Spectrum of Doubly Ionized Lanthanum (La III)
5
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA Spectrum of Doubly Ionized Lanthanum (La III)* HALIS ODABASI Joint Institute for Laboratory Astroplzysics,t University of Colorado, Boulder, Colorado 80302 (Received 12 June 1967) Sixty-five new spectral lines of doubly ionized lanthanum in the interval from 2000 to 12 000 1 are reported. Four newly discovered terms (lOs, 9p, 9d, 9f) are given. Fine-structure splittings of 5g, 6g, 7g, and 8g terms are determined, and their peculiar behavior discussed. The hyperfine structure of the 6s 2S1,2 level is 1.03 40.10 cm-'. By using the new terms, the previously reported ionization energy is corrected to 154 664±t15 cm-'. The theoretical values of spin-orbit coupling constants are calculated for the first three elements of the Cs isoelectronic sequence. INDEX HEADINGS: Spectra; Lanthanum; Fine structure. IN 1932 Russell and Meggers' reported ten lines of doubly ionized lanthanum as a result of their mea- surement of 1500 lines in the interval from 2100 to 11 000 A. Analysis of these ten lines gave the 6s, 7s 2S, 6p 2 P', and 5d, 6d 2D terms. Later, in 1935, Lang 2 de- rived two more terms, namely 8s 2 S and 5f 2 F 0 , from observations in the vacuum-ultraviolet region. Re- cently, in 1965, Sugar and Kaufman 3 published 45 new La III spectral lines in the interval from 700 to 2000 A which led to the discovery of 13 more levels. The purpose of the present work was to search for new lines in the region from 2000 A to 12 000 A. The observations revealed 65 such lines. The results of the new measurements and calculations are different from the old ones for certain terms. EXPERIMENTAL PROCEDURE The source was the same sliding spark described previously by Sugar 4 and used by Sugar and Kaufman. 3 The second, third, and fourth spectra were produced by using 6-, 50-, and 500-ampere peak currents respec- tively, and photographed on the same plate. The lines belonging to the third spectrum were identified by studying the behavior of each line in these three different exposures (Fig. 1). Throughout the entire region, lines of the first spectrum of iron produced by a microwave-excited electrodeless Fe I2 lamp were taken as standards. These lines were recorded separately on the plate between the second, third, and fourth spectra of lanthanum, each time with a different exposure time. The spectrograph was of the Wadsworth type with a grating having 600 lines per mm. Different regions and orders were used to record the spectra; for example the 2000-2200 A region was recorded in third order on uv-sensitized Kodak 103-0 plates; the 2200-5500 A * This research was supported by the Advanced Research Projects Agency (PROJECT DEFENDER), monitored by the U. S. Army Research Office-Durham, under Contract DA-31- 124-ARO-D-139. t Of the National Bureau of Standards and the University of Colorado. I H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std. (U. S.) 9, 625 (1932). 2 R. J. Lang, Can. J. Res. 13A, 4 (1935). J. Sugar and V. Kaufman, J. Opt. Soc. Am. 55, 1283 (1965). 4 J. Sugar, J. Opt. Soc. Am. 53, 831 (1963). region in second order on 103a-0 or 103-0 plates; the 5500-12 000 A region in first order on 103a-F, I-N, I-M, and I-Z plates. The N, M, and Z plates were hypersensitized. The plate factor was 1.68 A/mm for the third order. Exposures varied from 10 sec up to 6 h duration depending on the sensitivity of the plates, and the type and number of filters used. During the long exposures the source spark chamber was replaced every 2 h with a newly prepared one. Comparison of the iron impurity lines in the lanthanum spectrum with those in the calibration spectrum did not reveal any shift, but the impurity lines were very scarce. The repeatability of measure- ments on different plates indicated an uncertainty of the wavelength of about 4±0.006 A in the third order, ±40.012 A in the second order and ±t0.018 A in the first order. WAVELENGTHS AND ENERGY LEVELS Seventy-five lines of doubly ionized lanthanum were observed in the region 2000-12 000 A. Ten of these were previously reported by Russell and Meggers' and classi- fied