JOURNAL OF THE OPTICAL SOCIETV OF AMERICA

Level Structure of Singly Ionized Thulium (Tm II) t

NISSAN SPECTOR

Israel Atomic Energy Commission, Soreq Nuclear Research Center, Yavne, Israel

(Received 26 September 1966)

The structure of about 40 low-energy levels of singly ionized thulium is given. The twenty 4f" (3'16) 5d6slevels are interpreted in J1 J1 1 and JILI, coupling schemes, and the twelve 4f"1('H 6)6s6p and six of the4f"36p levels are given JiJji designations. The first three levels of 4f"6s' are established. The intensityrelations of the transitions connecting some of the levels are discussed. The following values for the inter-action parameters are obtained directly from these levels:

f _= 2 5 06 cm-'rd= 121

3 cm-1¢, = 2111 cm-' (from 4f"6p)rp = 3467 cm-' (from 4f"6s6p)

More than 200 lines are classified.INDEX HEADINGS: Thulium; Atomic spectra.

Gf,= 212 cm-'Gd8 = 1535 cm-'G,,= 2613 cm-'

IT has recently been shown' that the structure of thelow levels of neutral erbium and thulium, whose

ground levels belong to a configuration of the type4fN6s2, can be well understood by considering first onlythose levels based on the lowest core level of 4fN. Theodd and even subconfigurations of the type 4fNll' ob-tained by adding to this core level the outer electrons6s and 6p then combine according to simple L-S selec-tion rules. These subconfigurations can therefore beeasily recognized and their levels grouped into terms,thus allowing classification of many prominent lines ofthe spectrum concerned.

These results have a wider application, mainly tocases where N> 9. In this paper we extend the idea ofconsidering transition selection rules between subcon-figurations to the case of Tm ii where the rare-earth issingly ionized and one of the I electrons is a 5d electron.

Although the ground configuration of most of thesingly ionized rare-earths with N> 9 is 4fN6s, the exci-tation of a 4f electron to an outer orbit requires littleenergy, and configurations of the type 4 fN-1ll' supplymost of the low-energy levels of these ions. In whatfollows, it is shown that the application of the ideasintroduced in Ref. 1 opens the way to an interpretationof the structure of the energy levels of Tm ii and totheir correct grouping into terms according to thevarious coupling schemes encountered in this ion.

REVIEW OF THE SITUATION IN Tm ii

In 1942, Meggers2 published values for all the levelsof the Tm+ 4f116s configuration, which he establishedas the lowest configuration of this ion. Along with itsfour odd levels, whose J values range from 2 to 4,seventy-two even levels which combine with these fourwere given, without J or g values or configuration as-signments. Obviously, the J's of the 72 even levelscould range only from 2 to 4. It was clear, however, that

t Supported in part by the National Bureau of Standards,Washington, D. C.

1 N. Spector, J. Opt. Soc. Am. 57, 308 (1967).2 W. F. Meggers, Rev. Mod. Phys. 14, 96 (1942).

such a high number of levels could be obtained only byexciting a 4f electron out of the 4ff" core, thus givingrise to configurations of the type 4f 12 'll.

Indeed, 20 years later we extended3 the analysis ofTm ii, using the line list which Meggers kindly made

TABLE I. Observed energy levels of Tm II, even parity.

Configuration Design

4f 126S2 3J/

IF

3(

4f 136p 4f 13 (2F

4f 125d6s ('16)

lation

16

4

3I) 6 po,

6pil

'[4]

'[5]

'[8]

'E6]

3[7]

'[4][8]

1[5]

[7]

'[6]

'N. Spector, Ph.D.(1962).

Energy levelJ (cm-1)

6 12 457.25

4 17 974.28

5 20 619.01

3 25 980.024 26 574.66

5 28 875.143 29 424.992 29 285.714 30 377.19

5 16 567.484 18 291.353 21 608.26

6 19 526.805 21022.004 22 308.84

7 19 619.078 19 682.969 20 465.79

7 22 052.426 22 355.445 23 768.85

8 23 024.316 23 904.457 23 961.56

4 23 803.26

8 24 059.10

5 25 014.75

7 26 256.25

6 26 478.30

thesis, Hebrew University of Jerusalem

312

MARCH 1967VOLUME 57, NUMB3ER 3

LEVEL STRUCTURE OF Tm i1

TABLE IT. 4f'2 (311C'5d6s levels in JI-(SL)Jii notation.

