using this linelist vs Russell's levels, however, did not produce thedesired level-system B.

We decided, therefore, to use the remaining lines tobuild up system B as an unconnected structure and tosearch for its connections with Russell's system A at alater stage.

B. New Levels of the System 4f'C1F)[(5d±6s)-6p](System B)

(a) 4f8 (IF) 6s

This subconfiguration furnished the lowest terms ofsystem B, namely, 8 6 F. They split into 13 levels withJ values from 4 to 64. In order to establish their energyvalues, we turned to 6s-6p type transitions whose out-standing strength had clearly been demonstrated inRussell's square array of system A. The 6s-6p energydifference places most of the lines involved in a narrowwavelength region around 4000 A. In gadolinium, King'scoverage of this wavelength region may be regarded ascomplete. We thus expected to find the desired levels,using only the 1450 unclassified lines of King's list.4

A search for significant intervals was therefore madeusing only these lines. After a few trials, we established11 out of 13 possible even levels of the group I I on thebasis of 215 strong transitions from 75 odd upper levels.

Int. Desig.

Wave-length

(A)3378.9443609.4103674.4303135.2833112.4724046.8453975. 1063232.6964004.9363232.9483626.41041 10.4333 163.0713564,636

3275.26041 13.7703626.9003616.4583639.0503662.5603016.3653175.3104039.6663 151.9154,009.2234284.5703723.240

3640.2903834.9903713.7603672.0003022.3944111.7453649.0003156. 7203229.3234587.9303038.9703302. 1953298.5184151.6264330.319

3212205

1506050150803030440

20151512308406

100208058

5150

5155

1001010251S

101003020

Line(cm-,)

26237.54932572.04923222.8383 1385.83 126604. 17931425.7473 1054. 16724247.34326558.869

22374.04825891.74523976.47222960.59530244.82030524.88232085.49023342.70826336.52723788.52726749.96529561.68533748.24325355.76629564.07223601.19423367.65326512.81326684.42126206.66826604.81732364.137

30274. 17126200.07530040.46526120.46329079.67123492.02433263.82331601.062233G4.09726265.53631879.758

8F11

30563.51036898.01027548.80035711.80030930.1535751.72035380. 14028573.33030884.860

27412.45030930.1529014.88027999.01035283.25035563.31037 123.92028381. 14031374.96028826.96031788.40034600. 12038786.68030394.21034602.52028639.65028406.11031551.29031722.90031245. 15031643.31037402.650

35796.99031722 .90035563.31031643.31034602.52029014.88038786.68037 123.92028826.9603 1788.40037402.650

4325.9614325.9614325.9624325.9694325.9714325.9734325.9734325.9874325.991

5038.4025038.4055038.4085038.4155038.4245038.4285038.4305038.4325038.4335038.4335038.4355038.4355038.4,375038.4,445038.4485038.4565038.4575038.4775038.4795038.4825038.4935038.513

5522.8195522.8255522.8455522.8475522.8495522.8565522.8575522.8585522 .8635522.8645522.892

3810.2503069.2254304.8953 185.2303757.7403 181. 1843219.2,504123.0003764. 151

4468.2103861.1404169.5804354.0643305.3993275.0723115.7704282.7883795.9304202.5233737.2603381.7862962.2523942.7603381.5134235.8814278.2163770.6903 746.4403814.7403757.6503088.943

3302. 1953815.7003327.8863827.3303437.8434255.5663005.3933163.5354289.8843806.1903135.878

S20

4006808

I52015

5503

408S105040801040301106025300

8100

48

10210801020S1080415

6Fff1

June 1970 765

NISSAN SPECTOR

observed even levels.TABLE 11

Configuration

4ff F)4s

Designation

8F

6

S1F8F8r

GF

IFBFl

6r

4F8GSG

8GSG

SD

SG'

SD

SG

SF

SD

8r

8D

8r

811

In Table I, we demonstrate the quality of the newlevels by dividing the 215 transitions into 11 groups,each consisting of all the lines going to the same 4ff-(7 F)6s level. Column 1 gives the transition wavenumber,columns 2 and 3 the energy and J value of the upper oddlevel. Column 4 gives the position of the new even level.Columns 5 and 6 give for each transition the wavelength(A) and intensity, both from King. Column 7 gives thedesignation of the new level. This table clearly indicatesthe low position of the " 8F group of levels.

(b) 4f3( 7 F)6p

This odd subconfiguration was found in the course ofestablishing the even levels of 4fJ8 QF)6s. The numberof theoretically possible levels of 4f8 ('F)6p is 37. Sincesome 60 odd levels were found during our searches, wehave to select the ones that belong to 4J8Q(F)6p. This isdone in Sec. IIIB, where a full theoretical interpreta-tion of this subconfiguration is given.

(c) 4f 8 U(F)5d

We attempted to find some levels belonging to thissubconfiguration by seeking the 6p-5d transitions,which should be quite strong. BY interpolation betweenPr it and Tmr ii, we expected the first 4f8 (7 F)5d level inGd ii, 8G74, to lie 10 758 cm-' above 8F6% of 4f8 (7F)6s.

d. i1 II New

I

5-

4,2

4,21

'3~1-

3-4-44

241x34

7-1-14

5444

32I4-2 1:

S2434

-1

I144437-13462

Position (cmr-)

7992.319092.489943.78

10292.5511084.3011343.5111669.8112071.7412318.2513030.7513515.1618366.9518389.1418690.1419377.0620093.3120098.3520574.1920631.1721157.5421364.8322531.3122533.1422677.2923025.3923270.4923473.0623970.24

4f'( 7F)5d

Position(cm-,)

32595.3032677.5634108.4634608.1034900.4435111.8435272.5835362.6435404.7835541.1535605.2735991.3436144.6036373.4636398.4236565.6236631.9736687.4736723.6936819.2536821.8237007.2037569.5437642.8737871.7038010.6138230.3338386.5238466.9538555.8038877.15

i

54,64415234647462

22X44543-l224

1432

42

2_1

4204

1

641462-4451262x44-3 4l

4234!

Position(cr-l)

38922.4539237.4639367.2739543.6039635.6239715.1839780.7140086.8441256.3641385.1841439.4941497.4241784.4142574.6042592.4442594.8342626.1843275.5643279.1943372.4543555.6243704.1143744.0443789.3043987.5344890.3245116.2345214.5745394.9646778.99

J

21321421.

