JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Configurations 4f'6s and 4f'6p in Doubly Ionized Pr

NISSAN SPECTORNational Bureau of Standards, Washzington, D. C. 20234

(Received 27 June 1964)

Energy parameters are given for the 4f26s and 4f26p configurations of Pr2 +. An average agreement ofbetter than 0.5% of the total configuration spread is obtained between the predicted and observed energylevels, in both cases. Designations in (LS)J-j coupling are given.

INTRODUCTION

RECENTLY, Sugar' published his results of theanalysis of the Pr iiI spectrum in which he paid

special attention to four major configurations: 4f26s,4f26p, 4f25d, 4f3. The interpretation of the last two wasdone by Trees.' In this paper we interpret the first two.

I. CONFIGURATION 4J26s

The radial interaction parameters in this configu-ration are: Eo, El, E2, and E3, which are the electro-static interaction of the 4f2 core; if-the spin-orbitinteraction of the core; G3-the f-s interaction; and a,the Trees L(L+1) correction. Sugar gives the resultsof a calculation made with constant ratios kept amongthe core electrostatic parameters. Since then he hasfound two more energy levels and has corrected one.With 21 out of 24 possible levels given now, we did notconsider it justified to impose restrictions on the pa-rameters, and therefore in the calculation we let themall change freely. Since we also wanted to check theneed for a, we performed one calculation with a andone without it. Table I gives under "Diag." the initialparameters we used for the diagonalization. Under"L.S. 1." appear the parameters which resulted from aleast-squares calculation, together with their rms errors.Under "L.S. 2." we give the results of a least-squarescalculation done without a. We see that there is a bigimprovement by using a, showing again the significanceof this parameter in the fn shell. In what follows we usethe results of L.S. 1.

The rms error in Table I is the average rrns error forthe whole configuration, reflecting the general fit of the

TABLE I. Parameters for the 4f'6s configuration.

Diag.(cm-')

35 5344917

23478311

18733

rms error

L.S. 1.(cm-')

35 328 ±634918 ±40

22.2± 0.3478 ± 2306 ±43118 ± 2

732 ±17

±119

L.S. 2.(cm,)

35 645 ±984985 ±t85

21.7± 0.6470 ± 4305 ±t67

not included in diag.727 ±36

±4253

calculated to the observed energy levels. The agreementis very good (less than 0.5% of width of the configu-ration). We see that, within their mean error, the least-squares adjusted parameters did not change from those

TABLE II. Energy levels for the 4J'6s configuration.

Exp. Percentage Observed Calculated O-CJ name composition (cm-,) (cm-1 ) (cm-)

34 3H4 98% 3H4 28 399 28 562 -16344 92% 3H4 28 885 28 998 -11354 3H, 98% 3H, 30 734 30 786 -5244 94% 'H5 30 995 31 061 -6662 'H6 100% 3W6 32 760 32 745 1554 98% 3H6 33 466 33 470 -414 3F2 98% 3F2 33 338 33 220 11824 88% 3F2 33 660 33 574 8634 3F3 90% 3F3 34 825 34 688 13724 90% 3F3 35 384 35 122 26244 3F4 72% 3F4 +27% 'G4 35 291 35 272 1932 53% 3F4 +36% 'G 4 35 801 35 859 -5841 IG4 71% IG4 +28% 3F4 38 448 38 520 -723- 59% 'G 4 +40% 3F4 38 727 38 716 1124 'D2 88% 'D2 45 807 45 855 -4814 90% ID2 45 845 45 900 -5504 3P0 85% 3Fo 49 709

14 3P1 96% 3PI 50 228 50 257 -2954 '16 100% '16 50 647 50 572 7564 100% '16 50 659 50 570 8904

3P, 85% 3P1 (50 869) 50 947 (-78)24 3P2 90% 3P2 51313 51364 -5114 90%'P2 52 027 52 130 -10304 'SO 100% 'So 79 507

TABLE III. Parameters for the 4f26p configuration.