as 6 2 S-6 2p 0 , 6 2 P 0 -6 2 D, 6 2pO-7 2 S, and 5 2 D-6 2 P 0 transitions. The results of the present work are tabulated in Table I, and plotted as a Grotrian diagram in Fig. 2. Table I contains the wavelengths, estimated relative intensities, wavenumber of the lines in vacuum, and their classifications. The energy levels of La iII resulting from the present work, as well as those reported by Russell and Meggers, Lang, and Sugar and Kaufman, are given in Table II. For some levels, the agreement between present and previous work is good, but for others it is not. The dis- agreement arises because the energy levels for the 7s 2 S 1 , 6d 2D., and 6d 2DA terms found in the present investiga- tion differ by nearly 2 cm-' from those given by Russell and Meggers. From private correspondence it was learned that Sugar and Kaufman did not question the known energy of the 6d 2 D- and 6d 2 DA levels and that they based their calculation on it. In particular, they evaluated the energy of the 4f 2F 5 / 2 ' and 4f 2F 7 / 2 ' levels, by using the three lines designated 4 2FP-6 2D. Thus the energy levels determined by using any of the transitions which involve either 4f- or 6d-levels show the discrep- ancy. It is reassuring that energy levels such as 1459 VOLUME 57, NUMBER 12 DECEMBER 1967
Transcript of Spectrum of Doubly Ionized Lanthanum (La III)
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
Spectrum of Doubly Ionized Lanthanum (La III)*HALIS ODABASI
Joint Institute for Laboratory Astroplzysics,t University of Colorado, Boulder, Colorado 80302(Received 12 June 1967)
Sixty-five new spectral lines of doubly ionized lanthanum in the interval from 2000 to 12 000 1 arereported. Four newly discovered terms (lOs, 9p, 9d, 9f) are given. Fine-structure splittings of 5g, 6g, 7g,and 8g terms are determined, and their peculiar behavior discussed. The hyperfine structure of the 6s 2S1,2level is 1.03 40.10 cm-'. By using the new terms, the previously reported ionization energy is corrected to154 664±t15 cm-'. The theoretical values of spin-orbit coupling constants are calculated for the first threeelements of the Cs isoelectronic sequence.INDEX HEADINGS: Spectra; Lanthanum; Fine structure.
IN 1932 Russell and Meggers' reported ten lines ofdoubly ionized lanthanum as a result of their mea-
surement of 1500 lines in the interval from 2100 to11 000 A. Analysis of these ten lines gave the 6s, 7s 2S,6p 2P', and 5d, 6d 2D terms. Later, in 1935, Lang2 de-rived two more terms, namely 8s 2S and 5f 2 F0 , fromobservations in the vacuum-ultraviolet region. Re-cently, in 1965, Sugar and Kaufman3 published 45 newLa III spectral lines in the interval from 700 to 2000 Awhich led to the discovery of 13 more levels.
The purpose of the present work was to search fornew lines in the region from 2000 A to 12 000 A. Theobservations revealed 65 such lines. The results of thenew measurements and calculations are different fromthe old ones for certain terms.
EXPERIMENTAL PROCEDURE
The source was the same sliding spark describedpreviously by Sugar4 and used by Sugar and Kaufman.3
The second, third, and fourth spectra were produced byusing 6-, 50-, and 500-ampere peak currents respec-tively, and photographed on the same plate. The linesbelonging to the third spectrum were identified bystudying the behavior of each line in these three differentexposures (Fig. 1).
Throughout the entire region, lines of the firstspectrum of iron produced by a microwave-excitedelectrodeless Fe I2 lamp were taken as standards. Theselines were recorded separately on the plate between thesecond, third, and fourth spectra of lanthanum, eachtime with a different exposure time.
The spectrograph was of the Wadsworth type with agrating having 600 lines per mm. Different regions andorders were used to record the spectra; for example the2000-2200 A region was recorded in third order onuv-sensitized Kodak 103-0 plates; the 2200-5500 A
* This research was supported by the Advanced ResearchProjects Agency (PROJECT DEFENDER), monitored by theU. S. Army Research Office-Durham, under Contract DA-31-124-ARO-D-139.
t Of the National Bureau of Standards and the University ofColorado.
