JOURNAL OF THE OPTICAL SOCImTY OF AMERILA

Configurations 4fN-16s26p in Neutral Gadolinium, Dysprosium,Erbium, and Ytterbium*

NISSAN SPECTOR

Israel Atomic Energy Commnission, Soreq Nutclear Research Centre, Yavne, Israel(Received 18 March 1971)

The groups of six levels obtained by adding, in J-j coupling, a 6p electron to the lowest level of the4fN-1 core have been identified in gadolinium, dysprosium, erbiumr, and ytterbium (N=8, 9, 12, 14).They account for strong transitions to the corresponding 4fxN15s6s2 configurations. Values for the spin-orbitparameter of the 6p electron are (in cm-') fl=1835, 1840, 2049, 2257, respectively.INDEX HEADINGS: Gadolinium; Dysprosium; Erbium; Ytterbium; Spectra.

Neutral lanthanons have two systems of energy levels:in system A the lowest configuration is 4fN6s2 and insystem B it is 4fN"l5d6s2, for the Nth lanthanon (N = 1for La). The excitation of Sd to 6p requires little energy(1.0 to 1.5 eV). Therefore, in atoms where system B islow, the configuration 4fN M6s26p will be of importance.It will produce low energy levels. Owing to the favorablejump 6p-5d, it will account for some prominent spec-tral lines. Finally, since a single 6p electron always com-hines with each 4fN core level of Jr in good Jr-j cou-pling (even if all other configurations exhibit good Rus-sell-Saunders coupling), it will produce distinct struc-tures of six levels: a lower group of two levels withJ=Ji 2, and an upper group of four levels with J fromJ-i to /Jr+%. These structures are easily recognized.The energy interval between their centers of gravity is

6 Hence a good estimate for g6% can be derived fromonly six levels.

In this work, we report four such structures: in neutralgadolinium, dysprosium, erbium, and ytterbium.

GADOLINIUM

Russell' (1950) analyzed Gd i and found that systemB was the lowest. He located the lowest level of the con-figuration 4fQ(8S)6s 26p of neutral gadolinium at13 433.82 cm-' and designated it as UPS. This is thelowest level of opposite parity to the ground level aOD 2

0 .Thus the importance of this configuration should not beoverlooked.

Russell identified the group of three 9P levels, but notthe three 7P levels. This 7P is the lowest of all 7P termsin neutral gadolinium. Russell thus designated it ZVP,and expected it around 19 000 cm-'. Failing to find it,he left blank rows for its levels in his Table VIII. He

TABLE I. 4f 7 (8S)6s'6p levels of neutral gadolinium.

Designation J Position (cm-') Observed g g(LS)

4fI5S31 )6s26po1 3 13 433.82 cm-' 2.2504 13 962.28 1.950

6pil 5 15 665.39 1.8004 16 824.60 1.903 1.7503 16 920.37 1.994 1.9172 16 923.36 2.354 2.333

gave a possible-but very dubious-candidate for 7P4,

a JJ=4 level at 18 509.18 cm-', marked with a questionmark. The problem with this level is clear: although thethree 9P levels combine2 with the O'D0 levels by promi-nent lines of temperature class I and arc and furnaceintensities in the hundreds and thousands, the dubious'Pt is based on only two lines: one already classified, andthe other of class IV, that is, absent in the arc and weakin the furnace.

With a total of 21 terms splitting into 118 levels plus85 unassigned ones, all ranging between 13 433 and37 424 cmnl, why should this particular low 7P termhave been difficult to find?

The answer is that Russell grouped the entire systemof 118 levels into Russell-Saunders terms. That thisgrouping is generally correct was manifest immediatelyby the regular splitting of all the terms in his TableVIII, except Z"1P (and Z9 F). The Z"1P term looks verydistorted; the interval between "P6 and "lP5 is 634.77cm-1 whereas the interval between liP 5 and "P 4 is2700.77 cm-'. Clearly "lP4 is an incorrect designation.