Diag. L.S. 1. L.S. 2.(cm-') (cm-,) (cm-,)

Eo 67 900 67 984 ±155 67 247 ±97El 5038 5033 4 46 4969 +54E2 23 23.6±t 0.4 22.5± 0.4E3 492 492 ±4 3 488 3F2 54 52 ± 5 58 ± 7G2 5 4.8±t 1.6 6 ±t 2G4 16 16 ±t 3 16 ± 4a 31 32 ± 3 23 ± 3Pf 749 748 ± 20 709 ±t24Dp 2417 2411 ± 44 2424 ±455-y -87 -90 ±t 16 not included in diag.

rms error ±198 ±252

1359

' J. Sugar, J. Opt. Soc. Am. 53, 831 (1963).2 R. E. Trees, J. Opt. Soc. Am. 54, 651 (1964).

VOLUME 54, NUMBER 11 NOVEMBER 1964

36 NISSAN SPEcTOR Vol.o

TABLE IV. Energy levels for the 4f26p configuration.

Exp. ObservedJ name Percentage composition (cm-')

32t ('HI4)Pol

4t4-4

5-4

41

34

24

54

5-

6-

2

4-

3X

5264

22-

4-24

31

34t

5-4

64

74

04

12

44t

34A2

24

3-4

44

1 -4

341,

4-4

5I2-24

34L

2-2-

4-424

44

54

12

21 -.2

24

04I

14

34-

0-2

(3II6j ) PO

('I14)PI

(3I,)PO j

(3F2)poi

(3]16)pll

(aF3)pO0('110 )p1 1

(3 F2)p I

( LIG)PIf(2FI)p,}

(1G4)poj

(3F3)p11

('G4 )p0 j

(3F4)pij

(3F3)pjj

(3F4)pIJ

94%(II4)poI96%Q(UI4)Po,

94%(IHI)pol

98%Q(IIs)poj

92%( 3 fH4)p 31

92%Q(I14)pl H

88% (3H4)p,

61% (II6)poi+31 %(14)p61%(QIl4)pIj+36%(H3 6)p0 i96% (31I6)poi

98% (3F2)POJ

88% (3F2)POi

90%(I115)pli64% (3 H)p,1 +30% (G3,)poi90% (3jI6)pl3

100% (311.,)p, I

98% (3F,3)poj

59% (3F'4)POf +30% (IG4)POJ

42%Q(TF4)pO,

50%('rF3)poI

96%(3Ij6)pij

96%(IHo)pii

100% (3II6 )p

98% (3rF2)Pl}

94%(3F2)pll

79% (311,)pj}

90%(3F2)pI3

86% (3F2)p,1

64% (QG4 )po,+32% (F 4)p,1

46%('G 4)poj+26%('G 4)p,196%(3F3)pt74% (3F3)pIj

62%(3F3)pli

66% (3F4)p1 1 +30% ('G4)p,145% (3F4)P1j+31% (QF3)pij

38%(3F4)piJ+36%(lG4)pli55%Q(3F3)pli

48% (3F4)pli+36% (QG4)p1 j59% (1G4)p1 1+34% (3F4)p1 j

58%('G 4)pii+40% (3F4)p1 j

66% ('G4)p,1 +32% (QF4)p11

53%Q(G4)p1j+44% (3F4)pj

88% (ID2)poI

86% (IDO)pO,

83%Q(D2)pli

86% ('D2)p,186%Q(D2)pll

88% (1D2)p1 j

72%(3Po)po,

-

(3p1)poj

58 158

58 174

60 166

60 420

61 357

61 606

61 718

62 241

62 559

62 679

63 221

63 576

63 593

63 769

63 817

64 215

64 401

64857

64 979

65 296

65 922

66 148

66 301

66 325

66 867

67 049

67 240

67 395

67 679

67 871

67 965

68 332

68 375

68 526

68 677

68 802

68 979

69 138

71 536

71 592

71 736

71 979

75 410

75 561

7831378 889

79 378

79 396

79 742

Calculated(cm-,)

58 291

58 230

60 182

60 375

61 609

61 590

61 596

62 193

62 315

62 590

63 407

63 501

63 701

64 024

63 827

64 188

64 642

65 008

64 991

65 159

65 907

66 033

66 287

66 394

66 647

67 042

67 184

67 003

67 730

68 053

68 275

68 382

68 403

68 700

68 283

68 852

69 121

68 821

71 537

71 637

71 616

71 900

75 336

75 597

78 491

79 101

79 420

79 033

79 580

O-C(cm-,)

-133

-56-16

45

-25216

122

48

244

89

-18675

-108

-255-10

27

-241-151

-12137

15

115

14

-69220

7

56

392

-51-182-310-50-28

-174394

-50-142

317

-1-45120

79

74

-37-178-212-42362

162

1360 Vol. 54

4f 26p IN Pr III 1361

TABLE IV (continued).