I H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std.(U. S.) 9, 625 (1932).
2 R. J. Lang, Can. J. Res. 13A, 4 (1935).J. Sugar and V. Kaufman, J. Opt. Soc. Am. 55, 1283 (1965).
4 J. Sugar, J. Opt. Soc. Am. 53, 831 (1963).
region in second order on 103a-0 or 103-0 plates; the5500-12 000 A region in first order on 103a-F, I-N,I-M, and I-Z plates. The N, M, and Z plates werehypersensitized. The plate factor was 1.68 A/mm forthe third order. Exposures varied from 10 sec up to 6 hduration depending on the sensitivity of the plates, andthe type and number of filters used. During the longexposures the source spark chamber was replaced every2 h with a newly prepared one.
Comparison of the iron impurity lines in thelanthanum spectrum with those in the calibrationspectrum did not reveal any shift, but the impuritylines were very scarce. The repeatability of measure-ments on different plates indicated an uncertainty ofthe wavelength of about 4±0.006 A in the third order,±40.012 A in the second order and ±t0.018 A in thefirst order.
WAVELENGTHS AND ENERGY LEVELS
Seventy-five lines of doubly ionized lanthanum wereobserved in the region 2000-12 000 A. Ten of these werepreviously reported by Russell and Meggers' and classi-fied as 6 2S-6 2p
0 , 6 2 P0-6 2D, 6 2pO-7 2S, and 5 2D-6 2
P0
transitions. The results of the present work are tabulatedin Table I, and plotted as a Grotrian diagram in Fig. 2.Table I contains the wavelengths, estimated relativeintensities, wavenumber of the lines in vacuum, andtheir classifications.
The energy levels of La iII resulting from the presentwork, as well as those reported by Russell and Meggers,Lang, and Sugar and Kaufman, are given in Table II.For some levels, the agreement between present andprevious work is good, but for others it is not. The dis-agreement arises because the energy levels for the 7s 2S1,6d 2D., and 6d 2DA terms found in the present investiga-tion differ by nearly 2 cm-' from those given by Russelland Meggers. From private correspondence it waslearned that Sugar and Kaufman did not question theknown energy of the 6d 2D- and 6d 2DA levels and thatthey based their calculation on it. In particular, theyevaluated the energy of the 4f 2F5/ 2' and 4f 2F7/2' levels,by using the three lines designated 4 2FP-6 2D. Thus theenergy levels determined by using any of the transitionswhich involve either 4f- or 6d-levels show the discrep-ancy. It is reassuring that energy levels such as
1459
VOLUME 57, NUMBER 12 DECEMBER 1967
TABLE I. Observed spectral lines of La iII. In the interval from 2000 to 12 000 A.
X.i, (A) Intensity a(cm-') Classification Xnir (A) Intensity or(cm-')
10 937.89810 370.33510 284.790
9923.9899212.6289184.3808583.4538321.1078287.7528275.3888252.6038135.9648114.4156348.2136219.9996141.9876119.2546055.8386017.1145932.7065888.6205875.6325813.4475778.1385744.0885529.5425518.1875511.7215491.9025467.8125158.4105145.7294499.0504482.9674137.4284129.2443517.217,
- Transition to 2Sj (F =4).
1220
14080
100120300250200100250
23
6055
120352023
5532
2001
4512
55685
300200
3600
9140.029640.259720.43
10 073.8310 851.6910 885.0611 647.1212 014.3312 062.6812 080.7012 114.0612 287.7312 320.3615 748.1116 072.7316 276.8716 337.3416 508.4216 614.6616 851.0516 977.2017 014.7317 196.7317 301.8117 404.3818 079.6618 116.8618 138.1218 203.5718 283.7719 380.4219 428.1822 220.6822 300.4024 162.8024 210.6828 423.44
- .