24

2424

324251

6444,5321,

24

2442

321

3114

222

122X2-12A

I 1

766 Val. 60

Indeed, we found, beginning at 10 374 cur- above8Fj a group of even levels, whose first member hadJ 7-. Unlike the case of 4 J{QF)6p, whose levels over-lap those of other configurations, the new group is quiteisolated and seems to consist of levels belonging to4fJ(PF)5d only. Despite the seemingly advantageouslocation of this group, its theoretical interpretation,given in Sec. III.C, proved to be more difficult than for4f8(7F)6p. Tables II and III give the observed even andodd levels, respectively, of system B, raised to theircorrect positions (see following paragraph).

C. The 4ft-4f7 Connection

Having established the basic structure of system B,we turned to finding its connections with Russell'ssystem A. Two arguments led us to conclude that theconnecting lines between the two systems would lie inthe photographic infrared:

(1) The strong transitions involved in the newsquare array (partly demonstrated in Table I) clearlymark the 8 6'F of 4f8 (7F)6s as low-lying terms.

(2) The unique structure of the 4f'(8S)5d6s+4fl(8 S)5d2 system places three aD terms at the stra-

TABLE III. Gd Ii: New observed odd levels.

June 19-1U EXTENSION OF ANALYSIS OF Gd ii 767

TABLE IV. Newly classified lines of Gd ii.

Wave- In- In- Wave- Wave- In- In- Wave-length tensity tensity number Even level Odd level length tensity tensity number Even level Odd level

(.& in arc in E.D. (cm'l) (cm-') J, (cm-,) ~Ja (1.) in arc in E.D. (cm-,) (cm-,) J (cm-,) J

11153.793 1 0 8963.105 11084 3 20047 3 7347.321 1 1 13606.655 23025 4 36631 310974.624 3 0 9109.435 10292 4 19402 4 7324.903 100 25 13648.298 22533 5 8884 410919.893 5 2 9155.091 22533 5 13378 5 7299.296 1 0 13696.178 22677 1 36373 110627.306 15 2 9407.145 23270 7 32677 6 7201.410 150 13882.343 23025 4 9142 310571.374 2 3 9456.917 22533 5 13076 4 7191.490 20 13901.493 23970 6 37871 510469.552 4 1 9548.891 9092 5 18641 5 7189.57 800 13905.21 18690 5 32595 510430.658 30 10 9584.497 9092 5 18677 6 7164.300 80 13954.251 21157 6 35111 610271.728 1 0 9732.793 '7992 6 17725 5 7147.310 500 13987.422 18690 5 32677 610268.318 2 2 9736.025 25668 3 35404 2 7135.730 250 14010.121 20098 3 34108 410195.743 5 1 9805.327 18690 5 8884 4 22677 1 36687 010161.755 2 0 9838.123 18389 6 8551 5 7133.16 100 14015.18 20093 5 34108 410048.278 3 0 9949.227 23025 4 13076 4 22533 5 36565 49860.141 8 1 10139.063 18690 5 8551 5 7123.630 2 14033.918 20574 4 34608 59829.288 6 0 10170.888 27988 3 17817 4 7120.610 4 14039.870 21364 3 35404 29697.109 1 4 10309.525 9092 5 19402 4 7082.700 4 14115.018 21157 6 35272 79397.748 60 80 10637.929 23970 6 34608 5 7069.930 80 14140.513 23025 4 8884 49387.865 10 50 10649.128 7992 6 18641 5 7069.240 1 14141.893 22677 1 36819 29380.343 20 100 10657.667 9292 5 19750 5 7068.090 150 14144.194 23473 3 9328 29356.571 10 100 10684.745 7992 6 18677 6 7045.020 80 14190.511 22533 5 36723 59290.444 800 20000 10760.796 7992 6 18753 7 7037.810 30 14205.048 21157 6 35362 69282.987 2 10 10769.440 20098 3 9328 2 7037.260 600 14206.159 18389 6 32595 59125.412 10 60 10955.402 20098 3 9142 3 6996.76 1500 14288.40 18389 6 32677 69020.227 10 8 11083.153 23025 4 34108 4 6985.890 1500 14310.621 18366 7 32677 68915.391 10 10 11213.479 20098 3 8884 4 6978.270 60 14326.248 20574 4 34900 38845.355 10 10 11302.265 20631 2 9328 2 6976.350 125 14330.191 23473 3 9142 3

23970 6 35272 7 6906.900 15 14474.282 23025 4 8551 58748.525 10 3 11427.360 23473 3 34900 3 6887.630 300 14514.778 20093 5 34608 58745.623 0 2 11431.152 20574 4 9142 3 6852.94 4 14588.26 23473 3 8884 48718.845 0 2 11466.260 22533 5 11066 4 6839.240 3 14617.474 23025 4 37642 48702.155 2 11488.251 20631 2 9142 3 6835.050 3 14626.435 21364 3 35991 38678.163 30 8 11520.012 21157 6 32677 6 6766.920 15 14773.694 20631 2 35404 28661.477 300 80 11542.205 20093 5 8551 5 65.1 0 40.5 09 408636.697 4 4 11575.321 22533 5 34108 4 65.1 0 40.5 09 408631.136 3 2 11582.779 23025 4 34608 5 6679.560 80 14966.914 20574 4 35541 48502.604 50 15 11757.872 7992 6 19750 5 6656.620 15 15018.492 20093 5 35111 68499.807 5 8 11761.741 18366 7 6605 7 6616.440 10 15109.695 22533 5 37642 48483.829 2 4 11783.893 18389 6 6605 7 6547.280 10 15269.300 20093 5 35362 68442.617 150 25 11841.415 23270 7 35111 6 6517.740 40 15338.504 22533 5 37871 58418.650 2 2 11875.126 23025 4 34900 3 6508.540 15 15360.185 20631 2 35991 38359.947 0 1 11958.512 23025 4 11066 4 6483.980 50 15418.366 18690 5 34108 48329.556 4 1 12002.143 23270 7 35272 7 6473.680 20 15442.897 20098 3 35541 48316.415 100 30 12021.108 20574 4 32595 5 6468.860 12 15454.404 21364 3 36819 2