Exp. Observed Calculated O-CJ name Percentage composition (cm-') (cm-') (cm-,)

04 72%(3P1 )p0o+25%(3Po)po1 79 873

12 (CPN)p0N 94%(QPi)pop 80 164 80 198 -34

51 ('16)poP 96% ('I6)po 80 361 80 308 53

12 (3P2)po0 83%('P 2 )p01 80 898 80 918 -20

6I ('I6)Poi 9 4 %('I6)PoQ 80 989 80 483 506

22 (3P2)p51 90% (P 2 )po- 81 405 81 423 -18

14 (3P1)p14 76%(3Po)pq 83 026 83 075 -49

54 ('I6)pl3 94%(fI6)p11 83 607 83 973 -366

64 94%('I 6 )p1i 83 703 83 744 -41

24 98%(QP1 )p11 83 757

14 79%(3P1 )p1 j 83 834

01 88%(QPi)p11 83 875

42 ('I!)p13 100%('I6)p1I 84 411 84 800 -389

3 92%(P 2 )pJ 84 683

7§ (16)P13 100%(1I6)P1i 84 992 84 756 235

24 (3P2)p1 J 92%(3 P2)p,1 85 306 85 323 -17

04 88% (P 2 )p,3 85 318

14 86% (P 2)p1, 85 76204 100% ('S)p 0 3 110 850

1 100%('So)p1 1 114 484

used for the diagonalization, which proves that thecalculation converged.

Table II gives the calculated and observed energylevels. The coupling scheme is one in which the coreelectrons show Russell-Saunders coupling, and each Jfthen couples to the spin of the s electron. Under "Exp.names" are given Sugar's designations for the levels.The percentage compositions of the parents are alsogiven (components of less than 25% are not indicated).Except for one case in which there is a mixing between'G4 and 3F4 of the core, all the names are purer than85%. The mixture between 1G4 and 3F4 was expectedsince our calculations 3 for the configuration 4f2 of Ce iIIindicated a mixture between the levels of almost 50:50.Sugar later found another level (given in parentheses)which fitted the predicted value very well.

II. CONFIGURATION 4f26p

Out of 69 expected levels of this configuration Sugarreported 59 in his paper, and later found another one.The adjustable radial parameters considered in this con-figuration are: Eo, E1 , E2 , E3, the electrostatic inter-action of the 4f2 ; F2, G2, G4, the electrostatic interactionbetween the 4f and 6p electrons; the two spin-orbit interactions, Pf and Dp; the two core-correctionsa and -y, the coefficient of 12g(U), the eigenvalues ofCasimir's operator for f 2 . Recently there has been quite

I N. Spector, J. Opt. Soc. Am. 53, 1349 (1963).

an interest in -y and other electrostatic corrections [K.Rajnak and B. G. Wybourne (to be published)]. There-fore, we introduced this correction to investigate itsinfluence on the general fit, and to obtain more infor-mation on its value. Table III gives under "Diag." theinitial parameters we used for the diagonalization.Under "L.S. 1.," we give the parameters which resultedfrom a least-squares calculation. The sharpness of theparameters is also given. The results of a least-squarescalculation which was done without y are shown under"L.S. 2." As in the case of a in the previous configura-tion, a marked improvement is obtained here by using-y. Therefore, we consider -y a significant new correctionin the f

2 core, and in what follows we use the results ofL.S. 1. Trees came to the opposite conclusion about -yin the configuration 4f 2 5d, since the calculations withand without y gave the same rms error, which is rathersurprising.