8p 'P 1 / 20-8d 2D3,2
6d 'D.,2 -Sf 2'F,2,
6d 'D.,52 -5f 2F7/ 2164d 'D,,2 -5 2F ',,26d 2D312 -7p 2P,/ 2
0
7s 2512 -7p 2P,/20
64 'D5., -7p 2P3,2 °
6f 'F7,2'-6g 2G9/26+ F5/2°-6g G7/26d 'D3/ 2 -7p 'P3,2
0
7s 2SI/2 -7p 'P3/2,
5g 2G7,2 -7f 'F,/2'5g 'GC,2 -7f 'F7/,27p 'P3/2
0-8s 2SI/2
7p 'P3/,2-7d 2D32,7p 'P3,/2-7d 'D,,127d 2D5', -7f 2'7F, 27d 2D3/2 -7f 'F,/2,8p 2p3,°0 -lOs '2S1,Sp 2p,,2°- 9d 2D5/27p 2P,/2,- 8s 2Si,,7d 2D3,2 - 9p 2P',,7d 2D52, - 9p 2P3j217p 2P'I,2- 7d 4D3128p 2P1 1 2
0- 9d 2D3' 2
5f 2F,5/2- 7d 2D3126f 2'F/2, - 9d 2D3/26f 2F7,,2- 9d 2D4/25f 2F7,2,- 7d 2D,/25f 2F,/2,- 7d 'Ds,26f 2F7,2,- 7g 'G,/26f 2'F,2
0 - 7 g C2G725f 2'7F2, - 5g 2G,,25f 'F5,2
0 - 5g 'G7, 26f 2Fr72
0-
8g 2G,,2
6J 2F5,,2 - 8g 2G7C,6s 28/,2 - 6p 2P1 /2
3517 .090b3327.6553301.4813289.1103196.8443172.6893171.735a3171.632b3116.7383111.9693096.2553093.02803085.3793075.1733009.2233006.1862992.0982953.7712950.8432904.5762897.8752684.7572682.3452651.5012604.8272588.8672513.4322478.6522476.5992392.4922387.9882379.3742297.7372260.2952258.6092238.3552216.067
b Transition to 'SI(F =3). 0 Very close to an impurity line.
5f 'F,,2,7,2, 6f 2F,,12,7 /2, and 7f 12 .,120 , which were
evaluated by using the uf 2F0 -5d 'D transitions, agreevery well with those found in the present work. None ofthe transitions involving 4f 5',,2 and 4f 'F7,2' levelsfalls in the region of the present investigation. However,the energies of these levels, which are given in Table II,were calculated by using reported wavenumbers of thetransitions 4f 2F0 -6d 2D and 4f 'F0 -7d 2D.
For the wavelengths of lines of Fe I, Crosswhite's'values in the region from 2200 to 12 000 A and Edl6n's'
calculated values in the region from 2000 up to 2200 Awere used as standards. The tabulated results are theaverages of measurements of three plates. The repeat-ability, as mentioned before, is good. On the other hand,the lines from 2476 to 2685 A involving 6d 2DI and6d 2D, levels are so strong that it is impossible to mis-identify them. Under these circumstances, it is difficultto explain the disagreement with the measurements ofRussell and Meggers.1 Remarkably enough, the lines ofsingly ionized lanthanum measured in the neighborhood
2 1' j 1 1 ,I 1I11Iik1 1' tl
P l k .l' 111. 1. 1. .11 Ih, , l1;. e! i1,l
A B
FIG. 1. Spectrograms of lanthanum sliding spark.
I H. 2M. Crosswhite, Spectrum of Iron, private communication to Spectroscopy section of Natl. Bur. Std., Sept. 27, 1965.B B. Edl6n, Transactions of International Astronomical Union IV, 218-224 (1955).