Another confirmation of the general validity of Rus-sell's grouping of system B (with the above exception)came 17 years later when Zeeman-effect observations byPinnington' gave g values for many levels of the system.These values were very close to the pure L-S couplingg factors expected for the levels on the basis of Russell'sdesignations, with one exception: The g factor Of Z"P4had a value closer to 7P4 than to llP4. Also, the first twoof the unassigned even levels had g factors that clearlymade them 'P3 and 7P12. Thus the entire Z7P group canbe identified among Russell's levels as

Z'P 4 :16 824.60 cit'

Z7P 3:16 920.37

Z7P 2:16 923.36.

The irony of the situation becomes outstanding whenthe three ZIP levels are now placed together with thethree Z9P ones: The six levels clearly split into two Jr-jcoupling groups given in Table I.

This is the only configuration in the entire levelstructure of neutral gadolinium that exhibits good Jri-coupling. From the interval between the two groups, wededuce that 5p6 = 1835 cm'l.

1350

VOLUME 61, NUMBER 10 OCTOBER 1971

October1971 CONFIGURATIONS 4fN-16s26p IN Gd I, Dy I, Er I, AND Yb I

TABLE II. Intensity array in Gd i.

ZIP ZIP Z"1P 7 7P?J 3 4 5 4 3 2 6 5 4 4

a9D' 2 200 600 6 600 4 3003 150 400 30 600 20 200 8 800 15 1000 5 100 -4 400 800 200 600 ... 25 800 *-- 100 1500 ?.. ?255 1500 2000 150 500 80 1500 400 2500 ... 30 250 --6 3000 2000 200 800 125 1500

The reason why some of the g factors still retainvalues that are to within a few percent of the L-S valuesis that their admixture into Jy-] does not alter sub-stantially their L-S composition. (The Z"P4 and Z7P4terms probably mix also.)

In Table II, we give the intensities of the lines fromthe a9D0 ground term to the new structure of 4f6s2 6pas well as to the new Z'1P term (we suggest Russell'slevel 74 at 19 164.76 cm-' as a replacement for hisZ'P 4 ). For comparison, we give the line to his oldquestionable Z7P4 (?). Doubly classified lines are notused.

DYSPROSIUM

Neutral dysprosium has recently been analyzed byConway and Worden.4 Five out of the six 4J7 (8 )6s26plevels can be identified among the even levels. Thesixth, with J=6&, can be found on the basis of the J-jcoupling character of the structure, by using the de-scription of the dysprosium spectra by King el al/A InTable III, we give the six levels based on 6H7§1' of 4fX.

In Table IV, we give the intensity array between thefirst six 4f95d6s2 levels and the levels in Table III,along with another even level with J=7. This arraydemonstrates how a distinction can be made concerningthe configuration assignment of the J = 7 levels, on thebasis of intensities only.

Thus, the distance from the first 4fJv-5d6s2 level tothe lowest 4fJ'6s26p level is 13 433.82 cmnr in Gd i and13 048.72 cm-' in Dy I. By interpolation it should bebetween these two values in Tb i. We should, there-fore, expect there the two levels designated 4f8(7F6 )-6s2 6po0 with J= 5 and J=6 6 of neutral terbium.

Klinkenberg6 has observed such levels, one withJ=5t at 13 330.86 cm-l and the other with J= 6 at13 337.30 cm'-. From his intensity scale, it is hard todecide whether the same intensity relations hold be-

TABLE III. Observed 4f9g(Q7)6s'6p levels of neutral dysprosium.

Designation i Position (cm-')

4f1(fH7,a)6s26poj 7 20 614.338 20 789.86

4f 9 (6EH7,6s'6pji 9 23 218.596 23 360.578 23 534.527 23 799.42

tween these two levels and the corresponding 4f8 5d6s2

levels, as found in the arc descriptions of Gd i and Dy i.From arc spectrograms of terbium that we had taken inour laboratory, we derive the intensity arrays given inTable V, which confirm our identification. We give inthis table our visual estimates of intensities in the arc,beside those given in Ref. 6. The identification of thefour levels based on 6pi,, however, especially of theJ=74 level expected below 16 000 cm'l, has not beenpossible yet.