The rms error in Table III has the same meaning asin Table I. The agreement of the calculated energylevels with the observed ones has a mean error of lessthan 0.5% of the width of the configuration. Again, theleast-squares parameters are, within their sharpness, thesame ones as in the diagonalization, which shows thatthe calculation reached convergence.

Table IV gives the calculated and observed energylevels, with their experimental designations and theo-retical percentage compositions in (SL)J-j coupling.When the percentage of the major component is lessthan 25%7, its composition is not given. As in the f 2s case,

November 1964t CONFIGURATIONS 4f26s AND

16 NISSAN SPECTOR V.

we notice the strong core mixture of 'G4 and 3F4. Thereare some interchanges in the designations, which aresuggested by the percentage compositions, but out of5 such pairs, 3 are simply strong mixtures, where asingle name has-not much meaning. The only level with

a serious deviation from the calcualtion is ('I6)poj6!,80 989, for which the deviation is 506 cm-l. All the restof the calculated levels agree with the observed valuesto within twice the rms error. We consider this agree-ment as establishing the values of the parameters.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 54, NUMBER IX NOVEMBER 1964

Dispersion of Argon

EDSON R. PECK AND DONALD J. FISHIER*

University of Idaho, Moscow, Idaho(Received 22 April 1964)

Determinations of the refractivity of argon from measurements made with a corner-reflector Michelsoninterferometer are given for 17 vacuum wavelengths from 4679 to 20 586 A. Sixteen of these measure-ments resulted in the dispersion formula (ni-1)10 7 =643.2135+[286060.21/(144-u2)], at 15'C and 760Torr, where a is the wave number in reciprocal microns. Comparison is made with other workers who madesimilar measurements.

REFRACTIVE measurements of argon gas havebeen limited to the ultraviolet and visible regions

of the spectrum. Recent advances in instrumentationand accurate measurements of wavelengths suggestmeasuring the dispersion of argon in the near infrared.

The work of four previous researchers who havemeasured the refractivity of argon may be representedby their dispersion formulas. They are:

Burton 1 (1908):

1.6X 10-14n= 1.0002792+

X2

where X is wavelengths in centimeters;

Cuthbertson2 (1910):

9.43264X 1027ns-1=

17008.9X 1027-o.2

where oC is frequency in hertz;

Quarder 3 (1924):

15.58(108)(-1)107:= 2778.26+

\2

where X is wavelength in angstrom units;

* Present address: Eastman Kodak Company, Rochester, NewYork.

'W. Burton, Proc. Roy. Soc. (London) ASO, 390 (1908).2 C. and M. Cuthbertson, Proc. Roy. Soc. (London) A84, 13

(1910).IB. Quarder, Ann Physik 74, 255 (1924).

Larsen4 (1934):

R=C[ fl + f2 + 3 ]X1 -2- X-2 X2-2 - X-2 X3- 2 - x-2

F 0.208972 0.208972=1.2098X 1061 +

L0.87882X 1010-X- 2 0.9100X101 0 -X- 2

4.925837 1

2.69636X l100 -X-2

where the wavelength X is measured in centimeters,R='2'F(i9-1)/(ni+2)], and C= e2ON/27rmc2, N beingLoschmidt's number. Burton's and Cuthbertson's workwere performed in the visible, while Quarder and Larsenmade measurements extending into the ultraviolet aswell as the visible region of the spectrum. Larsen'sequation was formed by using the two known resonancewavelengths of argon in the first two terms of the sum,and computing two oscillator strengths fi, f3 (assumingf = f2) and the third absorption wavelength in the last

sum.The equipment and method used for the present proj-

ect have been described by previous publications.f 7

The equipment consists of a Michelson interferometerof the corner cube type, with fringe counters and staticfringe interpolator. The gas cell was approximately 24

T. Larsen, Z. Physik 88, 389 (1934).E. R. Peck, J. Opt. Soc. Am. 45, 795 (1955).

5 D. Schlueter and E. R. Peck, J. Opt. Soc. Am. 48, 313 (1958).E. R. Peck and Baij Nath Khanna, J. Opt. Soc. Am. 52, 416

(1962).

1362 Vol. 54