Classification
5003515702050
15001000
5020015254
100154
40107
160110150100400
242
501002010
400250
5252060
28 424.4730 042.5630 280.7230 394.6131 271.8131 509.8931 519.3631 520.3932 075.5332 124.6832 287.7132 321.4032 401.5232 509.0533 221.4933 255.0433 411.6233 845.1433 878.7234 418.3534 497.9337 236.2637 269.7537 703.2638 378.8038 615.3939 774.2640 332.3340 365.7841784.7041 863.5042 015.0443 507.6844 228.3244 261.3444 661.8045 110.93
7p 2P3/20 - 9s 21827p 2P3/ 2 t- 8d 2D3/27p 2P./20 - 8d 'D51 27p 2p, °'- 9s 2SI/27p 2P112°- 8d ID3/26s 281/2 - 6p 2P31 2 '
6d 2D5/2 - 6f 2F5 ,,0
6d 2'D,2 - 6f 'F7, 2'Sf 'F,/20 - 8d 2D3125f 2F7/2°- 8d 2D5/25f F1F52
0 - 8d 2D5,26d 'D3/2 - 6J 'F526d 2D3/2 - 8p 2P1 /,7s 281/2 - 8p 2p1 26d 2D5/2 - 8p 2
P3/,,6d 2D,/2 - 8p 'P3/27s 281/2 - 8p'P,,i f 'F7/,2
0- 6g 2G'l2
5f 2'F5/,2- 6g 'G7C26p 2p P °,- 7s 28,26p 2'P32,- 6d 'D3/ 26p 2p3/,,- 6d 'D5/2
17, p °-,2 10s '2S 27p 2P3/2°- 9d 2D51,27p2 plF,,- 9D2fl6p 2P'1 2
0- 7s 2S 1/26p 2P, ,2 °- 6d 2D3/25f 'F712'- 7 g 2G9,25f 2F,,°2 - 7g 2G7,25d 2D38 2 - 6p 2P1 1 2
0
5d 2'D5/2 - 6p 2P3/20
6d 2'D,/ 2 - 7f 2F5/2,6d 2'D5, 2 - 7f 2'7F2,6d 2'D3,2 - 7f 2F7,,25d 2D3,2 - 6p 2P3,,2
1460 Vol. 57HA L IS OD AB AS I
December:1967 SPECTRUM OF DOUBLY IONIZED LANTHANUM La III
:A62 /
I15.104
OSoo OPa,,2,o 2Csz,s2 'CsZ,7rZ 2Gr2^9'2
FIG. 2. Grotrian diagram for doubly ionized lanthanum.
of the above-mentioned lines during the present studyagree very well with the ones reported by Russell andMeggers as a result of the same work that revealed the5d term. This makes the situation more puzzling.
The maximum uncertainty involved in thedetermination of energy levels in the present workis estimated to be ±0.2 cm-l.
HYPERFINE AND FINE STRUCTUREOF CERTAIN TERMS
The hyperfine splittings of 6s 2S, 6p 2 P_0 , and 6p 2P40
levels were measured by Crawford and Grace,7 in 1935,and later by Wittke,8 in 1940. Their results are givenbelow
Level
6s 'S6s 2Sj6p 2p_'6p 2pi'6p 2Pt'6p 2pfl
7 M. F. Crawford and1935.
Author
1.09 cm-t C-G1.076 cmnf W0.276 cm'l C-G0.242 cm-' W0.12 cm-' C-G0.12 cm-' W
Norman S. Grace, Phys. Rev. 47, 536,
1461
In the present work, the only hyperfne structure mea-sured was of the 6s 2S, term. Theoretically, the trans-ition 6s 2S4-6p 2pT should split into four lines and6s 2S'-6p 2Pi0 into six, provided that the 6p 2p4
0 and6p 2P1° terms have measurable hyperfine-structuresplitting. For the lanthanum nucleus I= 2, in the J=case, we obtain two values for total angular momentum,namely F= 4, 3 and in the case of J= 2 the four valuesF=5, 4, 3, 2. If neither of the 6p 2
p_0 and 6p 2pf
0 levelshas appreciable splitting, then there would be two linesin each case. By using the tabulated values of linestrengths in Russell-Saunders multiplets, we can deducethe relative strengths of the lines in question. A simpleand straightforward calculation gives a relative linestrength of 171.5 for 6S 2 84 (F=4)-6p 2P (F =4,3), of133.4 for 6s2 S4(F=3)-6p2 fl0 (F=4,3), of 163.6 for6s 2 S4(F=4)-6p 2P;0 (Fao5,4,3,2), and finally of 127.2for 6s 2 83-6p12 P 4
0(F=5,4,3,2). The observation agreescompletely with theory in the latter form, showing thatthe hyperfine splitting of the 6p 2
P0 term is very small
compared to the 2s 28 term. This explains why no split-
TABLE II. Energy levels of La iII.