6444.240 15 15513.446 20631 2 36144 28315.030 80 15 12023.110 20574 4 8551 5 6422.420 200 15566.152 21157 6 36723 58284.083 1 0 12068.025 23473 3 35541 4 6382.190 150 15664.272 21157 6 36821 68267.532 20 1 12092.184 23270 7 35362 6 6368.810 50 15697.181 22533 5 38230 48179.770 30 0 12221.923 21364 3 9142 3 6290.310 15 '15893.072 20098 3 35991 37996.459 10 8 12502.097 20093 5 32595 5 6280.480 10 15917.947 18690 5 34608 57987.664 8 10 12515.862 23025 4 35541 4 6247.920 10 16000.900 20631 2 36631 37986.123 1 1 12518.277 23473 3 35991 3 6104.780 15 16376.074 20631 2 37007 17944.233 50 20 12584.286 20093 5 32677 6 6046.590 5 16533.669 20098 3 36631 37930.241 8000 5000 12606.490 21157 6 8551 5 6011.390 4 16630.482 20093 5 36723 57913.224 0 6 12633.599 23025 4 10391 3 5981.320 2 16714.088 21157 6 37871 57889.512 8 4 12671.569 23473 3 36144 2 5976.200 30 16728.407 20093 5 36821 67854.831 20 15 12727.517 22677 1 35404 2 5970.320 60 16744.882 18366 7 35111 67844.950 300 300 12743.548 21364 3 34108 4 5921.350 40 16883.363 18389 6 35272 77838.821 100 80 12753.512 23970 6 36723 5 5913.550 800 16905.632 18366 7 35272 77814.691 0 2 12792.891 18690 6 5897 6 5882.210 60 16995.703 18366 7 35362 67778.992 25 15 12851.600 23970 6 36821 6 5867.650 4 17037.876 22677 1 39715 27734.586 2 2 12925.383 23473 3 36398 3 5815.380 3 17191.015 21364 3 38555 47710.338 3 6 12966.032 23025 4 35991 3 5722.770 8 17469.209 23970 6 41439 57685.450 25 20 13008.020 22533 5 35541 4 5662.180 15 17656.142 20574 4 38230 47660.917 2 4 13049.676 18389 6 5339 5 5579.660 60 17917.264 20093 5 38010 67635.835 0 2 13092.541 23473 3 36565 4 5513.690 60 18131.637 18690 5 36821 67597.344 10 10 13158.872 23473 3 36631 3 5462.080 3 18302.957 20574 4 38877 37490.709 15 8 13346.196 23473 3 36819 2 5452.680 50 18334.510 18389 6 36723 57475.617 1 2 13373.139 23025 4 36398 3 5423.630 40 18432.712 18389 6 36821 67432.572 40 20 13450.588 21157 6 34608 5 5417.120 20 18454.863 18366 4 36821 67386.630 8 4 13534.245 20574 4 34108 4 5274.806 20 18952.769 18690 5 37642 47379.126 1 2 13548.008 18389 6 4841 5 5211.880 1 19181.594 18690 5 37871 57377.264 200 30 13551.428 23270 7 36821 6 ,5174.420 5 19320.456 18690 5 38010 6

a Only the integral part of J is given.

Y - 4 ALA

NISSAN SPECTOR

TABLE IV (continued)

Wave-length

(A)

5131.3505095.0604587.9304482.4904468.2104427.0334417.8004397.5104354.0644330.3194314.2804304.8954303.4684297.1734289.8844284.5704282.7884278.2164255.5664253.6124243.8394238.7824235.8814202.5234197.6814195.8514169.5804151.6264137.1044131.475

4123.0004113.7704111.7454111.4384110.6024110.4334087.6904084.6844080.3104063.3904062.5904061.2964056.0104053.2944049.8584046.8454042.7574039.6664013.7984009.2234004.9363996.3203990.1103989.2483975.1063972. 1663963.6603949.2463942.7603938.9713932.9773923.3293918.0613890.1303884.6603861.1403842.2003834.9903829.4623815.700

In- In-tensity tensityin arc in E.D.

Wave-number

(cmr')

Wave-number(cm-')

Even level Odd level(cm-,) J (cm-,) J

Odd level |/- l T j

k'-" I

Wave-length

(A)

1

55

201

300402010

40025

400805

502520

800150500

6080

800203

30500200

2015

10050015030

200302

1500500

8030

10002000

15020

100250

80150800

2506030

15025

1505080

1506

I550

400150

42

19482.62119621.38521790.21622302.77122374.04822582.15122629.34622733.75522960.59523086.49523172.32123222.83823230.53823264.56823304.09723333.00023342.70823367.65323492.02423502.81523556.93823585.04223601.19423788.52723815.96723826.35423976.47224080.15824164.68224197.605

24247.34324301.74524313.71424315.52924320.47424321.47424456.79124474.78924501.02424603.04524607.89024615.73024647.81024664.32524685.25124703.62924728.60924747.53024907.01824935.44024962.13125015.94725054.88025060.29425149.44725168.06125222.07125314.12525355.76625380.15625418.83625481.34325515.60325698.80025734.98525891.74526019.37526068.29226105.92226200.075

Even level(cm-') J

18389183891231810292130301231813515

994313030123181351512318116691134313515120711303013030135159092

113439092

1303013030102921231813030123189943

11343183771231812071123181029211084116091108411669123187992

102921207111343

99437992

1166911669120711108412071116699092

1134311084116699943

113431108413030113439943

110849092

1029211084130309092

123181029213515

3787138010341083259535404349003614432677359913540436687355413490034608368193540436373363983700732595349003267736631368193410836144370073639834108355414257436565363733663134608354043599135541361443681932595349003668735991346083267736373363983681935991370073663134108363983614436819351113656536398383863672335362365653460835991368193892235111383863639839715

5645232632043522,1',31 I5363342134

54S35234,225303561323134322643356452326332

3810.2503805.5203805.0903801.2903795.5103782.3403779.8303770.6903768.5003764.2053764.1513757.7403756.0903755.2403746.4403741.9103733.0803723.2403719.4503696.7603686.3303682.7303674.4303673.7703672.0003668.3203664.6003661.6633655.2203652.5403649.0003639.1003639.0503638.8803630.8803624.8933618.0603616.4583609.1903605.2653597.0143586.5763578.3583564.6363561.9083537.1483534.2383501.5773497.3803494.03234917373478.0723467.6643457.0473446.9983437.8433430.9803393.0693381.7863381.5133355.3903345.8253330.3403327.8863321.7443316.5583302.1953275.2603275.0723232.9483232.696

In- In-tensity tensityin arc in E. D.