ERBIUM

In neutral erbium, system B, whose lowest structureof 10 4f"5d6s2 levels was first observed by Spector7

to exhibit good Jj-j coupling, starts with J=6 at7176.56 cm-1 above zero. The 10 levels are obtained bycoupling in JI-j the 5d electron to the 4I71 levels of the4f'1 core. This coupling makes transitions to the JI-jcoupled 4f"1(QI;z)6s 2 6p structure very favorable, andthe lines connecting the two structures are expected tobe prominent. They were found in our new list of erbiumlines observed in the photographic infrared.8

In Table VI, we give the six levels based on 417-.In Table VII, we give the intensity array between the

new levels and the 10 4f 11(4I7 4)d56s2 levels. We see thatthese transitions give rise to some of the most outstand-ing lines in the photographic infrared. Other lines,

-f

t E

0"I0

8 9 10 11 12 13 14Gd Tb Dy Ho Er Tm Yb

N

FIG. 1. The 4fX-16s26p-4fVN~15d6s2 interval.

1351

NISSAN SPECTOR

TABLE IV. Intensity array in Dy I.

4f1('1170)6s' 6poi 6pol 6p,1 6p q 6pl 6p,1J 7 8 6 7 8 9 7

5d 8 ? 200 I 250 600 1 50 400 11 100 80 II 400 300 I 3 6 II7 200 600 I 200 300 1 15 20 III 10 15 II 10 40 III 1 5 III9 6 V 150 300 III 80 150 II6 630 II 5 20 II 50 125 III6 1 5 III ? 12 60 III8 4 15 III 15 30 III ... 25 80 III

however, in particular those connecting the new levelsto the upper "umbrella," namely, the 4 f"( 4J7I)5d216s'group, fall beyond the peak sensitivity of our 1-Zplates. Their recorded intensities, therefore, do not re-flect the correct ratio, as compared to the lines that fallwithin the photographic range. Five of these lines ap-peared only once on a strong electrodeless-dischargeexposure, and therefore had not been published by usbefore. Lines expected beyond the limit of our observa-tions are marked I.R.

In Table VIII, we classify 23 infrared erbiumn lines astransitions between the new and the old levels. Threeof the levels in Table VI and the 17 lines they produceby combining with the old levels were published byHeld,9 who observed also the position of the first levelin this table.

From the two groups in Table VI, we obtain for Pe,the value 2049 cmul. A well-established 4fN-l5d6s2structure is essential for obtaining the corresponding4fN-16s26p.

YTTERBIUM

The special position of ytterbium as the last lanthanonraises three obstacles on the way of establishing the4f"36S26p levels.

(a) System B, with 4f"35d6s2 , involves breaking theclosed 4f'4 shell. This requires almost 3 eV. At thisexcitation energy, there are already many other levelsand correct identification of 4f"15d6s2 requires greatcare.

2300

2200

2!00

2000 -

900W-

180C8 9 10

Gd Tb Dyi1 12 13 14

Ho Er Tm YbN

I'io. 2. P6, from 4f-Al6S26p levels.

(b) The good Jr-j coupling that existed in the4f'1 5d6s2 configuration of neutral erbium and facilitatedthe identification of 4f'16s26p gives way, in Yb I, toJr-1 coupling. The first indication of this change of cou-pling was observed in Tm ii, where the 4f"15d configura-tion exhibits good Jr-1 coupling.

(c) The relative position of the first 4fN1v6s2 6p levelabove the lowest 4ftl5d6s2 level drops from 13 434cnrl in Gd I to 9289 cm'l in Er i, and becomes evensmaller in Yb I; its total energy above zero jumps from2 to 4 eV.

I overcame the first two obstacles during my workwith the late W. F. Meggers in 1964. My preliminarypredictions of the levels of 4f'3 5d6s2 helped us in estab-lishing its lower structure of 10 levels based on the2F3,. This unmistakable structure with a low J = 2 levelof g value 1.47 followed by two levels of J=5 and 6 canbe explained only on the basis of JI-1 coupling. Thelow J=2 level is at 23 188,5 cm 1 l. The observed levelsfitted well the theoretical predictions. Later on, Camuset al.'0 published the analogous structure in Tm iI(4f"S5d) as observed by Sugar. The striking similarityserves as a confirmation of our identification of the levelsof 4f"P5d6s2 of neutral ytterbium.