Energy leve!Designation J (cm-,)

('Ji) 2'D, 5 16 567.486 19 526.807 22 052.42

`D2 4 18 291.355 21 022.006 22 355.447 19 6t9.078 19 682.96

3D3 3 21 608.264 22 308.845 23 768.856 23 904.457 23 961.568 23 024.319 20 465.79

D2 4 23 803.265 25 014.756 26 478.307 26 256.258 24 059.10

available to Racah, and were able to identify at leastthree configurations involving a 4f"2 core, namely4f'26S2, 4f

12 5d6s, and 4f"26s6p. The range of J values was

also increased to include several J's of 5, 6, and 7. Ap-plying the usual theoretical methods for interpretingthese configurations, we calculated their energymatrices, but the number of observed levels was too

small to permit a significant least-squares fit.In 1965, Blaise and CaMus4 extended the observations

on Tm II to include Zeeman-effect data in the infrared.This enabled them to identify several new levels,

notably a group of eleven 4f"15d levels (of which onlyone had been established earlier)3 , and to obtain newg values for these as well as previously reported levels.They compiled a list of 15 odd and 95 even levels, butno attempt was made to interpret the latter by groupingthem into terms. It was thus difficult to estimate therelative strength of the various interactions in theabove-mentioned configurations, and as a consequence,the coupling schemes dominating the observed structure

of Tm II remained unrecognized.

THE NEW LEVELS AND THEIRINTERPRETATION

By applying the intensity considerations set forth in

Ref. 1, we were able to extend the results of Ref. 3,finding new levels with J values of 8 and 9, and es-

tablishing the following complete groups of levels:

(a) 4f" ('I16, F 4, 3HI5)6s' . . . 3 even levels

(b) 4f"2('Ho)5d6s . . . 20 even levels

(c) 4f 1'('H 6)6s6p . . . 12 odd levels

(d) 4f" (2 F3)6p . . . 6 even levels.

J. Blaise and P. Camus, Compt. Rend. 260, 4693 (1965).

These levels are collected in Tables I, TI, and III, andgiven with their configuration assignments and cou-pling designations. Table I[I also gives, without designa-tions, some high levels which helped in establishing thelow ones. In Table IV, we give the lines in Meggers's listwhich are classified by the levels of Tables I-III.

Together with the four 4f 136s and ten of the 4f"15dmentioned previously, we thus have all the levels of thelowest group in each parity. These give rise to most ofthe prominent lines of Tm Ii, represent the fundamentalconfigurations of singly ionized thulium, and displaythe features of the essential coupling schemes involvedin this ion.

As already mentioned in Ref. 1, the L-S coupling no-tations can be used to advantage in the 6s6p subcon-configuration. In this scheme, the twelve 4f"3QH 6)6s6plevels are divided into four groups, based on 'P0, 'Pi,3P2, and 'Pi of 6s6p. In a similar way, using L-S coup-ling designations in the 5d6s subconfiguration, we candivide the twenty 4f 12 ('H6)5d6s levels into four groupsbased on 3D,, 'D2, 'D3, and 1D2 of 5d6s. The advantageof doing so becomes evident when we consider Table V,where line intensities for the transitions between thesetwo configurations are given. We see that L-S multipletselection rules are fairly well obeyed by the four groupsobtained by the above-mentioned division. Table Vdemonstrates, for example, the strong lines in thediagonal, namely 3Dr-'Po, 3D2-'Pl, and 'D3-'P2, andthe gradual weakening of the satellites, namely 'D2-'Pi,3D2-'P 2, 'D3-'Pl, etc. The transition array of Table Vwas extremely helpful in determining, as explained in

TABLE III. Observed energy levels of Tm ai, odd parity.

Energy levelConfiguration Designation J (cm-1)4f"26s6p 4f"2(11h)6s6p 3Po t 38 225.43

3P, 5 39 863.786 39 477.587 39 638.36

3P2 4 43 217.645 43 840.806 43 998.807 43 717.208 42 570.90

'p1 5 45 987.876 48 195.947 47 299.66

4f"Q(3F4)6s6p 3P0 4 44 237.16'pI 3 45 338.23

4 44 838.235 45 191.24

Miscellaneous 6 47 927.126 49 195.017 49 765.675 49 792.395 50 274.635 51081.507 52 331.337 52 661.667 53 738.887 57 573.23

March 1967 313

NISSAN SPECTOR

TABLE IV. Classified lines of Tm ii.

x Intensity(A-) Spark Arc

0((cm-,)

