Vol. 57

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 57, NUMBER 3

4f'2 (PH6 )6s6p Levels of Neutral Erbium (Er I) tNISSAN SPECTOR

Israel Atomtic Energy Coimmission, Soreq Nuclear Research Center, Yavne, Israel(Received 2 August 1966)

The twelve 4f"(2II)66s6p levels of neutral erbium are reported and interpreted in the JJnI couplingscheme. Intensity relations of the lines connecting 10 of them to the ground level are discussed. The valuesof G, (6s6p) = 3373 cm-' and r,= 1870 cm-' for the interaction parameters are obtained directly from theselevels.INDEX HEADINGS: Erbium; Ytterbium; Atomic spectra.

THE relative intensities of the rare-earth spectrallines, as determined on a uniform energy scale,

show that lines which arise from s -> p electron transi-tions are among the strongest. This is supported by theobservations of Meggers, Corliss, and Scribner,' whodetermined the intensities of the spectral lines of all theneutral and singly ionized lanthanum group of rareearths except promethium. Where analyses of thesespectra are available, as is the case for samarium,europium, gadolinium, thulium, and ytterbium, it turnsout that s -- )p transitions account for (a) the strongestfirst-spectrum line of each element, as indicated in thetables of Ref. 1, and (b) most of the other high-intensitylines given in these tables. Conway and Wybourne 2 cal-culated the low-lying levels of lanthanide atomicspectra, which, in all but Ce I and Gd i, were taken asbelonging to the 4fN6sI type of configuration, implyingthat the transitions 4fN6S2 > 4fN6s6p should give riseto some of the strongest lines of neutral rare earths.

Since the 6s6p electrons do not interact strongly withthe deep 4 fN core, the intensity relations of the above-mentioned strong lines can be easily understood. Also,the properties of the 6s-6p interactions, such as the

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

' W. F. Meggers, C. H. Corliss, and B. F. Scribner, NBS Mono-graph 32 (1961).

2 S. G. Conway and B. G. Wybourne, Phys. Rev. 130, 2325(1963).

values of the Slater electrostatic parameter Gl(6s,6p)and the spin-orbit interaction parameter 5,, can be de-rived immediately from the first few levels of 4fN6s6pconfigurations, even if the levels of the core itself arenot fully known.

The identification of the levels belonging to 4fN6s6pis therefore of importance for the understanding of thespectra and interpretation of the structure of theneutral rare earths.

Although a great deal of work has been done recentlyon Er I (see for example Refs. 3, 4, 5), some of thestrongest lines of this spectrum have not been classified,and the 4f' 26s6p configuration has not been adequatelyrecognized. The goal of this work, therefore, was toidentify the first few levels of this configuration, in orderto gain more understanding of the outstanding featuresof Er i.

STRUCTURE OF 4 fN6 s6p TYPECONFIGURATIONS

The lower levels of the 4fN6s6p configurations forN > 9 display an unmistakable structure which was firstrecognized by Racah8 in 4f'2 6s6p of Yb iI. This struc-

3L. C. Marquet and S. P. Davis, J. Opt. Soc. Am. 55, 471(1965).

4 G. Racah, Z. B. Goldschmidt, and S. Toaff, J. Opt. Soc. Am.56, 407 (1966).

'N. Spector, J. Opt. Soc. Am. 56, 341 (1966).6 G. Racah, Lunds Univ. Arsskr. 50: 21, 31 (1954).

MARCH 1967

308

M 1 4fl (3H6)6s6p LEVELS OF Er I

ture is a result of a unique situation in which the sub-configurations 4J7 of the core and 6s6p of the outerelectrons both manifest a distinct Russell-Saunderscoupling. This enables us to designate their levels bySL 1 Ji for 4fN and 1''Pi,, for 6s6p. Then JA and JA1combine in j-j coupling to give the final J and the easilydistinguishable structure of the 4fN6s6p configurations.The corresponding spectra also display unique features,since, within a certain J,, the intensities of the transi-tions 4fN (SrL1J,)6s'Jf -- 4fNv(SrL;Jj)6s6pJf aregoverned by L-S selection rules for S2 -÷ sp type tran-sitions, which are well known. To illustrate the structureof 4f"36s6p in Yb ii, we plot, in Fig. 1, the positions ofthe energy levels of this configuration versus their Jvalues, quoted from Racah,' who also pointed out thatthe level structure consists of two similar distributionsof energy levels. The first is obtained when the threestates of 6s6p 3PJ,, and the single state of 6s6p 'Piassume different orientations in the quadrupole field of4f7 13F,, thus splitting into 4 groups of 1, 3, 5, and 3levels, respectively. The second distribution is a repeti-tion of the first 10 000 cm-' higher, in the field of4f" 7F29. The four groups mentioned above are theresult of the superposition of the 3P0 , 3P,, 3P 2 , and iP 1