5200

80400

1530020

3006050158010308

30300

8800100100

20128

1525

200030

2200105

30103080151210

100I

1015408

304030

10080

1501540

3008

10200

3040103

80800

1015

2001020

58050

26237.54926270.16026273.12926299.39226339.44126431.15226448.70426512.81326528.22026558.48826558.86926604.17926615.86626621.89026684.42126716.72426779.91726850.69126878.05027043.01827119.53127146.04027207.35827212.24627225.36227252.67427280.33827302.21827350.34227370.41027396.96227471.49227471.86927473.15327533.68327579.15827631.24227643.48127699.14727729.30227792.90727873.79027937.80328045.34628066.82528263.28728286.55728550.39328584.65428612.04328630.84828743.33228829.60128918.13829002.44029079.67129137.83829463.38729561.68529564.07229794.23229879.40530018.33030040.46530096.00830143.06730274.17130523.13030524.88230922.59530925.006

2544445243336S225IS46

123189092

10292113431029210292

90921303011343110841231812318

79929943

13030116699943

120719943

113437992

1108411669113431231811669

799211084102927992

1231811084120719092

1134310292

90921207199439092

110841166910292116699943

1029299439092

102929943

110841134379929092

1108413515

90929092

130301303010292

79927992

1351511343

99431231812071130301166911669

3855535362365653764236631367233554139543378713764238877389223460836565397153838636723389223682138386351113823038877385553954338922352723838637642353623971538555395433656538877378713672339715376423682158877395433823039715380103855538230376423887738555397154008636821380104008642594382303855542592425944008637871380104355541439400864259242594435554259242594

.

Vol. 60

EXTENSION OF ANALYSIS OF Gd ii

TABLE IV (continued)

Wave- In- In- Wave-length tensity tensity number Even level Odd level

(A) in arc in E.D. (cm- 1) (cm-') J (cm-r) J

3225.460 600 30994.381 9092 5 40086 4

3209.660 60 31146.949 10292 4 41439 53201.019 30 31231.026 11343 4 42574 53175.310 6 31483.880 12071 1 43555 13174.117 30 31495.713 9943 5 41439 53172.868 40 31508.110 11084 3 42592 33172.623 5 31510.544 11084 3 42594 23135.283 20 31885.808 11669 2 43555 13096.802 50 32282.007 10292 4 42574 53095.084 8 32299.925 10292 4 42592 33090.579 60 32347.005 9092 5 41439 53063.702 10 32630.765 9943 5 42574 52985.800 8 33482.093 9092 5 42574 52890.805 20 34582.301 7992 6 42574 5

tegic positions of 4000, 9000, and 18 000 cmn', plus an'G at 18 5000 cm-l. (Term positions refer to theircentroids.) Each of these four terms (with the possibleaddition of the ground term 'OD) was believed to com-bine strongly with the new 8F. Lines from the first two'D terms, which belong to 4fl(S)5d6s, represent 4f-5dtransitions, which are allowved and even favored singleelectron jumps. The next two terms ("D and 8G), whichbelong to 4f ('S)5d2 , could still combine quite stronglywith 'F because of the strong interaction' between theodd subconfigurations of system A.

Since, in the photographic infrared, energy differ-ences as small as 8000 cm-' are observable, we concludedthat if the 'IF were lower than 10 000 cm-', it would berevealed by transitions from 'G and the high 'D. If itlay above 10 000 cm-', it could be observed, owing toits wide splitting and inverted structure, by its transi-tions to the low 'D, and possibly to the ground term"D. By searching our recently compiled list of gado-linium lines in the photographic infrared,6 we estab-lished the connection with system A on the basis of theoutstanding lines from 'G' and c'D0 to 'F, placing the'F61 at 7992.31 cm-l above zero.

In contrast with the prominence of the observed'0 0 -F transitions, we note the complete absence of'F-a'D0 transitions which, according to the calculations,should fall along with the 'G 0-8F transitions on the samephotographic plate. This is shown in Table IV whichgives the observed Gd ii lines now classified accordingto the new levels of Tables II and III and those ofRef. 2. Indeed, the strength of the double-electron

transitions fs-d' from the new levels to the higher4f 7 ( 'S)5d2 levels, compared with the total vanishing ofthe supposedly favored single-electron transitions d-fto the low 4f7('S)5d6s levels, is remarkable. We attri-bute the absence of the latter connecting lines to astrong selection rule, which we discuss in the followingsection.

II. ESTABLISHING THE SELECTIONRULE, A SI= O

A. Coupling in the Fundamental Configuration of Gd+

A selection rule governing the transitions betweentwo configurations can be better understood, and isstrictly obeyed, if each of the configurations manifest ahigh-purity coupling scheme.

The subconfigurations involved here are 4f'(7 F)6sand 4f7 ('S)5d6s. For the former, the mere presence ofthe 6s electron furnishes two resultant multiplicitiesconnected with the 7F parent term. For our argument,it suffices to note that the 7F has been calculatedtheoretically to be 95% pure in L-S coupling.7

As regards the coupling scheme in the subconfigura-tion 4fl('S)5d6s, two earlier proposals6 "s summarizedin paragraphs (a) and (b) below prove to have severedrawbacks, and we therefore propose a third scheme[paragraph (c)3.

The subconfiguration 4f'('S)5d6s has four terms:"D, 'D, and two of 8D. The latter are distinguished bydenoting the lower- and higher-energy terms by a'Dand VAD, respectively.

(a) In the easiest scheme for matrix computations,the 5d and 6s electrons enter into good L-S coupling, toyield ','D. When combined with the core 8S, these twoterms become the parents of two 'D terms, designated('D)'D and ('D)'D, respectively. This scheme, adoptedby Smith and Wybournes in 1965, yields total mixtures-50%--of the two parents in each 'V. Smith andWybourne therefore concluded: "The two 'D termsarising from 4f7 ('S)5d6s are intimately mixed to-gether." This precludes any selection rule based on thisscheme.

(b) Zeldes,' in 1952, reported results identical tothose given in Ref. 5, using the same coupling scheme.He noted, however, that since this scheme was selected"for reasons of convenience" it "has only a partialmeaning." According to him the "conventional desig-nation of states is by their limit, i.e., by the parent termof Gd iII to which they belong." Consequently, he also

TABLE V. Percentage compositions for 4f7(835)d6s a, MD0 .

Designation 4f '(8S)5d6s (Q"DD) 4Jr7Q(S)6s(Q9S)5d 4f7(8S)Sd(79D)6s

a3D 65% (eD)'D+35% (ID)sD 96%(7S)'D+4% (98)8D 96%('D)8D+4% ((7D)8DbMD 65% (1D)8D+35% (3D)8D 96% (9S)8D+4%S(7)8D 96%(7D)8D+4% (9D)8D

June 1970 769

NISSAN SPECTOR

TABLE VI. Observed transition array forGd II 4f8 (7F)5d-4f'(8S)5d6s.