Oddlevel

(cm-') J

6732.576419.536377.086364.136353.916299.456181.426017.305838.785811.185757.955737.235725.625709.985694.825684.775663.405634.605566.345561.965539.035492.115465.545416.915400.465391.975373.015372.165346.505342.415310.305305.885301.175267.345266.125260.935194.785149.405140.285128.095124.265114.555085.535060.435049.255043.125039.065034.245014.565010.945009.784993.784989.324980.684975.124970.874954.884941.784872.284831.204801.414781.324766.684750.754696.444679.944674.224666.704653.034642.964634.264626.33

Evenlevel(cm-i) J

x Intensity a.(Ak) Spark Arc (cm-')

63015105

40150

1200

503

203

60350

211

204

104

2020302

10081

502

303

104

402076

404

40566

80308

80155040303052

1050582

2012387

104020

1 14 849.072 15 573.162 15 676.811 15 708.74

15 733.996 15 870.01

10 16 173.0516 614.15

20 17 122.134 17 203.45

17 362.483 17 425.202 17 460.51

10 17 508.3517 554.95

15 17 585.971 17 652.33

17 742.5517 960.1417 974.28

4 18 048.691 18 202.87

18 291.3718 455.58

4 18 511.795 18 540.966 18 606.37

18 609.3320 18 698.622 18 712.95

18 826.0815 18 841.79

18 858.5110 18 979.63

18 984.042 19 002.76

19 244.7310 19 414.326 19 448.792 19 495.022 19 509.58

10 19 546.601 19 658.17

10 19 755.641 19 799.401 19 823.472 19 839.44

30 19 858.448 19 936.362 19 950.78

30 19 955.405 20 019.34

15 20 037,2412 20 071.9710 20 094.3910 20 111.601 20 176.49

20 229.973 20 518.53

20 20 692.992 20 821.403 20 908.90

20 973.125 21 043.41

21 286.7721 361.8321 387.94

1 21422.442 21 485.372 21 531.96.0 21 572.405 21 609.34

Odd Evenlevel level(cm-') J (cm-l) J

39 863 639 477 639 638 739 477 63( 638 738 225 638 225 639 638 739 477 638 225 643 840 539 477 643 717 739 863 539 863 539 638 743 840 543 998 643217 4

0 444 237 443 217 4

0 439 477 642 570 844 237 438 225 642 570 838 225 645191 543 840 539 863 539 477 044237 443 998 645 191 539 863 543 217 443 217 445191 545 987 542 570 843 717 743 717 745 987 544 838 445 338 339 477 643 840 539 477 639 638 739 638 743 998 643 840 543 998 639 638 745 191 543 998 642570 843 717 747 299 743 217 445 987 547 299 745191 543717 745 191 545 191 543 840 543 840 539 863 543217 4

25 014 523 904 623 961 723 768 523 904 622 355 622 052 723 024 822 355 621022 526 478 622 052 726 256 722 355 622 308 422 052 726 188 526 256 725 257 317 974 426 188 525 014 518 291 421022 524 059 825 696 419 619 723 961 719 526 626 478 625 014 521022 520 619 525 257 325 014 526 188 520 619 523 803 423 768 525 696 426 478 623 024 824 059 823 961 726 188 525 014 525498 219 619 723 904 619 526 619 682 819 619 723 961 723 768 523 904 619 526 625 014 523 768 522 052 723 024 826 478 622 308 425 014 526 256 723 904 622 355 623 803 423 768 522 355 622 308 418 291 421 608 3

4619.064615.954614.474613.204567.114559.044556.694555.284542.634522.574504.144437.404400.824381.124377.864367.894363.664358.214355.704350.994312.624292.974291.324252.424235.404221.964212.894201.144197.634161.564159.554148.514134.444132.694118.244100.614085.154063.364034.763996.523960.323912.873888.953879.663866.923865.693864.913853.103835.213833.993818.133817.403791.083786.033778.063771.713765.853738.463725.063724.783721.403716.433715.703699.873696.243683.203678.953678.543677.983673.143667.263660.88