of 6s6p on each level of the core, and are so designated.A good estimate can be obtained of the parameters

of 6s6p from the levels arising from a particular J, byusing the relations

G, (6s,6p) = 2 I('PI-3P2)+ (P1-'PI )], (1)

where bars signify the centers of gravity of the corre-sponding group of levels, and

= 23 eP2-3P) . (2)

Applying these formulas to Yb ii we find GI= 2945 cm-land Dp=3547 cm'1, which agree excellently with therounded-off values of 3000 cm-' and 3500 cmrl, respec-tively, obtained by Racah8 from extensive least-squarescalculations involving the complete 4f"36s6p configura-tion. The success of these equations is due to (a) theweak binding between the outer group 6s6p and theinner core 4f", and (b) the independence of both for-mulas with respect to the type of coupling in 6s6p. Theformulas should be used to show which intervals areneeded to obtain the parameters, but not as evidencefor L-S coupling.

Racah7 has noted that the 4fN6s6p configurationsshow a remarkable type of coupling, where the parentsof a level cannot be assigned, but the grandparents arevery well defined and supply good quantum numbersfor the designation of the energy levels. The usefulnessof such designations is demonstrated when we considerline intensities. In the case of Yb iI, the two groups oflevels (even and odd) with the same "core grand-parents" 4f1 'F.3 should be connected by lines whose

7 G. Racah, J. Opt. Soc. Am. 50, 396 (1960).8 G. Racah (private communication, 1961).

70

65

000

LiJ

60

55

50

I I I I I I I

l 'P D

-3

P2*

3p

- - I I

; l l l°2 1i 22 31

J42 52 6a

FIG. 1. 4f"6s6p levels of Yb ii.

intensities obey rules imposed on the other "grand-parents," namely 1'3P for 6s6p and IS for 6s'. Thismeans that 4f1"(2F3,)6s1('So)J=313 -* 4f"1(IF3,)6s6pX ('Pi)J= 4- should be the strongest line among them,as indeed it is.'

In general, we should expect the line 4fN(SILIJI)X6s'(So)Jx- 4fN(SLxJ,)6s6p(1Po)fi to be weakest,since it is practically a 'S O---P 0 transition. In goodRussell-Saunders coupling such a transition violatesboth the "AS=0" and "no J=0 to J=0" rules. Thelines from the 'Pi group to 4fN6s2 should be strong, andthe J-allowed lines from 'PF should, again, be somewhatweaker. The 4fN(SrLrJI)6s2('So)J -*4fN(SILIJI)X6s6p('P,)Juj should be the strongest of them all,since this a 'So -'P transition which, in pure L-Scoupling, is the only one allowed.

A situation very similar to the one in Yb ii occurs inthe isoelectronic spectrum Tm i, where the configura-tion 4f"6s6p has been observed by Blaise and Camus.YFrom their Table II, it is easy to recognize the two dis-tributions mentioned previously. The second is re-peated lower than in Yb It, at 8800 cmul above the first.This repetition is due to the splitting of the IF of4f"36s2 in Tm i. There is some confusion, however, inthe group of 3 levels based on 'P, there being a strikingdisagreement between the J values given in Ref. 1 andthose given in Ref. 9 in at least four cases. In one in-stance, the difference in J is 2 units. The determinationof the ('PI) levels is, therefore, not unambiguous. Usingonly those levels for which there is agreement between

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

March 1967 309

NISSAN SPECTORV

26

25

24

£23E

220

205 19

I619

°2 12 22 32 42 52 62

FIG. 2. 4f"3(F1F3)6s6p levels of Tm I.

the two works, we assign the first twelve levels of4f"6s6p in Tm i as shown in Fig. 2. The numbers inparentheses are the intensities of the transitions fromthe levels concerned to the ground level.1

Applying Eqs. (1) and (2), one gets G1(6s,6p) = 2917dm-l and 5,= 1793 cm- 1. The value for Pp is derivedfrom only SI2 and 3P0, whose identification is certain.Therefore it will not be affected by the eventual settle-ment of the disagreement mentioned above.