Desig- Energy (cm-')nation J Present wark
5d 2D 1 0.M022 1603.26
4f 2 2f 7195.342
3 2 8695.6926s IS 2F=3 13 590.56
2F=4 13 591.59
6p P'0
I 42 015.0412 45 110.94
7s 2S 4 82 347.286d 2D 2 82 380.76
2D 21 82 814.275f 2F
0 2- 92 454.54
2F0
34 92 534.73
7p 2P 1 93 232.392P
0 12 94 461.44
8s 2 15 110 209.577d 2D 14 110 534.20
2D 24 110 738.315g 2G 31 114 754.90
2G 41 114 755.346f 2F' 21 114889.80
2F' 32 114 938.908p 2P 4 115 602.26
2p' 14 116 225.92
9s 2S 4 124 504.108d 2D 14 124 742.24
2D 24 124 856.08
6g 2G 342 126952.472G 41 126 953.16
7f 2F° 24 127042.58
2F' 31 127 075.609p 2p 4 1 127 548.93
1 1 127 935.04
lOs 2S 4 132 840.41
9d 2D 11 133 006.652 '2 133 076.90
7g 2G 31 134318.022G 44 134 319.39
8f 2F' 24 134 373.83'
2F0
34 134 399.63'
8g 2G 31 139 100.482G 44 139 101.70
Others' Author
0.00 R.M. (Russell & Meggers)1603.237193.48693.6
13 590.76
42 0)4.9245 110.6482 345.082 378.7582 812.5192 454.692 534.793 232.494 461.5
110 207.6110 532.0110 736.1114 753.4
114 889.8114 938.8225 601.6116 225.3124 503.8124 741.8124 855.9126 950.2
127 042.6127 074.7
134 316.4
134 371.8
134 397.0
R.M.
S.K. (Sugar & Kaufman)S.K.R.M.
R.M.R.M.R. M.R.M.R.M.LangLang
S.K.S. K.S.K.S.K.S.K.S.K.
S.K.S.K.S.K.S.K.S.K.5.K.S.K.S.K.
S.K.S.K.
S.K.
S.K.
S.K.
a Calculated by using the data given by Sugar and Kaufman.8 Heinz Wittke, Z. Physik 116, 547, 1940.
1462HALIS ODABASI
TAiBLE III. All quantities in this table are cm-'.
Cs I Ba iI La iIITheoretical Observed Theoretical Observed Theoretical Observed
Z /1 x2 1}Y Z /1\ a2( a V\ Z /1\ 2~ 2XavXo2(_ -> =- -- > - (->=- -- ) - 28 - ) =-( -_
2 \r3 2 r r/2 \r/ 2 r or /2 \ 3 2 \r Or/
6p 363.566 349.441 369.407 1132.013 1090.172 1127.240 2095.266 2020.375 2063.9337p 128.958 124.034 120.673 440.996 424.914 414.113 867.783 837.142 819.3678p 60.038 57.760 55.093 217.339 209.459 200.000 443.223 427.661 415.7739p 32.684 31.447 29.780 122.932 118.488 ... 256.795 247.810 257.4075d 229.845 186.360 39.036 680.215 557.862 320.390 1133.436 936.731 641.2926d 69.288 56.382 17.176 128.439 105.574 82.156 226.073 187.117 173.4047d 28.240 23.005 8.388 54.871 45.165 37.868 101.391 84.058 81.6448d 14.412 11.746 4.676 29.120 23.985 20.644 55.383 45.957 45.5369d ... ... 2.864 17.413 14.349 12.588 33.755 28.025 28.1004f 0.338 0.111 -0.050 990.774 523.603 64.200 1464.942 798.259 428.6715f 0.297 0.119 -0.042 33.312 17.465 68.774 30.416 15.717 22.9116f 0.233 0.099 -0.029 14.450 7.581 28.791 18.870 9.971 14.0297f ... ... -0.020 10.616 4.155 13.931 11.809 6.292 9.4348f ... -0.013 7.760 2.552 7.849 7.747 4.147 7.3715g 0.029 0.000 0.000 0.238 0.009 0.000 0.877 0.053 0.0986g 0.016 0.000 0.000 0.140 0.006 0.000 0.544 0.035 0.1537g ... ... 0.090 0.003 0.000 0.359 0.025 0.3048g *-- ... 0.060 0.002 0.000 0.248 0.018 0.2719g ... ... ... ... 0.000 0.178 0.013
ting is observable with the resolving power of theinstrument used, for the 5d 2D and 4f 2 F' terms.