15801010204

2015

1100

210264

152042

10351,4132411

1524

1514248

200147

10338813I

8028

101

204

2003114

202

20306

802010

20

II

.21

1

3 21 643.3730 21 657.95

3 21 664.892 21 670.843 21 889.56

21 928.306 21939.613 21946.41

22 007.5140 22 105.11

22 195.572 22 529.39

22 716.681 22 818.80

22 835.793 22 887.943 22 910.091 22 938.74

22 951.972 22 976.77

23 181.241 23 287.37

23 296.301 23 509.38

23 603.8723 679.0323 729.99

1 23 796.3423 816.2624 022.68

3 24 034.3124 098.24

1 24 180.264 24 190.47

24 275.3924 379.7224 471.9724 603.20

2 24 777.6210 25 014.71

25 243.3425 549.J5

2 25 706.601 25 768.181 25 853.05

25 861.262 25 866.502 25 945.77

26 066.801 26 075.06

26 183.3710 26 188.44

26 370.252 26 405.412 26461.08

26 505.663 26546.87

26 741.4015 26 837.57

26 839.6026 863.9526 899.8926905.15

3 27 020.3027 046.86

8 27 142.615 27 173.962 27 177.00

10 27 181.113 27216.942 27 260.573 27308.07

43 998 638 225 643717 747 927 739 863 544 237 448 195 643 998 648 195 642570 843 217 444 838 449 195 643 840 545191 542 570 839 477 649 195 642 570 843 998 648 195 649 765 739 863 549 765 749 792 545 987 545 338 350 274 544 838 447 927 643717 743717 749 195 643717 747 299 743 998 643 998 651081 549 792 5

0 443 217 443 840 549 765 738 225 652 331 749765 743 840 544 237 451081 552 331 752 661 7

0 450 274 552 661 745987 550 274 544 838 449765 7

0 449 195 644 838 445 191 647 927 639 477 645 338 349 195 648 195 651081 539 638 745191 553 738 747 927 6

22 355 616 567 522 052 726 256 617 974 422 308 426 256 622 052 726 188 520 465 921022 522 308 426 478 621022 522 355 619 682 816 567 526 256 619 619 721022 525 014 526 478 616 567 526 256 626 188 522 308 421 608 326 478 621022 523 904 619 682 819 619 725 014 519 526 623 024 819 619 719 526 626 478 625 014 525 014 517 974 418 291 424 059 812 457 626 478 623 904 617 974 418 291 425 014 526 256 726 478 626 188 523 904 626 256 719 526 623 768 518 291 423 024 826 837 322 355 617 974 418 291 421022 512 457 618 291 422 052 721022 523 904 612 457 617 974 426 478 620 619 5

314 Vol. 57

LEVEL STRUCTURE OF Tm ii

TABLE IV (continued).

X Intensity(A) Spark Arc

3660.263653.413647.733647.233644.433643.663637.633637.503619.973613.033611.613609.543607.353574.783568.683548.483536.213536.033523.883520.083498.443495.193487.083483.313474.533417.523411.163398.033373.153369.643368.333357.303350.873335.063325.783323.213316.173301.673298.703266.053254.853251.333215.02

14

40402

15032

30128

502056

1580

2151

10151262

203

202085

156

30104436

103

Odd0f level

(cm-1 ) (cm-,)

27 312.6627 363.91

6 27 406.5010 27 410.23

27 431.3520 27 437.15

27 482.6027 483.58

6 27 616.661 27 669.72

27 680.5710 27 696.505 27 713.281 27 965.801 28 013.573 28 173.03

15 28 270.7628 272.2028 369.7228 400.3028 575.99

2 28 602.553 28 669.09

28 700.1028 772.66

1 29 252.6429 307.13

5 29 420.4229 637.38

3 29 668.204 29 679.742 29 777.251 29 834.432 29 975.881 30 059.506 30 082.702 30 146.59

30 278.9530 306.2530 609.19

1 30 714.562 30 747.78

31 095.02

J51 08145 33839 86349 76543 99849 79253 73849 79247 29944 23747 29945 98749 76550 27445 98749 19544 83852 33152 33147 92749 19552 66148 19552 66151 08150 27452 33145 98752 66149 19553 73853 73853 73652 33151 08147 29949 76552 33152 66152 66153 73850 27457 573

Evenlevel

(cm-,)

23 76817 97412 45722 35516 56722 35526 25622 30819 68216 56719 61918 29122 05222 30817 S7421 02216 56724 05923 96119 52620 61924 05919 52623 96122 30821 02223 02416 56723 02419 52624 05923 96123 90422 35521 02219 68219 61922 05222 35522 05223 02419 52626 478

X Intensity(A) Spark Arc

3198.053185.473173.583169.513168.193160.793155.013141.963125 733064.013062.063056.073054.043048.823047.483025.483019.623017.093008.912982.942981.482965.862935.492929.992922.092896.522893.602869.222838.632818.472814.422797.272721.192679.562643.502638.412633.972627.582588.272507.142486.532421.64

a1(cm-1)

130602

4032

10101512303020312

2015

1504042881

603

156

3030205531

30826

Ref. 1, not only the correct grouping of various energylevels but also the positions of hitherto unknown levels.