4f' (sS) Sd6saa8D2 3 4 5 bSD5 4 3 2

418 (7

F)5d'Gs ... . 2 Ob5 ... ... 8 1 5 14 ... ... ... 15 100 15 1003 .. ... ... ... o 10 10 60 2 102 ... ... 2 10 1o

$Ds ... . ... 300 80 ...4 .... ... ....... 80 15 -- 0 23 -..... .. ..... 30 0

Sfe ... 8 0 0 0 5 0 0 05 ... ... - 100 254 e . ... 15° 30 1503 ......... 125 150

a Only the integral part of J is given.b When two intensities are given, the source is Ref. 6.e When one intensity is given, the source is Ref. 4.

tried a scheme in which the 6s electron couples to theIS core term to give ',IS as parents. The 5d electron isthen coupled to these parent terms giving rise to twoID terms, which are now designated (7S) 8D, (9S)8D. Anapparent improvement is obtained since each 8D is now99% pure. Thus it seems that the "intimate mixture"between the two 8D terms mentioned in Ref. 5 resultsmerely from an unfortunate selection of the couplingscheme. However, even in the new coupling scheme"the conventional designation of states by their limit"is not satisfied. The new theoretical designations(7S)8D and (9S)8D correspond to Russell's a8D andbVD, respectively. This, however, brings them intoqualitative conflict with the common observation thatOS is lower than 7S. It also contradicts quantitativelythe experimental observations on the "parent terms ofGd iII" because it puts a 9S-based octet 5000 cm- 1 abovea 7 S-based one, whereas the 95 itself was observed9 tolie 2000 cm-' below the 7 S. We conclude, therefore, thathigh purity in percentage composition can sometimesbe obtained as a mathematical result, irrespective of thereal physical conditions. This situation is known tooccur mainly in the presence of an s electron. Thus suchpercentage compositions must always be carefullycorroborated by comparison with the experimental data(parent-ion structure, line intensities).

(c) After repeating the previous calculations andobtaining identical results, we tried a third couplingscheme. In this scheme, the 5d electron couples to thecore 8S, in good L-S, to give 7' 9D. These serve as parentsof the final 8D terms obtained by adding the 6s electronto them. The resultant terms are designated (9D) 8D and(7D)8D. When we calculated percentage compositionsin this scheme, almost no loss of purity was observedcompared with the Zeldes scheme, each term now con-taining 96% of one parent. The clear advantage of thenew scheme is in the correspondence it produces be-tween (9D)'D, (7D)8D, and a1D, b8D, respectively. Now,there is also close agreement between the a8D-b8Dseparation in Gd+ and the 9D-7D separation in Gd++.

The results of our calculation for the three couplingschemes are summarized in Table V. Adopting scheme3, we can now state the selection rule that leads to theabsence of the 1F-a8D lines.

B. The Selection Rule AS,= °

The two subconfigurations 4f8 (7F)6s and 4f7(8S)5d6snow have coupling schemes that explain the observedstructure and give a high degree of purity to leveldesignations. The transitions between these configura-tions are within the parent subconfigurations 4f8 (7F)and 4fl( 8S)5d. Let us denote the spin and angularquantum numbers of these parent terms by the sub-script i. Thus the 4f1 (7F) has 7F, with SI=LI=3,whereas the 4fl('S)5d has 7D, with L,=2, SI=3 and9Di with Li = 2, S=4. All of these terms are more than95% pure in L-S coupling. The selection rule

ASI = 0

makes 7 F-7D allowed and 7F-9D forbidden.

C. Experimental Manifeststion of the Selection Rule

Experimentally, the selection rule is manifest in twoways. One is the complete absence of the whole multi-plet (7F)8F-(9D)8D, as discussed above.

More positive evidence for the rule can be obtainedby considering the selectivity of transitions to the(9D)8D and (7D) 8D from other 7 F-based terms. In thephotographic region covered by our observations, suchterms arise from the 4f8 (7 F)5d configuration; they arethe 8G, 8D, and 8F, which start around 18 000 cm-'. InTable VI we give a partial transition array betweensome of their levels and the two 8D terms. The strongintensity of the fully developed multiplets to b8D andthe nonappearance of lines to a8D (which is lower inenergy) can be explained only on the basis of the coupl-ing scheme chosen and the strict application of theselection rule. Table VI may be regarded as experi-mental confirmation of the theoretical reasoning set outearlier.

D. The Irreducible Tensorial Characterof the Selection Rule

The one surprising aspect of the selection rule isconnected with its spin character. From experienceaccumulated in the spectroscopy of the rare earths, weknow that intersystem (ASFzO) combinations are oftenquite prominent. Even from Russell's list of classifiedgadolinium lines, we see that transitions with SS= 41,42 are numerous and intense. It seems that the use ofa spin selection rule to explain the absence of linesitself needs an explanation.

The explanation lies in the special form of the spin-orbit and electrostatic interaction expressions in thesubconfiguration f7(8S)ds.

770 Vol. 60

EXTENSION OF ANALYSIS OF Gd ii

Because N = 7, the f shell is exactly half-filled. In thiscase, according to Racah [see Eq. (74) of Ref. 11] thediagonal elements of all even tensors are identicallyzero. Therefore, the coefficients of ¢4f and all f k vanish,since V'11) is an even tensor and in the expression for fkonly even k's are allowed by triangular conditions. Theonly nonvanishing even tensor occurs in the energyexpression for the spin-orbit interaction of the 5d elec-tron. However, this interaction results in negligiblysmall splittings compared with the intervals induced bythe electrostatic interaction and so we can ignore it forthe purposes of this general discussion.

The vanishing of even tensors also affects the expres-sion of the f-d interaction. Except for a scalar factor(a constant), all U W have a vanishing diagonal matrixelement for the IS term.' 2

Thus, the complete energy expression ET for all theterms of f 7 (8S)ds is reduced to

ET= -22+2(Si-S)DcVG,

where i runs over the various l's involved. This equationdoes not depend on J (the final splitting into levels isdue solely to the rd). Its form is the well-known VanVleck vector model. It contains only spin-exchangeinteractions. We are confronted here with an unusualsituation in complex spectra, where the gross structureof a configuration results from scalar products of spinsonly, with no orbital contribution at all. Because thedominating interaction is entirely spin dependent, it isnow clear why a spin selection rule is so effective and soclosely obeyed. Because this is a tensorial selection rule,in contrast to a radial one, it cannot be predicted fromobservations on neighboring spectra.