CONFIGURATION 4f'26s6p OFNEUTRAL ERBIUM

Features analogous to those of Tm i and Yb iiappear in Ern; they are even more pronounced. Thesituation is however more complicated. First, the coresubconfiguration is 4f' 2 . This increases the theoreticalnumber of levels from 24 in 4f"6s6p to 138 in 4f 2 6s6p.Furthermore, from the data of Marquet and Davis on4f'2 6s2 of Er i,3 we should expect the second distributionof twelve levels to repeat only 5000 cm-" above the firstone, as compared with 8800 culr' and 10 000 cmnl forTm i and Yb aI, respectively; this increases the diffi-culty of distinguishing the distributions.

In such a situation, where the bulk of the energylevels of 4fl'6s6p is absent, a theoretical calculationfurnishing predictions for the missing levels would bemost welcome. Recently Racah, Goldschmidt, andToaff4 published a calculation of 4f' 2 6s6p, in which theyused a least-squares method to fit S known levels using11 interaction parameters, 6 of which were fixed. Trheyobtained an rms error of 71 cm'l, or 1.2% of the spreadof these 8 levels. Their method does not point up theunique structure of 4f' 2('f6)6s6P in Er i that results in

- I I I I I I I I

(400)

(700) C

(200)

3P2-

?_2W~i38) 3P(14)

(m) POI I I I I I I

I 7 I f -- . . TABLE T. 4f" '( e6))6s6p levels of neutral erbium.

Energy levelDesignation J (in cm-l)

4f 12 18iI) SP0 6 16 321.17

:PI 6 17 073.807 17 157.315 17 347.86

3P2 8 18 335.504 19 113.385 19 201.346 19 326.607 19 816.51

'P1 5 24083.177 24943.286 25 880.29

a group of prominent lines characteristic of this spec-trum, which structure deserves special mention.

The striking similarity between the level structure ofTm I and Yb It, evident from Figs. 1 and 2, led us toseek the corresponding levels in Er r. We were able tolocate all twelve levels of the first distribution, obtainedwhen 6s6p is added to 4f"2 H 6 . Their positions, J values,and designations, following Racabh7 are given in Table I.Their structure is displayed in Fig. 3. The number inparenthesis beside each level indicates the relative in-tensity on a unified scale' of the transition from it to theground level. In Table II we classify some of the linesconnecting the twelve 4f" (3H6)6s6p levels to the first3 levels of 4f'2 6s2. Seven of the lines have already beenclassified5 and are marked with a superscript a. Theyare included for the sake of completeness. The wave-lengths and intensities are based on recent observationsmade by us (M indicates a factor of 1000). Table Icorrects Table II of Ref. 5. The level 17 347.86 cm-l,J= 5, is now assigned to 4f' 2Q(3h6)6s6p('PI) and should

TABLE fl. Classified lines of Er I.

IsotopeWave- Wave- Even Odd shift"length number level level V16e-`168

(A) (cm-') Intensity (cm-') J (cm-') J (10-' cm-')

9883.184, 10 115.42 10 6958.34 5 17 073.80 69622.490a 10 389.47 80 6958.34 5 17 347.86 58223.755 12 156.55 20 6958.34 5 19 113.38 48165.829 12 242.79 7 6958.34 5 19 201.34 58119.472, 12 312.69 75 5035.19 4 17 347.86 57101.23b 14 078.19 2b 5035.19 4 19 113.38 46125.313 16321.18 SM 0.00 6 16321.17 65855.300a 17 073.81 9M 0.00 6 17 073.80 6 33.941.25837.850 17 124.85 20 6958.34 5 24083.17 55826.797a 17 157.33 811 0.00 6 17 157.37 7 33.4 1.05762.7993 17 347.87 9MJu 0.00 6 17 347.87 5 33.1-41.05283.399 18 921.94 20 6938.34 5 25 880.29 65248.442 19 047.97 20 5035.19 4 24083.17 552C6.520 19 201.34 3M¢ 0.00 6 19 201.34 55172.770 19 326.62 311 0.00 6 19 326.60 6 37.2 1. 0544.891 19 816.51 21 0.00 6 19 816.51 74151.111 24 083.15 10011 0.00 6 24 083.17 54007.967a 24 943.26 200 1M O.O 6 24 943.28 73862.851 25 880.28 10031 0.00 6 25 880.29 6

a Lines classified elsewhere.' b From Ref. 1.