Figure 1 is the energy-level diagram for both the4f'2 (H6)5d6s and 4f' 2 (H 6)6s6p configurations, groupedin J1-(S11 L11 )Jj1 coupling. We see that there is somecrossing of the terms for the low levels. If, however,following the suggestion made by Racah,5 we adopt theJ1Lij coupling scheme for the 4f'2Q(He)5d6s levels,shown in Fig. 2, we see that the arrangement becomesmore regular and very similar to the one in Yb ii.5 We,therefore, give JiL1i coupling designations for the4f 12 (3H6)5d6s levels in Table I.

We are confronted therefore, with a configurationwhich has a dual character. When we consider Table V,the way this configuration combines with 4f"2 6s6p in-dicates that its energy levels exhibit a J1-(S]iL 1 )Jj1coupling scheme. However, when we consult Fig. 2, wesee that these levels are better grouped and interpreted

I G. Racah, J. Opt. Soc. Am. 50, 396 (1960).

in JIL11 coupling. This phenomenon has already beenobserved by Stgar6 who says, "Therefore, the designa-tion of the energy levels in one of these two schemes ispurely a matter of taste".

Owing to the highly regular features of the groupingsin both the JL1 i and JIJrI coupling schemes, we tendto accept the level 4fl2 (3H6)5d 3I8]6s J = 9 at 20 465.79cm-' as real, although it is determined by only one line.

We find no evidence supporting the levels at 20 693.0cm-' and 22 105.1 cm-', both with J =5, reported inRef. 4. They are not confirmed by combinations withother levels, and the lines given there as connectingthem to the ground level are here classified as transitionsbetween other levels. The former level is assigned inRef. 4 to 4f"25d6s (the latter is given no configurationassignment), but owing to the regularity of the struc-ture of the low levels of 4f '25d6s, there is no room in thisconfiguration for a level of J = 5 at this position.

6 J. Sugar, J. Opt. Soc. Am. 55, 33 (1965).

Evenlevel

(cm-')J

Oddlevel

(cm-,)

31 259.984 31 383.43

10 31 501.0231 541.48

8 31 554.6331 628.4631 686.46

1 31 818.091 31 983.272 32 627.513 32 648.32

20 32 7.12.296 32 733.955 32 790.09

32 804.5133 042.9733 107.15

8 33 134.813 33 224.92

35 514.2420 33 530.5915 33 707.14

34 055.9134 119.83

3 34 212.0734 514.1034 548.90

30 34 842.412 35 217.942 35 469.852 35 520.94

10 35 738.6710 36 737.77

6 37 308.4337 817.37

2 37 890.3837 954.2238 046.56

20 38 624.294 39 874.07

40 204.521 41 281.76

J

43 71743 84049 79243 99851 08148 19553 73849 7925027449 19552 33152 33145 19151 08152 33152 66151 08152 66149 79257 57345 9875027453 73853 73853 73851 08157 57347 29957 5734792757 57348 19549 19549 76550 27457 57357 57357 57351 08152 33152 66153 738

12 45712 45718 29112 45719 52616 56722 0521797418 29116 56719 68219 61912 45718 29119 52619 61917 97419 52616 56724 05912 45716 56719 68219 61919 52616 56723 02412 45722 35512 45722 05212 45712 45712 45712 45719 68219 61919 52612 45712 45712 45712 457

658666666668766666

315MarCh 1967

NISSAN SPECTOR

TABLE V. Line intensities (in spark and arc) in the 4f'2

(3H 6 )5d6s-4f1'

2 (H6)6s6p transition array of Tm Ii.

Configuration 4f12

(3H 6)6s6p

2P, 3Pp 3P2 1p,

J 6 5 6 7 4 5 6 7 8 5 6 7

4f 12 (H6)6s2 6 10 1 40 6 20 3 80 10 30 4 2 0 1 0 50 20 30 10 60 30

4f 12(

3H6)5d6s D, 5 80 30 1 0 20 3 2 0 20 5 3 06 100 20 8 2 30 10 2 0 15 4 10 2 15 37 150 10 20 3 50 15 15 3 10 3 10 3

3D2 4 40 10 4 0 50 105 50 4 50 15 4. 0 2 0 6 1 10 2 30 56 40 6 60 10 200 2 7 2 15 3 2 0 2 07 30 6 80 30 15 5 4 0 2 0 2 0 8 08 80 30 15 3 15 3 30 6