III. THEORETICAL INTERPRETATION OFSYSTEM B: 4f3 Q(F)6s,6p,5d

A. 4fs(7F)6s

From the 11 levels that we established as belongingto the IF and IF of this subconfiguration, we can deducethe two-electron interaction parameters Pf and Gf3 .These parameters are the only ones (except for anadditive constant) involved in the energy expressionsfor the new levels. We obtain the values Gf, = 220 cm-',Of= 1200 cm-'. It should be noted that this is the onlycase in which a value for the spin-orbit-interactionparameter of a 4f electron configuration in gadoliniumhas been obtained directly from the level structure ofthis atom itself. All 330 gadolinium levels hithertoobserved 2 (both of the neutral and singly ionized atom)are based on the 8S term of 4f7. None of them, therefore,involves Rf in its energy expressions. Our value of Pf issomewhat lower than would be exprected from inter-polation, but it is corroborated by least-squares resultsfrom 4 fl( 7F)6p, which are given in the next section.

B. 4f8( 7F)6p

As mentioned in Sec. I.B(b), this subconfigurationhas 37 levels that are interspersed among the 60 oddlevels given in Table III. The fact that it gives intenselines to 4f'( 7F)6s is not enough to permit segregation ofits levels, nor to obtain their correct grouping. Albert-son13 recognized this problem when he analyzed theconjugate configuration 4f6(7F)6p of Sm ii. In his"attempt to assign values of L and S to the odd levelsand thus to pick out multiplets, only moderate successwas attained" since "the intensities were quite anomal-ous" and "the assignments nearly always led to am-biguous results." He thus acknowledged the "futility ofassigning L and S values to the odd terms."

We thus attempted a theoretical calculation of the4f'( 7F)6p subconfiguration in order to interpret it inJ-j coupling. We compare our results with those ofBlaise and Van Kleef' who recently published a list ofodd levels similar to ours and picked out the 4f'('F)6plevels and gave them L-S coupling notations. Ourleast-squares calculations also supply a list of bestvalues for the 4f-6p interaction parameters, which arenot so well known around the middle of the 4f shell.

For the purpose of the calculations we computed theelectrostatic and spin-orbit matrices for the six ad-justable radial parameters of this subconfiguration,namely, Fo, F2, G,, G4, the Slater electrostatic inter-action parameters between 4f8 and 6p, and Pf and Pp.the two spin-orbit parameters.

The calculation of the electrostatic matrices isfacilitated by using the symmetry properties of thetensor operators under conjugation. Because fk dependson the I values only, and not on the spins, we may takeadvantage of the fact that, for the f'(7F) parent, allspins are parallel. This means, in the I space, a completeshell minus one electron. For the f2 in this case, nofurther calculation is needed because the f2 are just thenegative of the F2 coefficients of fp given in Ref. 14§57. For gk, we have

g=--j'+'(S 5s )](311c(11 11 )22;(- 1)r

6

X (2r+ 1) W (3311; re) Z (ufi(r) *u()).i-l

(1)

The only dependence on spins is through the firstbrackets. Thus, following the previous reasoning con-cerning the conjugate of the ur) tensors for parallelspins and an almost closed half-shell, we can write,according to Racah" [his Eq. (74)],

6

E (iL|Wf r)Il/)= (-l)+l(lIu1 (r)I|l') R#o). (2)i=1

771June 1970

NISSAN SPECTOR Vol. 60

TABLE VII. Electrostatic matrices for f6(7F)p and f8(7F)p.

F2 G2 G 0 G2 04

8D -12 -42 -84 -105 -84F 15 -105 -84 -105 -84G -5 -105 -36 -105 -84

CD -12 7 14 14 -28F 15 35/2 14 35 7G -5 35/2 28/3 -35 77/6

For r=O, we can write

6

E uif i(°) = 6tuf 0°) = 7'tif (°) -uf (1).i 1 (3)

We note that 7WV(3311; ok) (uf(O) .u, 0 ') = (-1)-k13 = -because k is even. According to Racahl" [his Eq.(40a,b)],

W1(3322; rk)= (-1)k 0 W (3rk1; 31) (4a)

W1(3131; Lir) = (-1) LWV(3rL1; 31) (4b)

so that

32( 1)2r±l(2r+1)W(331l; He) (uSr) .u 2/r))-2(-1)2r+I1t(2r+1)W(3311; rk)W(3131; Li),

which becomes

( 1)- ±2L>rk+ r±L(2r+1)I1r(3rkI; 31)W(3rLl; 31)

and this in turn reduces, according to Eq. (42) of Ref.11, simply to

6k/(2k+1). (5)Thus, the right-hand side of Eq. (1) becomes

+(7/12)[jS(S+ ) 1-391/4JcaxL[36LO/ (2k+ 1)-1l], (6)

which gives the final simple expression for calculatinggo.

Following Judd,'5 we can very easily derive the ex-pressions for gk in ftp from those for f6 p. Thus, for thesextets, we have

goQ L)=( 0 ' j (8/7)gk(IL),

where gk denotes the coefficient for fJ. For the octets,

TABLE VIII. Parameters for 4f8 (7F)6p.

Diag. Least squareName (cm-,) (cm-,)

FO 37100 37095±77F2 55 48± 10G2 8 8± 1Go eliminated eliminatedt4! 1225 1234±313 rp 1700 1769±i-71rms error (cm'-) 197

(%) 2.7%

we do not even need to know gk, and we get

gk(OL/7 k 1's)2Rk (8L)=-7t

which is independent of L. This striking invariance ofgQ('L) with respect to L has already been noted byJudd, and stems directly from the properties of tensoroperators under conjugation. In Table VII we give thecoefficients of -k and Gk for fl(7F)p, and of G0 forf01 (7)p.

It should be remarked that

Fo = 105

F2G=7

G4 =-4 = 3

result in the identical vanishing of expression (1), andcan serve as a check for the calculated matrix elements.

For the spin-orbit interactions Jf and 5,t we used theconventional formulas (see, for example, Ref. 7, Ch. 2).The matrices for the case of f 3 (7 F)p are given inAppendix I. Those for Pf of f( 7IF)p are the negatives ofthe ones given.

In order to diagonalize the matrices, we used esti-mated values for the radial parameters by interpolationfrom other rare-earth spectra, mainly Sm i.16 Our finalparameters, after reaching convergence in the least-squares process, are given in Table VIII. They canserve as good initial values for further calculations. Thefijp configuration interacts with the fA`'ds; therefore,the rms error cannot be expected to be small in a treat-ment that neglects this interaction. Our rms error of197 cm-l (2.7% of the observed width) thus seemsreasonable.