The lines resulting from transitions of the type nif 2IF-zg 2G are very broad when they are strong and verydiffuse when they are weak. As a result it is difficult tomeasure the fine-structure splitting. The difficulty arisesbecause observation and measurement of the weakestof three lines, namely the line resulting from thezif 2F7 1 2
0-ng
2G7/2 type transition, is not possible. This issometimes due to the weakness and diffuseness of theline itself and sometimes due to the broadness of thestrongest line that results from 2 F712°-2G9 ,2-type tran-sitions. This does not prevent calculation of the splittingby use of the measured values for two strong lines, sincethe splitting of the If 2F0 term involved is known fromnf 2JFd 2.D transitions. Of course, such a calculationincludes the assumption that the If 2F 712
0 -ng 2G 7 ,2transition does not contribute significantly to thestrongest line. (Theory gives their ratio as 2.9 to 100.)Otherwise the calculated intervals would be too small.In other words, if the weak third component were not asweak as theory would give it, neglect of it in obtainingsplitting would give incorrect 2G splitting.
The following values for ng doublet intervals wereobtained:
it An (cm-,)
5 0.44±0.106 0.6940.107 1.37±0.108 1.22±0.10
The preceding results are peculiar in that A5, <A6, <A7 ,-AA8, where the opposite is expected. There is anotherexample in the same isoelectronic sequence. In Cs i, the4f2F° and 5J'FF terms are inverted, and in Ba ii theintervals of these terms are positive with A5f larger than
Phillips9 in 1933 explained the inversion andanomalous narrowness of doublets in alkali-like spectraby configuration interaction, David'0 in 1934, andArakill in 1939 explained similar cases by exchangeeffects. Recently Blume, Freeman, and Watson' 2 con-cluded that it is a combination of both, while Zarel" wasable to account for a similar kind of behavior in the Mgisoelectronic sequence by configuration interaction. Wedecided, therefore, that it would be instructive to see towhat extent theory predicts the observed doubletintervals for the first three elements of the Csisoelectronic sequence.
Unfortunately, at the very first step we realized thatthe nonrelativistic Hartree-Fock-Slater wave functionsthat we obtained by a procedure slightly modified byZare" from the one given by Herman and Skillman,'4
are not good enough to give any idea about the magni-tude of the exchange effect. Oddly enough, the roughestapproximation gave the best agreement with observa-tion. The spin-orbit coupling constants calculated byusing the equation given by Blume and Watson'5 wereunreasonably off, while the well-known, old, and ad-mittedly not-too-complete relation gave results closestto the observed ones. Spin-orbit coupling constantsobtained by theoretical calculation and from observeddoublet intervals are given in Table III. Because of theirimportance in the calculation of hyperfine structure andin giving an idea about the screening of nuclear charge
9 M. Phillips, Phys. Rev. 44, 644 (1933).W E. David, Z. Physik 91, 289 (1934)."1 G. Araki, Proc. Phys. Math. Soc. Japan 21, 592 (1939).12 M. Blume, A. J. Freeman, R. E. Watson, Phys. Rev. 134,
A321 (1964)."R. N. Zare, J. Chem. Phys. 45, 1966 (1966).'4 F. Herman and S. Skillman, Atomnic Structure Calculations
(Prentice-Hall, Englewood Cliffs, New Jersey, 1964).1' MI. Blume and R. E. Watson, Proc. Roy. Soc. (London) A,
270, 1340, 127 (1962).