TABLE V. Intensity array in Tb i.

4f8

(7F) 6s2 6pot 6poi

J 51 6-8G 64 300 7W 1000 9W

74 4000 8W,54 1000 8W 600 9W44 100 8

8D 54 *.. 3 IW 9W41 1000 9W8F 64 ... 3 5 3S

TABLE VI. Observed 4f" (9I71)6s26p levels of neutral erbium.

Designation J Position (cm-,)

4f" (4 17j)6s26po0 7 16 464.948 16 727.45

4f"1(4 17j06s26p1i 9 19 355.148 19 723.266 19 817.047 19 915.85

I I I r I I

0

I0

00

1 1 I I I. . .

Vol. 61

)

October 1971 CONFIGURATIONS 4fN1- 6s26p IN Gd I, Dy I, Er i,

TABLE VII. Intensity array in Er i.

6p0o 6poi 6pj 6p,1 6pj 6pj

4f 11 (417 ) 6s' 7 8 6 7 8 9

5di 6 200 40 0 20 400 1 100 100M* 107 100 1500 0 30 3000 0 2 150 5 50 50M* 20 2000 200M* 8008 I.R. I.R. 50 1800 30 60 8000 8 15 10M* 809 1 6W 0 30 300 30 200 40M* 500

5d21 5 3 20 06 I.R. 0 1 0 0 1 07 I.R. I.R. I.R. 0 2W 0 I.R.8 I.R. I.R. 2 20 0 0 3 0 I.R.9 I.R. 1000 200 0 30 1000 0

10 3000 2000 80

TABLE VIII. Classified Er I lines.

Intensity

Electrodeless Sliding(A) arc discharge spark a- (cm-,) Classification

12 469.268 0 1 0 8017.14 11 79960 -19 817612 452.651 0 2 WH 0 8028.22 11 8877' -19 915712 331.846 1 6 W 0 8106.87 86209' -16 727812 318.055 0 1 0 8115.94 11 79960 -19 915712 243.230 0 3 0 8165.54 11 55780 -19 723,11961.311 2 20 0 8358.00 11 5578' -19 917711 879.441 3 20 0 8415.60 11 40150 -19 817611402.052 100 1500 0 8767.95 769670 -16464711 364.151 30 1000 0 8797.19 10 55790 -19 355911 070.567 30 3000 0 9030.49 769670 -16 727810 907.731 1000 200 0 9165.29 10 5579' -19 723810 763.215 200 40 0 9288.36 717660 -16 464710 307.253 3000 2000 80 9699.25 9655,o0-19 3559

9992.253 15 10 M* 80 10 005.02 93508' -19 35599637.638 60 8000 8 10 373.14 93508' -19 723a9462.034 50 1800 30 10 565.65 935080 -19 91579313.119 200 10 M* 500 10 734.60 862090 -19 35599004.347 3 300 30 11 102.70 8620,o -19 72388312.823 2000 200 M* 800 12 026.30 769670 -19 723,8248.630 2 150 5 12 119.89 769670 -19 817,8181.847 50 50 M* 20 12 218.82 769670 -19 91577908.914 20 400 1 12 640.48 717660 -19 81767847.547 100 100 M* 10 12 739.33 717660 -19 9157

TABLE IX. The 4f 125d6s' levels of Yb i and Tm II.

Yb I Tm iI

Percentage Calculated Observed Observedcomposition J level (cm7-) gc (cm-,) go (cm-') go

977cKA] 2 23 707 1.470 23 188.5 1.47 17 624.7 1.4798%2C 2 5 26 401 1.021 25 859.7 20 228.8 1.02

100%1[1-] 6 27 140 1.167 27 314.9 21 133.7 1.16786% [C] 3 28 036 1.271 27 445.6 1.22 21 713.7 1.2252%![A] 1 28 227 1.337 28 857.0 1.27 22 141.9 1.3298%/t1] 2 28 551 1.025 28 195.9 1.01 21 978.8 1.0262%1IiZ] 4 29 244 1.145 28 184.5 22 457.559%([2] 4 30 463 1.068 29 774.9 23 524.196% 2C] 5 31023 1.169 30 524.7 24 273.2 1.1882 3 31 306 1.109

100%K[1] 0 32 978 0/0 30 025.695%5-[9] 4 35 087 0.841

1 353AND Yb I

NISSAN SPECTOR

TABLE X. Observed 4fler,31i)6sl6p levels of neutral ytterbium.