We also calculated eigenfunctions and percentagecompositions for the energy levels. The latter plus acomparison between predicted and observed levelpositions and J values are given in Table IX. The L-Snotations3 and the present J-j designations are alsogiven. The J-j names seem to solve Albertson'sdilemma, showing the high purity of the J-j com-ponents and general good fit of the g factors. The J-jcoupling also gives a clue to the anomalous intensityrelations governing the transition array 4ft(7 F)6p-4f(7F)5d6s. The low levels of 4f8(QF)6p which give thestrongest lines in this array are extremely pure in J-fjcoupling. Of the 28 levels with JŽ 24, all but one havea major component above 60% in J-j, whereas only 11of them do in L-S. The general agreement between ourtheoretical and Blaise and Van Kleef's observed gvalues is marred in two or three cases. But the pre-liminary character of this calculation does not allow acloser fit. We will be glad to furnish the eigenvectors(amplitudes of components) in L-S and J-j couplingupon request.

772

EXTENSION OF ANALYSIS OF Gd ii

TABLE IX. Predicted positions, percentage compositions, and calculated values for 4f8(7F)6p levels.

Observed Calcu- LSlevel lated O-C names

J Percentages in J-j Percentages in L-S (cm ') (cm-') (cm-') g.bs. gcalc. (Ref. 3)

5162

44513462

742244523214

42021

521

212

62

12

024421

3244,543222

44231<22 2

3212

212

0212

22

1a

1202

32595 32795 -200 1.575 1.55 8D95% ('F6,,2)90% (7 F6,,)92% (7 F5,2)93% (7 F", )90% (7

F4,2)85% (7 F,2,)

100%, (7F6,12)

89% (7F3,2)95% (7F4,2)98% (7F6,2)60% (7 F3,2) +40% (7F5,2)86% (7 F3,2)73% (7 F6,2) +20% (7F5,2)77% (7 F1,2)84% (7 F5,2)95% (7 F2, )94% (7 F6,2)93% (7F, 1)85% (

7F,,2)

77% (7Fs, ) +20% (7 F6, A)41% (7 F5,2) +29% (7 F3,2) +25% (7 F4,2)79% (7F4,3) + 16% (7 F3,a)88% (7F4,2)68% ('F4 ,2) +16% (7 F5,2)64% (7F4,2) +28% (7

F3,2)81% (7F3,2) +18% (7F4 ,2)72% (7F3,2) +20% (7F2,2)60% (7 F3,2) +24% (7F4 ,2)74% (7F2,2) +24% (7F3,2)62% (

7F3,,) +30% (

7F2,2)

64% (7 F2 , 2) +25% (7F1, 2)58% (7 F2,2) +41% (7F,2)51% (7 F2,2) +25% (7F3,2)64% (7 F,2,) +32 (7F2,2)56% (

7F1,A) +30% (7F0,2)

52% (7

F 0,) +41% (7F1, 3)

50% (7FI,2) +30% (7F2,2)

a See Ref. 3.

C. 4f5(JF)5d: Preliminary Interpretation

As mentioned in Sec. I.B(c), the low terms of the4f'(7 F)5d subconfiguration, namely, 'G, 8F, 8D, wererelatively easy to locate because, unlike the 4f'(7 F)6plevels, they stand separately as an isolated group whoseposition could be estimated quite accurately by inter-polation. However, they are less amenable to least-squares treatment because only 16 out of the 57 possiblelevels are known, as compared with all 37 of the4f8(7 F)6p levels, which could be selected out of 60 oddlevels. Clearly, such a limited representation of thissubconfiguration does not permit a significant theo-retical treatment. We note only that the L-S notationused in Table II is supported by intensity relations andcould be expected from Albertson's designations of theconjugate subconfiguration 4f'( 7F)5d of Sm ii.

IV. CONCLUSIONS

The symmetry properties of the electron configura-tions near the middle of the f shell and their experi-mental manifestation are demonstrated in the case ofGd ii. A new system of configurations, starting with themetastable level 'F6A only 0.92 eV above zero, wasestablished. A very strict spin selection rule and un-usual intensity relations are inherently connected withthis symmetry and with the pure-coupling schemeswhich prevail in all subconfigurations. We believe thatdetailed intensity calculations of the transition array4fl('S)(5d +6s) 2 +4f'( 7 F)6p-4f'(7 F)(5d + 6s) wouldbe very revealing. Our least-squares calculation of4f'( 7F)6p could furnish initial values for the fp inter-action parameters.

36%8 D+38% 8F+18%6F100%'G54%8F+22%8D30%6F+26%8G+20%6G+13%8F

63%8 F+14%8D+13%8G43%8F+52%6G100%8G67%8 F+16%8G42%6 F+35%8G+13%6G50%6F+38%8D43%'G+41%6F70%'F+ 16%8G61%6D+24%6F76%8F+13%6D45%8F+33%6G+17%8F49%8G+36%6F80%8G+18%6G55%8G+30%6F64%8G+25%6F35%6D+25%8D+25%6F43%6D+37%6F39%8D+38%8F+180,'6G61%8G+33%6G49%6D+17%8D+16%6F49% 6 F+28%6 D+13%8G48%6G+45%'G60%8D+28%8F60%6D+11%8D+11%6F61%6G+31%8G60%6F+15%',oD+18%'3G77%8D+16%8F71%6F+23%8G

70%6D+13%8F74%8G+ 18°,'8G

91%8D

88%6G80%6D+16%8F

32677 3275534108 3391134608 3421534900 3488735111 3519835272 3549735404 3570135541 3531635605 3576435991 3613636373 3634036565 3662036687 3678736723 3649936819 3670936821 3673537007 3705737057a 37200

3710037522a 3766637642 3762737871 3778938386 38183

3851038555 3866038877 38569

3902039237 3934939367 3914639543 3930939610a 39557

3961039635 39861

3983739936a 40204

39949

-7819739313

-87-225-297

225-159-145

33-55

-10022410986

-50-143

-1441582

203

-105308

-11222123453

-226

-268

1.475 1.481.571 1.571.46 1.461.62 1.57

1.451.47 1.471.92 1.651.45 1.431.51 1.511.55 1.391.79 1.831.59 1.512.81 3.351.48 1.491.39 1.321.44 1.451.19 1.10