'D3 3 20 54 3 0 8 3 10 2 3 05 10 1 20 6 40 12 2 06 5 0 30 2 5 0 30 8 30 10 0 07 15 2 50 15 40 10 2 08 1 0 50 20 40 10 1 09 100 40

ID2 4 40 105 4 1 1 0 3 0 3 06 3 0 2 07 2 0 3 2 6 2 20 6 5 2S 4 1 20 4 20 5

23 4 5 6J

7 8 9 10

In Table IV of Ref. 4 the levels at 26 188.4 cm-l and28875.1 cm-', of J=5, are both assigned to 4f"36p.Since in this configuration only one level with J= 5 ispossible theoretically, we suggest that the designationof 26 188.4 cm'l be 4f"2(QF 4)5d 3[4]6s J= 5. Also, thelevel at 34 157.7 cm1l is given J= 7 whereas there is astrong line connecting it to the ground state of J= 4.

PARAMETERS

Some of the interaction parameters of singly ionizedthulium can be deduced directly from the energies of thelevels given in Table I, by using Eqs. (1) and (2) ofRef. 1. The values obtained are

(a) From 4f 136s: ¢4f= (2/7)(3F2-3F4)= 2506 cm-'Gf8,= 2( (1F38-F2)+ (3F3 -3F4 )}

=212 cm-.

TE

000

.G

DIci

FIG. 1. Observed levels based on the core level 4f 12 (3I), of thesubconfigurations 6s2 , 5d6s, and 6s6p of Tin II, grouped accordingto Jj-(SjiL1 1 )Ji 1 coupling.

- 2 3 4 5 6J

7 8 9 10

FIG. 2. Observed levels of 4 f12(H 6)5d6s of Tm ii groupedaccording to J1 L1 i coupling.

45

40

E000

' 250-1

0)C

20

15

- - I I I I I-P'P

3-P2

3D

I ( Hs)-,! I I I II I

JU I I I I I

IH

20 a \[

I r I f II I I I I I

I

. . . . . . .

| | - |-, , - - - - . -. . . .

316 Vol. 57

T-----F-

ID2

3D3

2

D22

LEVEL STRUCTURE OF Tm it

It is interesting to note that the theoretical relation7

3F3-8 F2 3 (F 4- 8 F2=-- - - 1

3F 4 - 3 F3 4 1 F3 - 3 F2

is well obeyed by the observed levels. The closeness ofthe experimental value to the theoretical value indicatesthat the 4f'3 6s configuration is not perturbed. Since,within 40 000 cm-l of the ground level 3F4 of 4f'36s theonly configuration of the same parity is 4f' 3 5d, we con-clude that the interaction between these two configura-tions is small.

(b) From 4f 12 Q(H6)5d6s: Ad= 1213 cm-'

Gd, = 1535 cm-l

(c) From 4f 2 (3 H6)6s6p: P,=3467 cm-l

G,,=2613 cm-1 .

The value for G, seems somewhat too small, sinceinteraction with 4f T25d6p was neglected.

(d) From 4f 13 (F 31 )6p: p= 2111 cm-l.

7 E. U. Condon and G. H. Shortley, Theory of Atomic Spectra(Cambridge University Press, 1963), p. 273.

The striking difference between the values for P, ob-tained from 4f 12 6s6p and 4f'8 6p should not be surprisingwhen we take into account the fact that they are ob-tained from configurations which differ in the number ofthe 4f core electrons. Such behavior is well knownthroughout the rare-earth series. For example, in theright-hand neighbor of Tm ii, namely Yb ii, the valueof D, obtained from 4f 14 6p is 2220 cm-' (Ref. 5) whilefrom 4f' 36s6p we obtained' the value 3547 cm-'. Also,to the far left, in La ii,8 we deduce from 4f6p the valueD,= 1475 cm-l, and from 4f0 6s6p we derive 945 cm-'.This situation should be borne in mind when choosingstarting values for calculating interaction para-meters in unknown rare-earth configurations of thetype 4fNl or 4fNl-ll'. These values are usually obtainedby linear interpolation on N between known values ofthe parameters. It is thus important to use the appro-priate value of N in the interpolation.

The values of the interaction parameters given hereshould serve as good initial estimates for least-squares-fit computations if and when the number of observedlevels becomes sufficient to make such a fit meaningful.

I H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std.(U. S.) 9, 625 (1932).

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

317March 1967

VOLUME 57, NUMBER 3 MARCH 1967