Designation J Position (cm-')

4f"('1F3)6s'6poj 3 32 065.304 32 273.58

6pt 5 35 178.742 35 196.973 35 807.504 36 061.03

In Table IX, we give the observed low 4f"5d6s2levels" of neutral ytterbium and compare them withthe corresponding structure in Tm ii. We also give ourpredictions for the first 12 levels of 4f'3 5d6s2 and theirg values, as well as their percentage composition inJI-1 coupling. We use the usual notation Ji[E]J foreach level. These predictions were obtained by use ofthe radial parameters (in cm'l)

Fo=32 000 G1=170 rf=2500

F1 =163 G3=30 Pd= 5 5 0

F4 =10 G5=2.5.

In view of our present knowledge of the radial param-eters in ytterbium, some of these values, in particularthe D's, could be modified to advantage. The generalstructure predicted by them, however, corresponds wellto the observations, and was very helpful and reliablefor establishing the levels. The high percentage in Jr1-demonstrates the validity of this coupling scheme for4f"5d6s2. With the 4f"15d6s2 structure identified itbecomes possible to identify the 4f'3 6s26p levels. Welocated the six levels of this configuration based on the2F31 core level at the positions given in Table X.

The separation between the lowest J=3 level of4f"36s26p and the lowest J = 2 level of 4f"35d6s2 is8876.76 cm7-. This is almost the strongest infrared linein the listl2 of 1966.

From the interval between the centers of gravity ofthe two groups based on 6 pol, and 6 p'i, we get P6,=2257

cm'l in neutral ytterbium. A comparison of this withthe value of 1615 cm1l for D,, that was obtained fromthe 4f'4 6s6p configuration, indicates the effect of theclosed 4f shell in screening the nuclear charge.

THE 4fN-16s2 6Ap.4f N-15d6s2 INTERVAL

In Fig. 1, we use the results obtained in the previoussections along with the Tm i results'" to plot the intervalbetween the lowest levels of 4fN"15d6S 2 and 4fN-l6s26pagainst N. The remarkable feature of Fig. 1 is the sud-den drop of about 4200 cm'l from a nearly constantvalue of 13 200 cm'1 for Gd i, Tb i, and Dy i to anothernearly constant value of 9000 cmrl for Er I, Tm i, andTb i. This sudden change occurs in Ho i, which has notyet been analyzed, but which is presently under investi-gation by us. Figure 1 should serve as warning againstlinear interpolation in rare-earth spectra.

In Fig. 2, we plot the values of P6p obtained in theprevious sections against IV. A similar behavior is ob-served also in this case.

We conclude that despite the full knowledge of thebehavior of the 4fN'l6s2 6p levels for N=10 and 12,little can as yet be said in the case of N=11.

REFERENCES

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

' H. N. Russell, J. Opt. Soc. Am. 40, 550 (1950).2 A. S. King, Astrophys. J. 97, 251 (1943).3 E. H. Pinnington, J. Opt. Soc. Am. 57, 1252 (1967).4J. G. Conway and E. F. Worden, J. Opt. Soc. Am. 61, 704

(1971).' A. S. King, J. G. Conway, E. F. Worden, and C. E. Moore,

J. Res. Natl. Bur. Std. (U.S.) 74A, 355 (1970).6 P. F. A. Klinkenberg, Physica 32, 1113 (1966).7 N. Spector, J. Opt. Soc. Am. 55, 576 (1965).8 N. Spector and S. Held, Astrophys. J. 167, 193 (1971).9 S. Held, Astrophys. J. 167, 203 (1971).'° P. Camus, G. Guelachvili, and J. Verges, Spectrochim. Acta

24B, 373 (1969).11 W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 75A (1971).12W. F. Meggers and C. H. Corliss, J. Res. Natl. Bur. Std.

(U.S.) 70A, 63 (1966).

1354 Vol. 61