-0.28 -0.661.53

1.55 1.461.42 1.561.29 1.411.39 1.55

1.371.16 1.361.52 1.68

1.601.25 1.241.24 1.111.69 1.94

-0.70 -0.631.79

1.03 0.972.71

0.18 0.123.27

6D

6F

6D

8G8D

6F

6D

6D6F

8G6F

6F

6F

June 1970 773

8G6F

6F

OG

6G

NISSAN SPECTOR

APPENDIX

Spin-Orbit Matrices for f Electron of f 6p

J=°2 6D2

6

8F

J-2 D

8G

J=l 6D 8D 6F 8F

8D IO 4 2 F0 5Th8-63 -7 441 49

6F 32V3441

8D 6F 8F

21

5542

6G 8G

8 10f3 32V35 Vii563 63 441 441

0

0

0

8F - 44!\4415

- 16 4/ - 2Vi1 09 63 63

4 v5 110 I11 3-- - - -8

63 63 252 28

2vFV5 I1( 99 3/F63 252 56 56

O - 3 3V/ - 1528 56 8

6G 8G 8G

8D 6F 8F 6G 8G

2 F0 5 5 5 1 1 /33 I -44! 126 252 98

V38 II 11- 11 ~ -

49 252 14 196

V 0h 5 V - 1398 196 14

V2 6v' 3V50 196 49 28

J=42 D 8D 6F 8F 6G 8G

6D 80 24 6 201 -7T A2 0 °D 63 63 44! 441 0

8D 2V6 2 5F2 8\/7 0 063 7 441 49 0 0

6- 20I77 5V4 22 55A 4V1 56-4 - - - 50 - 4-9

44! 441 63 50 49 392

8 42 8v'7 55\6 11 5/1V4 15 91441 49 -04 56 392 392

6G ° ° 4 21i 5\/14 2 3\/649 392 7 56

0 0 32 3159 36 33J v v 92 392 56 5

J=51 8D26F 8F 6G 8G

43

[52!

0 0

Vfr 3 F356 14

I [- -.0 95 05

42 56

- -1I 12 168

0 - - - -168 14 8

-11 V - -[9IG8 42 168

I1

6GI 0

-88 - 32 V1 - 2V70 0 063 63 441 147

4v\/6- 12 V/i 2 0 0 063 7 441 49

32Vi v1 i - 187 1 r 3V'3 15 F44! 441 126 168 98 392

2V V70 i 1 11 V7 3V3147 49 168 7 392 98

3V35 F 25 3 Vr0 0 98 392 14 56

0 0 15\/ 3 V3E5 3J/ 12392 8 56 7

J-22 6D

6D [ -

6D

774 Vol. 60

6F6D 0 0

0 0

196

6fl49

3\528

1514

6FI

8FI

8D

6F6F

6G

8G 0

EXTENSION OF ANALYSIS OF Gd ii

J=62 8F 6G 8G

8F ' 11 7 335F 8 28 56

r7 10 3v58 T7 28

3V3 3Vr 3956 - - -

J=22 6D

I F67* 74 13

- - -7 42

6F I3V2 2V449 49

8 2Iai58VF 49 147-49 147J- 7' 8GJ=2G

8G 3l

8D 6F 8F 6G 8G

6D

4i9 89 50 0 49 196 14

2756

0 50 V62 3v0155 V11196 392 28

Spin-Orbit Matrices for p Electron of fdp

J=°21 6D6

J=3 1 6D2

6F 8F 8G

I r5 4v'I53 1 - 21

_5 5 E 921 42 42 14

4 5 EV3 9 3 r321 42 56 56

0 9 3VF 5o 14I 56 9

8D 6F 8F 6G 8G

8D 6F 8F

8D 6F 8F

6G

6G 8G

1 5 F5 8 3-5 2I 0 042 21 147 147

-5V 1 4V - V 0 021 7 147 49

8V3 4\IU0 5 Im 3/5 3V314 7 147 168 42 392 98

2Iv SV3 3 1 3V5 6 F147 49 42 14 98 49

0 0 3 V1'5 3 V35 13 3 F392 98 56 14

0 0 3 -3 6 V7 3V - 598 49 14 14

J=2 6D

6D 5

6G 8G

775June 1970

3VE 2W 03 2 2iO 0 0

2V74 8\3 0 °- - - 0 0

1 V10 vr1 05 V5A -14 28 49 196

Ii0 19 3 72 3 iH28 168 196 392

8G

6D

6D

6F

8DI

6FI

8FI

8G 6GI

6F

8F

NISSAN SPECTOR

8J=51 'D

6 F

8F

6G

8G

- 1 2V3 7

2Vr7-

v65 v1321 28

5 v156 28

21

6F 8F 6G 8G

V6_521 0 0

56 28

3Vi 3Fi3- 4-

28 1 4

0 v' 3F556 28

0o - -- -28 14 4

J62 8F 6G IG

8 1 3VF 3V3F - 56

6G

8 G

3V7-w14

3V356

514

3V-14

3VF14

1356

COPYRIGHT AND PERMISSION

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J=7' 8G

8G L

REFERENCES

* Presented at the San Diego Meeting of the Optical Society~ofAmerica, 12 March 1969 [J. Opt. Soc. Am. 59, 488A (1969)].

1 W. E. Albertson, H. Bruynes, and R. Hanau, Phys. Rev. 57,292 (1940).

2 H. N. Russell, J. Opt. Soc. Am. 40, 550 (1950).J. Blaise and Th. A. M. van Kleef, Compt. Rend. 268, 792

(1969).A. S. King, Astrophys. J. 97, 323 (1943).G. Smith and B. G. Wybourne, J. Opt. Soc. Am. 55, 1278

(1965).6 N. Spector and S. Held, Astrophys. J. 159, 1079 (1970).

B. G. Wybourne, Spectroscopic Properties of Rare Eartlis(Wiley-Interscience, Inc., New York, 1965).

8 N. Zeldes, Phys. Rev. 90, 413 (1953).9 W. R. Callahan, J. Opt. Soc. Am. 53, 695 (1963).10 G. Racah, Phys. Rev. 63, 367 (1943).

11 G. Racah, Phys. Rev. 62, 238 (1942).12 C. W. Nielson and G. F. Koster, Spectroscopic Coefficients

(MIT Press, Cambridge, Mass., 1963).13 W. Albertson, Astrophys. J. 84, 26 (1936).14 E. U. Condon and G. H. Shortley, Theory of Atomic Spectra

(Cambridge University Press, New York, 1963).15 B. R. Judd, Phys. Rev. 125, 613 (1962).16 G. Racah and U. Ganiel, J. Opt. Soc. Am. 56, 893 (1966).

776 Vol. 60