310 Vol. 57

4f''('H6)6s6p LEVELS OF Er I

be replaced in Table II of Ref. 5 by 17 029.06 cm-l, assuggested by Racah, Goldschmidt, and Toaff.

Comparing Table I with Table I of Ref. 4, we notethat the levels at 19563.116 cm-' with J=5 and at19 125.248 cm-' with J= 7, in Ref. 4, have been re-placed here by 19 201.34 cm-' and 19 816.51 cm-', re-spectively. The former was attributed by Racah,Goldschmidt, and Toaff4 to 4f" (415,)5dI,6s2 and thelatter was not found by them. Also the level at24 083.171 cm-l with J= 5, given by Racah, Gold-schmidt, and Toaff4 without interpretation, can clearlybe designated 4f' 2 ('H6)6s6p ('Pl)J = 5.

It is interesting to note that the relative intensitiesmarked in Fig. 3 obey the relations discussed in Sec. II.In particular, the lines represented by 'So -4 'P1 , areindeed strongest, with intensities 550, 600, 1100 for thetransitions from the ground level to (P,)Jf= 5,6,7, re-spectively. The classification of these lines now com-pletes the assignment of all the Er i absorption lineswhich were characterized as VS (very strong) byMossotti and Fassel.10 Transitions to the 3P2 group oflevels are weaker than those to the 3Pi group, and areabout uniform, namely 17, 14, 14, respectively, for thelines to J= 5,6,7 from the zero level which agree satis-factorily with the L-S selection rules.

Another interesting feature is the weakness of thelines connecting levels arising from different grand-parents of the core subconfiguration 4f'2. This is alsoevident from Table II where, for example, the line(3H6) ('S.) - (3H6) ('P,)J= 5 is of intensity 100 000while to the same upper level from (3F4) ('SO) it is only20. The same is true for the lines (3H6) (S) -*> (3H6) (IP 1)XJ= 6 (100 000) and (3H5) ('So) -* (3H6) ('Pl)J = 6 (20).

We have applied Eqs. (1) and (2) to calculate the6s6p interaction parameters and obtained Gl (6s,6p)=3373 cm'l and p= 1870 cm-l. The GI(6s,6p) taken

10 V. G. Mossotti and V. A. Fassel, Spectrochim. Acta 20, 1117(1964).

27

26

25

24F

E000

CUi

23[

22

21

20

19

8

'7

- 3 4 5 6 7 8J

FIG. 3. 4fJ2('He)6s6p levels of Er i.

9

from Tm i as 2975 cm-' by Racah, Goldschmidt, andToaff4 is 13% lower than our value, which is takendirectly from Er i. Their final D, of 1547Lt78 cm-' isabout 20% lower than our value. This may explainwhy the 'Pi group of levels was not identified by them.

Finally, mention should be made of the measurementsof Wilets and Bradley" of the isotope shift of four of thelines in Table II, as given in the last column. As men-tioned in Ref. 5, the isotope shift of the 4fI16s - 4fllX5d6s' lines is around -45.5-41.5 mk. From Table II,one sees that for 4f1 26s2 -- 4f"26s6p lines, this shift isaround 33.5=t1.2 mK. This should permit discrimina-tion between some of the levels of these two overlappingconfigurations of odd parity.

11 L. Wilets and L. C. Bradley, III, Phys. Rev. 87, 1018 (1952).

Emmett N. Leith, University of Michigan, speaking at SecondRochester Conference on Coherence and Quantum Optics.

I I I I I

- (600)

(1100) 1

(550)

14)

- (\) (~3P2

) 3p-) 2

- (32) (3

3,

March 1967