1462 Vtol, 57
December1967 SPECTRUM OF DOUBLY IONIZED LANTHANUM La iii
ns np
nd~3 35- 305
2 45
0 330 300
2 40
_~35 325-'255
2 -35
1301290
20302
125
2 25-
1221 0-
-10
ad
0.02' T 7 :2 50 5 00 12 ISO
FIG. 3. Quantum defect An plotted against term value, T. Theordinate scale is shifted for each series but is not changed.
by electrons-thus about the electron contribution tothe spin-orbit coupling constant-the theoretical valuesfor the term a&(1/r 3)/2 are also tabulated. For the caseswhere there is no entry for theoretical values, the processof obtaining hfs wave functions did not converge.
As can be seen, the agreement between theory andobservation is very good for p-terms. But that is not sofor d- and f-terms. One interesting feature is that theagreement gets better along the isoelectronic sequencefor d-electrons, but we cannot say the same for f-states.We think that the very peculiar behavior of the 4f-terms along the isoelectronic sequence makes thatdifference. Obviously, theory in the present form cannotpredict this behavior very well or, as a result, the spin-orbit coupling constants involved. Furthermore it isreasonable to expect more deviation from the presentcalculation, due to either configuration interactions orexchange effects, if a state gets closer to the core.Finally, the theoretical calculations give a very strangeresult for f-electrons in Cs I. The spin-orbit couplingconstant for the Sf-state is greater than that for 4f,which is also observed later in Ba ii but not in Cs i.
Because of the approximations employed in the presenttheoretical calculations, it is impossible to point out themechanism which produces that result. On the otherhand, for g-electrons the theory does not predict any-thing of that nature that is observed in La iII. Since we
are dealing mostly with excited states, obtaining goodwave functions for the purpose of precise calculations isvery difficult.
IONIZATION ENERGY
If we denote by E the term value relative to theground term, and by El the value of the series limit onthe same scale, the absolute term value is defined as
T=E 1£-E.
By using the Ritz formula, T can be expressed in termsof the Rydberg constant R, effective charge It(=Z-N+1), quantum number n, and quantum defectS as
T=Rt2 / (n - 5)2= R210/*2.
Sugar and Kaufman3 calculated the ionization energy byusing s- and f-series and a quadratic approximation foran in the form of 6Z^=ahbTn+cT.2 (the g-series wasRitz).
For the present work we decided to take all of theobserved series and to plot a as a function of T for somedifferent values of El" and interpolate the value thatwill give the best approach to a straight line for large
-alues. That method, which is described by B.Edl6n1 6 and suggested to us by W. C. Martin, gives theionization energy for different series as
(E),, = 154 650 cm-1
(El),,= 154 623 cmn-
(E) nd =154 647 cm-l
(E1)q = 154 651 cm-1
(El),,= 154 677 cm-l.
Usually there are well-known reasons to prefer nf and ugseries to the others. In the present case, in spite of thefact that the mg series may be somewhat perturbed, wefeel that still it is best to take the average of these twowhich is
(El)av= 154 644 cm-
and adopt it as the ionization energy of La in, with anestimated uncertainty of at 15 cm-1 .
In Fig. 3 the term values for all..observed series areplotted against the quantum defects.
ACKNOWLEDGMENTS
I wish to thank Dr. E. U. Condon, Dr. R. H. Garstang,and Dr. K. G. Kessler for giving me the opportunity towork in Washington, D. C. at the National Bureau ofStandards during the summer of 1966. I also want tothank Dr. W. C. Martin, Dr. V. Kaufman, Dr. J. Sugar,Dr. R. Zalubas, and Dr. J. Reader of the spectroscopysection of N.B.S. for their invaluable help, suggestions,and wonderf ul hospitality.
1G B Edldn, in[ Encycylopedia of Phtysics (Springer-Verlag, Berlin,
1964), Vol. 27, p. 124.
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